Bibliography & Cited References

Bibliographia et Apparatus Fontium

This apparatus provides a comprehensive, critical reconstruction of all sources, classical treatises, mathematical works, and philosophical commentaries cited by Father Peter Hoenen, S.J. across De Noetica Geometriae: Origine Theoriae Cognitionis (Rome: Gregorian University, 1954).

Hoenen’s citations reveal his unique intellectual position: trained in theoretical physics under Nobel laureate H. A. Lorentz at Leiden before teaching scholastic philosophy at the Gregorianum, he confronts the foundational crisis of modern mathematics (formalism, logicism, and non-Euclidean geometry) directly with the rigorous epistemology of Aristotle and St. Thomas Aquinas.

The bibliography is organized as follows:

1. Alphabetical Index of Authors: An A–Z directory of all 64 cited authors with direct links to their entries.

2. Chronological Bibliography: All authors arranged strictly chronologically by death date (earliest first), spanning 2,400 years from Eudoxus of Cnidus (c. 355 BC) to José Alvarez Laso (1993 AD).

Each entry consistently provides:

• Author (Born–Died)

  • Book / Treatise Title (English Title) Year

    Scholarly notes on editions, co-authors, translators, and historical context

    • Citation: Specific chapter and footnote in Hoenen’s volume

      • What Hoenen refers to: The exact text, theorem, or doctrine cited

      • How it supports the text: How the citation functions within Hoenen’s philosophical argumentation (problem of necessity, problem of exactitude, intuitive formal abstraction, intelligible matter, or the existential act)

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Alphabetical Index of Authors

A

• Albert the Great, St., O.P. (c. 1200 – 1280)

• Alexander of Aphrodisias (fl. late 2nd – early 3rd c. AD (died c. 215 AD))

• Alvarez Laso, José, C.M.F. (1910 – 1993)

• Amaldi, Ugo (1875 – 1957)

• Aristotle (384 – 322 BC)

B

• Baeumker, Clemens (1853 – 1924)

• Boethius, Anicius Manlius Severinus (c. 477 – 524 AD)

• Bonitz, Hermann (1814 – 1888)

• Brentano, Franz (1838 – 1917)

• Burnet, John (1863 – 1928)

C

• Cantor, Georg (1845 – 1918)

• Carteron, Henri (1891 – 1927)

• Couturat, Louis (1868 – 1914)

D

• Dedekind, Richard (1831 – 1916)

• Descartes, René (1596 – 1650)

E

• Einstein, Albert (1879 – 1955)

• Enriques, Federigo (1871 – 1946)

• Euclid of Alexandria (fl. c. 300 BC (died c. 270 BC))

• Eudoxus of Cnidus (c. 408 – c. 355 BC)

F

• Freudenthal, Hans (1905 – 1990)

G

• Geyser, Joseph (1869 – 1948)

• Gilson, Étienne (1884 – 1978)

H

• Hadamard, Jacques (1865 – 1963)

• Hamelin, Octave (1856 – 1907)

• Hardy, Godfrey Harold (1877 – 1947)

• Hasse, Helmut (1898 – 1979)

• Hausdorff, Felix (1868 – 1942)

• Heath, Sir Thomas Little (1861 – 1940)

• Hessenberg, Gerhard (1874 – 1925)

• Hilbert, David (1862 – 1943)

• Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961)

K

• Kant, Immanuel (1724 – 1804)

• Killing, Wilhelm (1847 – 1923)

• Klein, Felix (1849 – 1925)

L

• Leibniz, Gottfried Wilhelm (1646 – 1716)

• Locke, John (1632 – 1704)

• Lonergan, Bernard, S.J. (1904 – 1984)

M

• Maier, Anneliese (1905 – 1971)

• Meyerson, Émile (1859 – 1933)

• Mill, John Stuart (1806 – 1873)

• Möbius, August Ferdinand (1790 – 1868)

N

• Nicole Oresme (c. 1320/1325 – 1382)

P

• Pasch, Moritz (1843 – 1930)

• Peano, Giuseppe (1858 – 1932)

• Pirotta, Angelo M., O.P. (1871 – 1939)

• Plato (c. 428/427 – c. 348/347 BC)

• Poincaré, Henri (1854 – 1912)

• Proclus Diadochus (412 – 485 AD)

R

• Riehl, Alois (1844 – 1924)

• Ross, Sir William David (1877 – 1971)

• Russell, Bertrand (1872 – 1970)

S

• Scholz, Heinrich (1884 – 1956)

• Simplicius of Cilicia (c. 490 – c. 560 AD)

• Stammler, Gerhard (1898 – 1977)

• Study, Eduard (1862 – 1930)

T

• Themistius (c. 317 – c. 388 AD)

• Thomas Aquinas, St., O.P. (1225 – 1274)

• Trendelenburg, Friedrich Adolf (1802 – 1872)

V

• Vallée-Poussin, Charles-Jean de la (1866 – 1962)

• Voss, Aurel (1845 – 1931)

W

• Waitz, Theodor (1821 – 1864)

• Weierstrass, Karl (1815 – 1897)

• Wellstein, Josef (1869 – 1919)

• Weyl, Hermann (1885 – 1955)

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Chronological Bibliography (Ordered by Death Date)

Eudoxus of Cnidus (c. 408 – c. 355 BC)

• Theoria Proportionum (in Euclidis Elementa, Liber V) (Theory of Proportions (in Euclid’s Elements, Book V)) c. 370 BC

  Notes: Preserved in Book V of Euclid’s Elements; formulated the first rigorous definition of proportionality for both commensurable and incommensurable continuous geometric magnitudes.

  • Citation: Caput I, § 4 (p. 21) & Caput I, n. 6

    • What Hoenen refers to: The Eudoxian theory of proportions as the Greek mathematical solution to the crisis of irrational/incommensurable ratios (e.g., diagonal and side of a square).

    • How it supports the text: Demonstrates that ancient Greek mathematics treated continuous extension as primary and sui generis. Instead of attempting to force continuous magnitude into discrete numerical fractions or arithmetic real numbers, Eudoxus developed a purely geometric theory of proportions, thereby demonstrating that geometric continuity cannot be reduced to discrete arithmetic.

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Plato (c. 428/427 – c. 348/347 BC)

• Meno (Μένων) (Meno) c. 385 BC

  Notes: Socratic dialogue on virtue and learning; contains the famous geometry demonstration with an uneducated slave boy.

  • Citation: Caput I, § 2 (82b–85b)

    • What Hoenen refers to: Socrates eliciting geometric demonstrations (doubling the area of a square) from the slave boy through guided questioning without direct instruction.

    • How it supports the text: Illustrates the classical recognition that mathematical knowledge possesses an intrinsic, necessary certainty that cannot be acquired merely through empirical generalization. While Plato explained this necessity through recollection (anamnesis) of transcendent Forms, Hoenen shows that the true ground is the intellect’s intuitive formal abstraction reading necessary relations directly within the imaginative sensible presentation.

• Respublica (Πολιτεία) (The Republic) c. 375 BC

  Notes: Plato’s foundational dialogue on justice and political philosophy; Books VI and VII formulate the divided line and the epistemology of mathematical hypotheses and dialectic.

  • Citation: Caput I, § 1 (VI 510c, VII 532c, 533c)

    • What Hoenen refers to: Plato’s observation that geometers assume primitive principles (the odd and the even, figures, three kinds of angles) as unquestioned hypotheses (hypotheseis), and that the dialectician must investigate and destroy (anairei) these hypotheses to attain unhypothetical first principles.

    • How it supports the text: Establishes the fundamental division of labor in the epistemology of mathematics: geometers construct their science from primitive postulates, but it belongs exclusively to the philosopher (the dialectician, metaphysician, or noeticist) to investigate the origin, truth, and necessity of those starting points.

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Aristotle (384 – 322 BC)

• Analytica Posteriora (Ἀναλυτικὰ Ὕστερα) (Posterior Analytics) c. 350 BC

  Notes: The foundational peripatetic treatise on the structure of demonstrative science (episteme), first principles (nous), and intuitive induction (epagoge). Standard recension by W. D. Ross (Oxford, 1949); edition and commentary by Theodor Waitz (Leipzig, 1844–1846).

  • Citation: Caput I, § 1 (I, c. 1–2, 71a–72a; I, c. 10, 76a–77a)

    • What Hoenen refers to: Aristotle’s classification of the primitive propositions of science: axioms (communes animi conceptiones / dignitates), hypotheses (suppositiones), and postulates (petitiones / aitemata).

    • How it supports the text: Provides Hoenen with the structural architecture of deductive demonstration, proving that analysis cannot regress infinitely or circulate, and demonstrating that geometry is the primary historical prototype of apodictic science.

  • Citation: Caput I, n. 1

    • What Hoenen refers to: Aristotle’s conception of postulates (aitemata) as propositions assumed by the teacher without the student’s initial assent, potentially including propositions like Euclid’s Fifth Postulate.

    • How it supports the text: Clarifies the difference between self-evident axioms and geometric postulates that demand assent without immediate self-evidence.

  • Citation: Caput I, § 2 (I, c. 12, 77b30)

    • What Hoenen refers to: The famous dictum: ταῦτα δ’ ἐστὶν οἷον ὁρᾶν τῇ νοήσει (‘these mathematical things are as it were seen by intellectual vision’).

    • How it supports the text: Serves as the textual cornerstone of Hoenen’s entire treatise, proving that for Aristotle, mathematical cognition is an authentic intellectual intuition (intuitus mentis) that perceives formal natures within the sensible imagination.

  • Citation: Caput III, n. 1 (I, c. 31, 87b35)

    • What Hoenen refers to: Aristotle’s argument: καὶ εἰ ἦν αἰσθάνεσθαι τὸ τρίγωνον ὅτι δυσὶν ὀρθαῖς ἴσας ἔχει τὰς γωνίας… (‘even if it were possible to perceive by sense that a triangle has angles equal to two right angles, we should still look for a demonstration and not possess scientific knowledge of it’).

    • How it supports the text: Refutes sensory empiricism (such as John Stuart Mill’s): sense perception only grasps contingent, individual particulars; scientific exactitude and universal necessity require intellectual cognition.

  • Citation: Caput VII, n. 1 (I, c. 1, 71a14 ff.)

    • What Hoenen refers to: The crux of commentators regarding whether ‘triangle’ in Aristotle’s opening demonstration is treated as a subject or as a passion/attribute (passio).

    • How it supports the text: Analyzed via St. Thomas to demonstrate that the intellect constructs geometric figures in intelligible matter and reads their necessary attributes directly within that construction.

• Analytica Priora (Ἀναλυτικὰ Πρότερα) (Prior Analytics) c. 350 BC

  Notes: Treatise on formal syllogistic logic and the validity of syllogistic figures. Edition and commentary by Theodor Waitz (Leipzig, 1844–1846).

  • Citation: Caput IV, n. 30 (I, c. 4, 25b37–39)

    • What Hoenen refers to: The formulation of the syllogism in Barbara: ‘If A is predicated of all B, and B of all C, necessarily A is predicated of all C.’

    • How it supports the text: Proves that Aristotle’s use of algebraic-like letters (A, B, C) was not an uninterpreted formalist calculus, but represented intelligible universal natures whose necessary connections are seen by the intellect.

  • Citation: Caput IV, n. 27 (I, c. 23, Waitz ed., I, pp. 427–429)

    • What Hoenen refers to: Aristotle’s resolution of geometric arguments into syllogisms, and Waitz’s commentary on the role of geometric diagrams.

    • How it supports the text: Shows that geometric reasoning relies upon the mental inspection of intelligible matter even when formulated syllogistically.

• Physica (Φυσικὴ ἀκρόασις) (Physics) c. 350 BC

  Notes: Treatise on natural philosophy, motion, the continuum, time, and place. Edition by W. D. Ross (Oxford, 1936); French edition by Henri Carteron (Budé, 1926).

  • Citation: Caput IV, n. 7 (IV, c. 11, 219b15 ff.; IV, c. 12, 220b24 ff.)

    • What Hoenen refers to: Aristotle’s definition of time as the number of motion according to before and after, and the continuity of time following the magnitude of the trajectory.

    • How it supports the text: Grounds successive duration and motion in the prior continuity of geometric magnitude, illustrating that motion in geometry is conceived within intelligible extension.

  • Citation: Appendix, n. 10 (IV, c. 5, 212b14 ff.)

    • What Hoenen refers to: Aristotle’s definition of place (topos) as the innermost motionless boundary of the containing body, and the textual variants (est id / est et).

    • How it supports the text: Supports Hoenen’s analysis of the category ubi and demonstrates that local motion requires a real relation to an actually existing surrounding body.

  • Citation: Appendix, n. 13 & § 6 (VIII, c. 1, 251a8–16)

    • What Hoenen refers to: The principle that things capable of being moved and the moving cause must actually exist (hyparchein / estin) prior to motion.

    • How it supports the text: Demonstrates that Aristotle’s physics explicitly establishes connections between existential acts (actual existences), proving that Aristotle was deeply concerned with the act of existing.

• Metaphysica (Τὰ μετὰ τὰ φυσικά) (Metaphysics) c. 350 BC

  Notes: Aristotle’s first philosophy, investigating being qua being, substance, act and potency, and the ontology of mathematicals. Editions and commentaries by W. D. Ross (Oxford, 1924) and Hermann Bonitz (Bonn, 1848–1849).

  • Citation: Caput II, § 4 (V, c. 9, 1018a9–14; X, c. 3, 1054b23–26)

    • What Hoenen refers to: The precise metaphysical distinction between diversity (diversum) and difference (differens): things are diverse by their whole selves (seipsis totis), whereas things are different through added differentiating marks.

    • How it supports the text: Provides the ontological framework for understanding diverse modes of being (substance vs. accidents; essence vs. existential act) which differ by their whole nature rather than through added generic/specific marks.

  • Citation: Appendix, n. 3 & n. 5 (IX, c. 3, 1047a30–b2; IX, c. 8, 1050a21–23)

    • What Hoenen refers to: Aristotle’s definition of actuality (energeia) as extended from movements to other things, and the distinction between energeia (activity) and entelecheia (perfection).

    • How it supports the text: Proves that non-existent things cannot be moved, and confirms that motion is an existential act that attributes actual being to its mobile subject.

  • Citation: Appendix, n. 18 (IX, c. 9, 1051a21–33)

    • What Hoenen refers to: The principle that potential geometric divisions are actualized by drawing constructions: ‘geometrical constructions are discovered by an actualization; for it is by dividing that they discover them.’

    • How it supports the text: Shows that the intellect actualizes potential mathematical relations by constructing divisions in intelligible matter, grounding mathematical discovery in the priority of act over potency.

• De Anima (Περὶ ψυχῆς) (On the Soul) c. 350 BC

  Notes: Treatise on the soul, sensible perception, imagination (phantasia), and intellect (nous). Edition and commentary by F. Adolf Trendelenburg (Berlin, 1877).

  • Citation: Caput I, § 2 (III, c. 7, 431a14–16, 431b2; III, c. 8, 432a5–9)

    • What Hoenen refers to: The peripatetic law that the intellect never thinks without a phantasm (οὐδέποτε νοεῖ ἄνευ φαντάσματος ἡ ψυχή), and that mathematical objects (ta ex aphaireseos) are abstracted from sensible things.

    • How it supports the text: Serves as the foundation of Thomistic-Aristotelian noetics: even the highest geometric abstractions remain intrinsically dependent on the imaginative sensible representation, where the intellect intuits formal necessity.

• Ethica Nicomachea (Ἠθικὰ Νικομάχεια) (Nicomachean Ethics) c. 350 BC

  Notes: Treatise on ethics and moral psychology; commentary by John Burnet (London, 1900).

  • Citation: Caput I, § 1 (VI, c. 8, 1142a12–20)

    • What Hoenen refers to: Aristotle’s observation that young men can become mathematicians and geometers, but cannot have practical wisdom (phronesis) or natural philosophy, because mathematics proceeds by abstraction while physics and ethics require extensive experience.

    • How it supports the text: Confirms that geometric knowledge does not depend on extensive inductive experience of the physical world, but on immediate formal abstraction accessible to any rational mind.

  • Citation: Appendix, n. 9 (IX, c. 9, 1170a31 ff.)

    • What Hoenen refers to: The argument on perception of self-existence: ‘he who sees perceives that he sees, and he who hears perceives that he hears… and if we perceive, we perceive that we exist.’

    • How it supports the text: Provides the ancient Aristotelian foundation for the Cartesian Cogito: in perceiving our own cognitive acts, we immediately perceive our own existential act of being.

• Categoriae (Κατηγορίαι) (Categories) c. 350 BC

  Notes: Treatise on the ten categories of being, predicaments, and postpredicaments.

  • Citation: Caput I, § 4 (c. 6, 4b20–5b10)

    • What Hoenen refers to: The division of quantity into continuous (magnitude, line, surface, body) and discrete (multitude, number).

    • How it supports the text: Underpins Hoenen’s entire defense of geometry against modern arithmetization: continuous magnitude is an irreducibly distinct category from discrete number, and cannot be constructed out of isolated zero-dimensional points.

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Euclid of Alexandria (fl. c. 300 BC (died c. 270 BC))

• Elementa (Στοιχεῖα) (Elements) c. 300 BC

  Notes: The thirteen books of Euclid’s Elements; standard critical edition and commentary by Sir Thomas L. Heath (Cambridge, 1908; 2nd ed. 1926).

  • Citation: Caput I, § 1, § 4, § 5

    • What Hoenen refers to: Euclid’s definitions of point, line, and surface; the Common Notions (axioms); Postulate V (the parallel postulate); and Book V on proportions.

    • How it supports the text: Represents the historical paradigm of axiomatic deductive geometry for twenty centuries. Hoenen examines Euclid’s definitions to show how intuitive spatial concepts served as the necessary foundation of classical geometry.

  • Citation: Caput IV, § 4, § 5 & n. 1

    • What Hoenen refers to: Euclid’s fifth postulate and the notion of direction in defining straight lines and parallels.

    • How it supports the text: Analyzes the transition from classical Euclidean geometry to non-Euclidean systems, demonstrating that non-Euclidean systems alter the geometric framework but do not invalidate the intuitive necessity of Euclidean relationships in intelligible matter.

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Alexander of Aphrodisias (fl. late 2nd – early 3rd c. AD (died c. 215 AD))

• In Aristotelis Metaphysica Commentaria (Commentary on Aristotle’s Metaphysics) c. 200 AD

  Notes: The premier ancient peripatetic commentary on the Metaphysics; edited by Michael Hayduck in Commentaria in Aristotelem Graeca (CAG Vol. I, Berlin: Reimer, 1891).

  • Citation: Appendix, n. 4 (ed. Hayduck, p. 573, line 16)

    • What Hoenen refers to: Alexander’s formulation of the first known principle: τὸ κινούμενον ἢ ἐνεργοῦν ὄν τί ἐστιν (‘that which is moved or acts is a certain being’).

    • How it supports the text: Confirms that ancient Greek commentators recognized motion as an existential act: movement can only belong to actually existing things, establishing a direct connection between physical mutation and existential being.

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Themistius (c. 317 – c. 388 AD)

• In Aristotelis Physica Paraphrasis (Paraphrase of Aristotle’s Physics) c. 370 AD

  Notes: Peripatetic paraphrase of the Physics; edited by Heinrich Schenkl in CAG Vol. V.2 (Berlin: Reimer, 1900).

  • Citation: Appendix, n. 11

    • What Hoenen refers to: Themistius’s resolution of the definition of place, adopted and praised by St. Thomas Aquinas in In IV Phys., lect. 7.

    • How it supports the text: Supports the realistic definition of place as the surrounding actual entity, grounding the category ubi in actual physical bodies.

  • Citation: Appendix, n. 21 (ed. Schenkl, p. 210)

    • What Hoenen refers to: Themistius’s repeated use of the technical Greek term προϋπάρχειν (prouparchein, to pre-exist) regarding the actual existence of mobile and mover.

    • How it supports the text: Provides decisive textual evidence from late antiquity that existential actualities must pre-exist before physical interactions occur, refuting the claim that Aristotle and his school ignored existential acts.

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Proclus Diadochus (412 – 485 AD)

• In primum Euclidis Elementorum librum commentarii (Commentary on the First Book of Euclid’s Elements) c. 470 AD

  Notes: Neoplatonic philosophical commentary on Euclid; edited by Gottfried Friedlein (Leipzig: Teubner, 1873); English translation by Glenn R. Morrow (Princeton, 1970).

  • Citation: Caput I, § 1 & Caput IV, § 4

    • What Hoenen refers to: Proclus’s exposition of the nature of mathematical imagination (phantasia) and historical documentation of Euclid’s fifth postulate and definitions.

    • How it supports the text: Corroborates the ancient understanding that geometric figures are projected into an imaginative medium that serves as the screen for mathematical reflection.

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Boethius, Anicius Manlius Severinus (c. 477 – 524 AD)

• De Hebdomadibus (Quomodo substantiae…) (How Substances Are Good in Virtue of Their Existence (De Hebdomadibus)) c. 520 AD

  Notes: Theological and philosophical opusculum formulating the axiomatic method in philosophy; translated and commented on extensively by St. Thomas Aquinas.

  • Citation: Caput I, § 1 & Appendix, § 7

    • What Hoenen refers to: The concept of communes animi conceptiones (common conceptions of the soul / self-evident axioms), which are evident to anyone once the terms are known.

    • How it supports the text: Supplies the classic definition of self-evident first principles adopted by St. Thomas and Hoenen: principles whose predicate is contained in the intelligible ratio of the subject.

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Simplicius of Cilicia (c. 490 – c. 560 AD)

• In Aristotelis Physicorum Libros Commentaria (Commentary on Aristotle’s Physics) c. 535 AD

  Notes: The monumental Neoplatonic commentary on the Physics; edited by Hermann Diels in CAG Vols. IX–X (Berlin: Reimer, 1882–1895).

  • Citation: Appendix, n. 21 (ed. Diels, p. 127, lines 9 and 14)

    • What Hoenen refers to: Simplicius confirming with Themistius that the active cause and passive subject must actually pre-exist (prouparchein) in nature before any act of change occurs.

    • How it supports the text: Affirms the scholastic thesis that existential actualities are necessarily presupposed for physical activity and motion.

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Thomas Aquinas, St., O.P. (1225 – 1274)

• In Aristotelis libros Analyticorum Posteriorum expositio (Commentary on Aristotle’s Posterior Analytics) c. 1270–1272

  Notes: Aquinas’s definitive epistemological commentary on scientific demonstration, certitude, and the cognition of first principles. Standard Leonine edition, Vol. I* (1989).

  • Citation: Caput I, § 1 (I, lect. 1, n. 10; lect. 5, n. 7; lect. 6; lect. 17, n. 4)

    • What Hoenen refers to: St. Thomas explaining why mathematics has the most certain mode of demonstration (‘propter certissimum modum demonstrationis’), and how higher sciences (metaphysics and natural philosophy) defend and establish the first principles of special sciences.

    • How it supports the text: Establishes that mathematics is the epistemological model of science, and proves that examining mathematical first principles belongs properly to the philosopher.

  • Citation: Caput VII, n. 1 (I, lect. 1, 71a14 ff.)

    • What Hoenen refers to: St. Thomas’s analysis of the crux regarding triangle as subject vs. passion/attribute.

    • How it supports the text: Demonstrates that the human intellect constructs geometric figures in intelligible matter and discerns their properties through active mental operations.

• Super Boetium De Trinitate (Commentary on Boethius’s De Trinitate) c. 1257–1259

  Notes: Aquinas’s profound treatise on the division and methods of the sciences; Question 5, Article 3 is the locus classicus on mathematical abstraction.

  • Citation: Caput IV, n. 2 (q. 5, a. 3, ad 3)

    • What Hoenen refers to: The complete transcribed text: ‘Quantitas autem indeterminata… dicitur materia intelligibilis… non tamen abstrahit a materia intelligibili individuali…’

    • How it supports the text: The cornerstone of Hoenen’s noetics: St. Thomas establishes that mathematics does not abstract from all matter, but retains intelligible matter (materia intelligibilis: continuous extended quantity imagined without sensible qualities). This resolves the problem of exactitude and individuation in geometry.

• Summa Theologiae (Summa Theologiae) c. 1265–1274

  Notes: The Angelic Doctor’s systematic theological synthesis. Primary editions: Leonine (Rome, 1888–1906); Marietti (Turin, 1952).

  • Citation: Appendix, n. 8 (I, q. 7, a. 1)

    • What Hoenen refers to: The dictum: ‘illud quod est maxime formale omnium, est ipsum esse’ (‘that which is most formal of all is esse itself’).

    • How it supports the text: Supports Hoenen’s metaphysical thesis that actual existence (esse) is the ultimate actuality and formal perfection of every entity.

  • Citation: Appendix, § 7 (I, q. 12, a. 4, ad 3 & I, q. 75, a. 6)

    • What Hoenen refers to: The teaching that ‘intellectus apprehendit esse absolutum, et secundum omne tempus’ (‘the intellect apprehends absolute esse, and according to all time’).

    • How it supports the text: Refutes the existentialist claim (Étienne Gilson) that esse cannot be conceptualized: St. Thomas explicitly affirms that the human intellect apprehends absolute esse in abstraction.

  • Citation: Appendix, § 7 (II-II, q. 24, a. 4, ad 3)

    • What Hoenen refers to: St. Thomas’s difficult teaching on the increase of accidental forms (charity and qualities) through greater participation in the subject.

    • How it supports the text: Shows that intensity in qualities represents a diverse mode of being within the existential order.

• In octo libros Physicorum Aristotelis expositio (Commentary on Aristotle’s Physics) c. 1268–1270

  Notes: Aquinas’s commentary on the physical world, movement, and the continuum. Leonine edition, Vol. II (1884).

  • Citation: Appendix, n. 11 (IV, lect. 7) & Appendix, § 7 (III, lect. 5)

    • What Hoenen refers to: St. Thomas adopting Themistius’s solution to place, and formulating the principle: ‘modi essendi proportionales sunt modis praedicandi’ (‘modes of being are proportional to modes of predicating’).

    • How it supports the text: Demonstrates that the Aristotelian categories are derived directly from diverse modes of actual being rather than mere grammatical distinctions.

• In duodecim libros Metaphysicorum Aristotelis expositio (Commentary on Aristotle’s Metaphysics) c. 1270–1273

  Notes: Aquinas’s profound metaphysical commentary. Edited by M.-R. Cathala and R. Spiazzi (Turin: Marietti, 1950).

  • Citation: Caput II, § 4 & Appendix, § 7 (V, lect. 9; IX, lect. 3; X, lect. 4, no. 2017)

    • What Hoenen refers to: St. Thomas explaining diversity by whole selves (seipsis totis) and the division of being into diverse modes of being.

    • How it supports the text: Underpins the distinction between quidditative differences and existential diversities.

• In Aristotelis librum De Anima commentarium (Commentary on Aristotle’s De Anima) c. 1267–1268

  Notes: Aquinas’s commentary on the soul, sensory faculties, and intellectual cognition. Edited by Angelo M. Pirotta (Turin: Marietti, 1936).

  • Citation: Caput I, § 2 (III, lect. 12, 13; Pirotta nos. 770–772, 777, 791) & Appendix, § 7 (II, lect. 16)

    • What Hoenen refers to: The necessity of conversion to the phantasm (conversio ad phantasmata) for all human intellectual cognition, and the analysis of sound as an entity with fluent rather than resting esse.

    • How it supports the text: Grounds Hoenen’s doctrine of intuitive formal abstraction: the intellect reads necessary relations directly within the imaginative presentation.

• In libros De Caelo et Mundo expositio (Commentary on Aristotle’s On the Heavens) c. 1272–1273

  Notes: Aquinas’s commentary on cosmology and astronomy. Leonine edition, Vol. III (1886).

  • Citation: Caput IV, n. 9 (I, lect. 2, no. 9)

    • What Hoenen refers to: St. Thomas noting: ‘He uses the mode of speaking used by geometers, imagining that a point by its motion describes a line, and a line a surface, and a surface a body.’

    • How it supports the text: Confirms that classical geometry legitimately constructs figures through imagined motion in intelligible matter.

• Summa contra Gentiles (Summa contra Gentiles) c. 1259–1265

  Notes: Aquinas’s philosophical defense of the Catholic faith against the gentiles. Leonine edition, Vols. XIII–XV (1918–1930).

  • Citation: Appendix, n. 31 (I, c. 26, no. 2)

    • What Hoenen refers to: The teaching that diverse esse are not diverse according to species, but things have ‘diverse natures, by which esse is acquired in diverse ways.’

    • How it supports the text: Proves that the diversity of modes of being flows from the diverse essences and quiddities that are actuated by esse.

• Quaestiones disputatae de Potentia Dei (Disputed Questions on the Power of God) c. 1265–1266

  Notes: Disputed questions on divine power, creation, and the Trinity. Marietti edition by P. Bazzi et al. (Turin, 1953).

  • Citation: Appendix, § 7 (q. 7, a. 2, ad 9; q. 8, a. 1; q. 9, a. 5)

    • What Hoenen refers to: The definition: ‘This that I call esse is the actuality of all acts, and on account of this is the perfection of perfections… esse is not so determined by another as potency by act, but rather as act by potency.’

    • How it supports the text: Provides the decisive Thomistic formulation proving that esse is not an abstract quiddity, but the ultimate act determined by essence as act is determined by potency.

• Scriptum super Sententiis (Commentary on the Sentences of Peter Lombard) c. 1252–1256

  Notes: Aquinas’s early masterpiece of theology. Edited by P. Mandonnet and M. F. Moos (Paris: Lethielleux, 1929–1947).

  • Citation: Appendix, § 7 (In I Sent., d. 2, q. 1, a. 3 & d. 19, q. 5, a. 1, ad 6)

    • What Hoenen refers to: The definition of ratio as that which the intellect apprehends of the meaning of a name, and the teaching that the ratio essendi is denied to the senses.

    • How it supports the text: Proves that understanding being (esse) requires an intellectual operation of reflection, which the sensory faculties are incapable of performing.

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Albert the Great, St., O.P. (c. 1200 – 1280)

• In Analytica Priora (Commentary on the Prior Analytics) c. 1250

  Notes: The Universal Doctor’s commentary on formal logic; edited by Pierre Jammy (Lugduni, 1651, Vol. I, tract. I, cap. 9, p. 298a).

  • Citation: Caput IV, n. 29

    • What Hoenen refers to: St. Albert’s teaching: ‘We use transcendent terms (A, B, C) in the place of things, because the necessity of consequence is better seen in transcendent terms than in particular matters.’

    • How it supports the text: Demonstrates that scholastic logic understood formal symbolic variables not as meaningless empty marks, but as universal formal placeholders expressing intelligible necessity.

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Nicole Oresme (c. 1320/1325 – 1382)

• Tractatus de configurationibus qualitatum et motuum (Treatise on the Configurations of Qualities and Motions) c. 1350

  Notes: Medieval mathematical and physical treatise pioneering the coordinate graphing of velocities and intensities; cited via Anneliese Maier (1943).

  • Citation: Appendix, § 7 and n. 33

    • What Hoenen refers to: Oresme’s geometric configurations representing the intensity of qualities and the velocity of motion across temporal duration.

    • How it supports the text: Shows that medieval scholasticism already recognized that fluent existential acts (motion, velocity) possess structural and qualitative configurations analogous to geometric figures in continuous extension.

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Descartes, René (1596 – 1650)

• Meditationes de Prima Philosophia & Responsiones ad Secundas Objectiones (Meditations on First Philosophy & Replies to the Second Objections) 1641

  Notes: Descartes’s foundational metaphysical work; critical edition by Charles Adam & Paul Tannery (AT VII, Paris: Vrin).

  • Citation: Appendix, n. 2 (AT VII, pp. 140, 18 – 141, 2)

    • What Hoenen refers to: Descartes explaining that the Cogito (‘I think, therefore I am’) is not a syllogism deduced from a universal major premise, but an immediate mental intuition of the singular existent.

    • How it supports the text: Supports Hoenen’s Thomistic interpretation of the Cogito: it is an immediate existential judgment in which the intellect perceives its own act of being directly within its cognitive exercise.

• Principia Philosophiae (Principles of Philosophy) 1644

  Notes: Descartes’s systematic exposition of metaphysics and natural philosophy; critical edition AT VIII-1.

  • Citation: Caput II, n. 7 (Part II, art. 4–11)

    • What Hoenen refers to: Descartes’s definition of the essence of body as extension alone (res extensa).

    • How it supports the text: Critiqued by Hoenen: while Descartes erred in reducing the entire physical nature of bodies to geometric extension, he correctly perceived that divisibility is an intrinsic and necessary proper attribute of extended quantity.

• Entretien avec Burman (Conversation with Burman) 1648

  Notes: Recorded interview of Descartes by Frans Burman on April 16, 1648; critical edition AT V, p. 164.

  • Citation: Appendix, § 7 (AT V, p. 164)

    • What Hoenen refers to: Descartes denying any real difference between a continuous body and an aggregate of parts touching each other in contact.

    • How it supports the text: Illustrates the philosophical confusion that results from failing to distinguish between an essential continuum (intrinsic continuous quantity) and a mere aggregate of contact (accidental existential unity).

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Locke, John (1632 – 1704)

• An Essay Concerning Human Understanding (An Essay Concerning Human Understanding) 1690

  Notes: Locke’s foundational epistemological work; critical edition by Alexander Campbell Fraser (Oxford: Clarendon Press, 1894, 2 vols.).

  • Citation: Caput V, n. 5 (Book IV, ch. 17, § 4; Fraser ed., II, pp. 390 ff.)

    • What Hoenen refers to: Locke’s famous critique of formal syllogistics: ‘God has not been so sparing to men to make them barely two-legged creatures, and left it to Aristotle to make them rational.’

    • How it supports the text: Employed by Hoenen to demonstrate that syllogistic reasoning is an intrinsic, natural mental activity prior to any verbal formulation or symbolic calculus, confirming the psychological and noetic reality of deduction.

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Leibniz, Gottfried Wilhelm (1646 – 1716)

• Nouveaux Essais sur l’entendement humain (New Essays on Human Understanding) 1704 (publ. 1765)

  Notes: Leibniz’s detailed chapter-by-chapter reply to Locke’s Essay; Book IV treats knowledge, truth, and necessary principles.

  • Citation: Caput II, n. 2 (Book IV, ch. 7, § 10)

    • What Hoenen refers to: Leibniz’s attempted proof of 2 + 2 = 4 using definitions (2 is 1+1, 3 is 2+1, 4 is 3+1) and the single axiom of substituting equals.

    • How it supports the text: Hoenen subjects Leibniz’s proof to rigorous forensic analysis: Leibniz applies the axiom not once, but at every single step of the substitution. This proves that even ‘analytic’ deductions depend upon repeated intuitive grasps of equality in intelligible matter.

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Kant, Immanuel (1724 – 1804)

• Kritik der reinen Vernunft (Critique of Pure Reason) 1781 (2nd ed. 1787)

  Notes: The foundational text of critical idealism; cited from the 1787 B edition (B14–15 on arithmetic judgments).

  • Citation: Caput I, § 2 & § 3

    • What Hoenen refers to: Kant’s theory of space and time as subjective a priori forms of external sensibility.

    • How it supports the text: Hoenen credits Kant with recognizing that mathematical knowledge requires sensible intuition (Anschauung) and possesses strict necessity, but refutes Kant’s subjectivism, demonstrating that extension is an objective property of being known through abstraction.

  • Citation: Caput II, n. 4 (B14–15)

    • What Hoenen refers to: Kant’s famous analysis of 7 + 5 = 12 as a synthetic a priori proposition that cannot be derived through mere conceptual analysis without recourse to intuition (counting points or fingers).

    • How it supports the text: Hoenen uses Kant’s example to show that arithmetic judgments require sensible phantasms, but demonstrates that the necessity is grasped by the intellect reading formal connections within intelligible matter.

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Waitz, Theodor (1821 – 1864)

• Aristotelis Organon Graece (Aristotle’s Organon in Greek) 1844–1846

  Notes: Critical Greek text and Latin commentary on the Organon (2 vols., Leipzig: Hahn).

  • Citation: Caput IV, n. 27 (Vol. I, pp. 427–429)

    • What Hoenen refers to: Waitz’s commentary on Prior Analytics I, 23 regarding the conversion of geometric proofs into formal syllogisms.

    • How it supports the text: Supports the view that geometric reasoning operates with essential terms and diagrams rather than empty formal symbols.

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Möbius, August Ferdinand (1790 – 1868)

• Ueber die Bestimmung des Inhaltes eines Polyëders (Das Möbiusband) (On the Determination of the Volume of a Polyhedron (The Möbius Strip)) 1858 (publ. 1865)

  Notes: Memoir presenting the discovery of the non-orientable one-sided surface (Möbius strip) in topology.

  • Citation: Caput II, § 2 & Caput III, § 2

    • What Hoenen refers to: The section of a cylinder and a Möbius strip as an objection against classical geometric intuition.

    • How it supports the text: Hoenen analyzes the cutting of a Möbius strip (which results in a single longer two-sided loop rather than two separate strips), proving that this counter-intuitive result is rigorously deduced from the intuitive axioms of continuous sectioning rather than contradicting them.

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Trendelenburg, Friedrich Adolf (1802 – 1872)

• Aristotelis De Anima libri tres (Aristotle’s Three Books On the Soul) 1877 (ed. altera)

  Notes: Renowned critical edition and commentary on Aristotle’s De Anima (Berlin: Weber).

  • Citation: Caput IV, n. 8

    • What Hoenen refers to: Trendelenburg’s note asking who are the ancient thinkers who spoke of points moving to generate lines.

    • How it supports the text: Traces the historical pedigree of motion in geometry back to ancient Peripatetic discussions.

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Mill, John Stuart (1806 – 1873)

• A System of Logic, Ratiocinative and Inductive (A System of Logic, Ratiocinative and Inductive) 1843 (5th ed. 1862)

  Notes: Mill’s magnum opus on epistemology, empiricism, and induction (London: Parker, Son, and Bourn, 2 vols.).

  • Citation: Caput I, § 2

    • What Hoenen refers to: Mill’s radical empiricist theory that mathematics is an inductive physical science of material bodies, lacking apodictic necessity and exactitude.

    • How it supports the text: Presents the classical empiricist challenge: Mill honestly admits that if mathematical ideas are drawn from senses alone, they can never attain absolute necessity or exactitude.

  • Citation: Caput III, n. 3 & n. 4 (Vol. I, Book II, ch. 5, pp. 255–257)

    • What Hoenen refers to: Mill’s assertions: ‘A line is length without breadth; but is there in nature such a thing as a line without breadth? There is not… none of these things exist in nature.’

    • How it supports the text: Hoenen uses Mill’s formulation to sharpen the Problem of Exactitude: because physical senses only perceive rough bodies with finite width, the mind’s exact geometric notions (point, line, surface) must arise through intellectual abstraction of boundaries within continuous quantity.

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Bonitz, Hermann (1814 – 1888)

• Aristotelis Metaphysica: Commentarius (Commentary on Aristotle’s Metaphysics) 1848–1849

  Notes: Classic Philological commentary on the Greek text of the Metaphysics (Bonn: Marcus, 2 vols.).

  • Citation: Appendix, n. 5 (Vol. II, p. 387)

    • What Hoenen refers to: Bonitz’s linguistic analysis distinguishing energeia (action bringing possibility to essence) from entelecheia (full perfection of the thing).

    • How it supports the text: Clarifies the precise Aristotelian vocabulary of act and actuality in existential changes.

  • Citation: Appendix, n. 13 (Vol. II, p. 401)

    • What Hoenen refers to: Bonitz’s explanation of Metaphysics IX, 3: ‘hanc causam motricem actu existere necesse est’ (‘it is necessary that this moving cause actually exist’).

    • How it supports the text: Confirms the textual necessity that motion presupposes the actual existence in time of the active cause.

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Weierstrass, Karl (1815 – 1897)

• Vorlesungen über die Theorie der Funktionen (Lectures on the Theory of Functions) 1872 (publ. 1886)

  Notes: Pioneering lectures establishing the epsilon-delta arithmetization of mathematical analysis without geometric intuition.

  • Citation: Caput I, § 4

    • What Hoenen refers to: Weierstrass’s program of arithmetizing analysis, eliminating geometric intuition and infinitesimals in favor of pure number sequences.

    • How it supports the text: Represents the historical movement that attempted to solve the problem of geometric inexactitude by reducing all continuous extension to discrete integer calculations.

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Hamelin, Octave (1856 – 1907)

• Le Système d’Aristote (The System of Aristotle) 1920 (posthumous)

  Notes: Comprehensive philosophical reconstruction of Aristotle’s thought, edited by Léon Robin (Paris: Alcan).

  • Citation: Caput I, n. 3 (pp. 234 sq., 258 sq.)

    • What Hoenen refers to: Hamelin’s analysis of Aristotelian abstraction and the relationship between sensible data and intellectual principles.

    • How it supports the text: Provides scholarly authority confirming that Aristotle derived first principles through intuitive induction from sensible experience.

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Poincaré, Henri (1854 – 1912)

• La Science et l’Hypothèse (Science and Hypothesis) 1902

  Notes: Poincaré’s classic work on the philosophy of science, conventionalism, and the nature of space (Paris: Flammarion).

  • Citation: Caput IV, n. 10 (p. 80; cf. p. 60)

    • What Hoenen refers to: Poincaré’s observation that geometric figures are ideal bodies, and that geometric axioms are disguised conventions chosen for convenience.

    • How it supports the text: Hoenen engages Poincaré’s conventionalism, showing that while physical bodies are imperfect, ideal geometric figures have an objective nature grasped through formal abstraction.

• La Valeur de la Science (The Value of Science) 1905

  Notes: Epistemological essays on intuition, logic, and the physical sciences (Paris: Flammarion).

  • Citation: Caput I, n. 9 & n. 10 (pp. 17, 22–23)

    • What Hoenen refers to: Poincaré’s distinction between three kinds of intuition: the appeal to sense and imagination, generalization by induction, and the intuition of pure number.

    • How it supports the text: Highlights Poincaré’s admission that modern analysis eliminated sensible intuition, but shows that Poincaré still required an irreducible ‘intuition of pure number,’ confirming that mathematics cannot exist without intuition.

  • Citation: Caput IV, n. 14 (p. 59) & Caput VI, n. 1

    • What Hoenen refers to: Poincaré describing continuous space as formless and ‘amorphous’ until metric relations are imposed, and his thought experiment on measuring a physical circle.

    • How it supports the text: Hoenen agrees with Poincaré that physical continuous extension is amorphous regarding fixed coordinate systems, but shows that it possesses intrinsic intelligible properties (divisibility, boundaries, dimensionality).

• Dernières Pensées (Last Thoughts) 1913 (posthumous)

  Notes: Final collection of essays on mathematics, logic, and physics (Paris: Flammarion).

  • Citation: Caput I, n. 11 & n. 12 (p. 65) & Caput IV, n. 14 (p. 62)

    • What Hoenen refers to: Poincaré’s sharp warning against arithmetization: ‘This definition makes cheap of the intuitive origin of the notion of the continuum… I do not mean to say that this arithmetization of mathematics is a bad thing, I say it is not everything.’

    • How it supports the text: Provides decisive modern mathematical backing for Hoenen’s central thesis: arithmetization leaves out the essential intuitive nature of continuous extension, which the philosopher must recover.

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Couturat, Louis (1868 – 1914)

• La philosophie des mathématiques de Kant (The Philosophy of Mathematics of Kant) 1904

  Notes: Major critical study in Revue de Métaphysique et de Morale (Vol. 12, No. 3, pp. 321–383).

  • Citation: Caput II, n. 3 & Caput III, n. 8

    • What Hoenen refers to: Couturat’s logicist deduction of arithmetic propositions (7 + 5 = 12) from definitions and logical substitution without Kantian intuition.

    • How it supports the text: Hoenen analyzes Couturat’s deductions to reveal that Couturat unconsciously presupposes intuitive operations at each deductive step, proving that logicism cannot dispense with intelligible intuition.

• Les principes des mathématiques (The Principles of Mathematics) 1905

  Notes: Systematic exposition of Russell and Peano’s logicism for continental audiences (Paris: Alcan).

  • Citation: Caput II, n. 3

    • What Hoenen refers to: Couturat’s exposition of the formal logical derivation of mathematical addition.

    • How it supports the text: Demonstrates that formal arithmetic definitions presuppose an intuitive understanding of multitude and equality.

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Dedekind, Richard (1831 – 1916)

• Stetigkeit und irrationale Zahlen (Continuity and Irrational Numbers) 1872

  Notes: Landmark treatise constructing real numbers via Dedekind cuts on sets of rational numbers (Braunschweig: Vieweg).

  • Citation: Caput I, § 4

    • What Hoenen refers to: Dedekind’s definition of continuity as an arithmetic cut in the domain of rational numbers.

    • How it supports the text: Analyzed as a prime example of the arithmetization of the continuum: Dedekind defines continuity through discrete sets, which inverts the true cognitive order where discrete number is abstracted from continuous magnitude.

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Brentano, Franz (1838 – 1917)

• Psychologie vom empirischen Standpunkt (Psychology from an Empirical Standpoint) 1874

  Notes: Brentano’s seminal work re-introducing intentionality and establishing the fundamental classification of mental phenomena (Leipzig: Duncker & Humblot).

  • Citation: Appendix, § 7 and n. 26

    • What Hoenen refers to: Brentano’s doctrine that judgment (Urteil: acknowledging or rejecting existence) is fundamentally diverse from representation (Vorstellung), constituting distinct basic classes of mental acts.

    • How it supports the text: Hoenen compares Brentano’s insight directly to St. Thomas Aquinas: both recognize that judging existence (esse) is fundamentally distinct from apprehending quiddity, validating the realism of judgment.

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Cantor, Georg (1845 – 1918)

• Grundlagen einer allgemeinen Mannigfaltigkeitslehre (Foundations of a General Theory of Aggregates) 1883

  Notes: Foundational treatise on set theory, transfinite numbers, and the continuum (Leipzig: Teubner).

  • Citation: Caput I, § 4 & Caput II, § 2

    • What Hoenen refers to: Cantor’s construction of the mathematical continuum as an infinite aggregate (insieme) of discrete real numbers with the cardinality of the power set of integers.

    • How it supports the text: Represents the ultimate modern formal replacement of the intuitive continuum with infinite discrete point sets, contrasting with the Aristotelian continuum whose parts are only in potency.

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Wellstein, Josef (1869 – 1919)

• Elemente der Geometrie (in Weber-Wellstein Enzyklopädie, Band II) (Elements of Geometry (in Weber-Wellstein Encyclopedia, Vol. II)) 1905

  Notes: Comprehensive German reference work on elementary mathematics from an advanced viewpoint (Leipzig: Teubner).

  • Citation: Caput III, n. 6 & n. 9 (Vol. II, pp. 9–10)

    • What Hoenen refers to: Wellstein’s analysis of sensory inexactitude and his attempt to formulate geometric congruence purely through static axioms without motion.

    • How it supports the text: Illustrates modern axiomatic attempts to bypass motion; Hoenen shows that even static congruence axioms secretly presuppose the imaginative mental translation of shapes in intelligible matter.

  • Citation: Caput IV, n. 6

    • What Hoenen refers to: Wellstein’s treatment of congruence and the avoidance of superposition.

    • How it supports the text: Demonstrates that avoiding physical motion in geometric proofs does not eliminate the intellect’s constructive abstraction.

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Killing, Wilhelm (1847 – 1923)

• Einführung in die Grundlagen der Geometrie (Introduction to the Foundations of Geometry) 1893, 1898

  Notes: Pioneering two-volume treatise on geometric foundations and Lie algebras (Paderborn: Schöningh).

  • Citation: Caput IV, n. 16, n. 17, n. 18, n. 19 (Vol. I, pp. 48–52)

    • What Hoenen refers to: Killing’s thorough dissection of the concept of ‘direction’ (Richtung): ‘Der Winkel misst den Richtungsunterschied zweier Geraden… Man darf nur sagen: sie haben gleiche oder ungleiche Richtung in Bezug auf eine bestimmte dritte Gerade.’

    • How it supports the text: Decisive support for Hoenen’s critique of attempts to define straight lines and parallels via direction: Killing demonstrates that direction cannot be defined without already presupposing the very parallel straight lines one is trying to define.

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Baeumker, Clemens (1853 – 1924)

• Das Problem der Materie in der griechischen Philosophie (The Problem of Matter in Greek Philosophy) 1890

  Notes: Monumental historical investigation of ancient Greek concepts of matter (Münster: Aschendorff).

  • Citation: Caput III, n. 2 (pp. 288 ff.)

    • What Hoenen refers to: Baeumker’s historical documentation of intelligible matter (materia intelligibilis / hyle noete) in Aristotle’s Metaphysics and Physics.

    • How it supports the text: Provides definitive historical authority for Hoenen’s Thomistic doctrine: mathematical objects retain extension as intelligible matter within imagination, while abstracting from physical matter.

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Riehl, Alois (1844 – 1924)

• Logik und Erkenntnistheorie (in Die Kultur der Gegenwart) (Logic and Theory of Knowledge (in The Culture of the Present)) 1921

  Notes: Systematic epistemological essay in Die Kultur der Gegenwart (Teil I, Abt. 6, 3rd ed., Leipzig: Teubner, pp. 71 ff.).

  • Citation: Caput V, n. 6 (p. 71)

    • What Hoenen refers to: Riehl’s analysis of the objective logical relationship between concepts in syllogistic deduction.

    • How it supports the text: Supports Hoenen’s thesis that the mental syllogism expresses an objective connection between essences, which cannot be reduced to verbal formalism.

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Klein, Felix (1849 – 1925)

• Anwendung der Differential- und Integralrechnung auf Geometrie: Eine Revision der Prinzipien (Application of Differential and Integral Calculus to Geometry: A Revision of Principles) 1902 (2nd ed. 1907)

  Notes: Famous lectures re-evaluating the foundational principles of calculus and geometry (Leipzig: Teubner).

  • Citation: Caput I, n. 7 & n. 8 (pp. 7, 11)

    • What Hoenen refers to: Klein’s explicit formulation: ‘In allen diesen praktischen Gebieten gibt es einen Schwellenwert der Genauigkeit… Im ideellen Gebiet der Arithmetik gibt es keinen endlichen Schwellenwert.’

    • How it supports the text: The primary modern formulation of the Problem of Exactitude: Klein proves that all physical measurements have a finite threshold of exactitude, whereas mathematics demands infinite exactitude, proving that geometry is not an empirical science.

• Elementarmathematik vom höheren Standpunkte aus (Band II: Geometrie) (Elementary Mathematics from an Advanced Standpoint (Vol. II: Geometry)) 1925 (3rd ed.)

  Notes: Klein’s celebrated masterwork on geometric pedagogy and foundations (Berlin: Springer).

  • Citation: Caput IV, n. 23 & n. 24 (Vol. II, pp. 189–194)

    • What Hoenen refers to: Klein’s demonstration that within physical measurement limits, Euclidean and non-Euclidean geometry are indistinguishable, and his discussion of the threshold of exactitude regarding parallel lines.

    • How it supports the text: Proves that physical experiment cannot decide between Euclidean and non-Euclidean geometry, confirming that geometric structures are evaluated by the intellect.

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Hessenberg, Gerhard (1874 – 1925)

• Ebene und sphärische Trigonometrie (Plane and Spherical Trigonometry) 1904

  Notes: Textbook comparing physical observation with geometric proof (Leipzig: Göschen).

  • Citation: Caput II, n. 10

    • What Hoenen refers to: Hessenberg’s comparison between physical judgments and mathematical judgments.

    • How it supports the text: Illustrates the fundamental epistemological divide: physical judgments are contingent hypotheses subject to revision, while geometric judgments are perceived with apodictic necessity.

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Carteron, Henri (1891 – 1927)

• Aristote: Physique (Collection Budé) (Aristotle: Physics (Budé Edition)) 1926

  Notes: Standard French critical edition and translation of the Physics (Paris: Les Belles Lettres, 2 vols.).

  • Citation: Appendix, n. 10 (Vol. I, p. 134)

    • What Hoenen refers to: Carteron’s French rendering of Aristotle’s definition of place in Physics IV, 5.

    • How it supports the text: Provides philological backing for Hoenen’s translation and interpretation of the containment relation in place.

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Burnet, John (1863 – 1928)

• The Ethics of Aristotle (The Ethics of Aristotle) 1900

  Notes: Masterly critical edition and commentary on the Nicomachean Ethics (London: Methuen).

  • Citation: Appendix, n. 9 (on EN IX, 9)

    • What Hoenen refers to: Burnet’s analytical outline of Aristotle’s argumentation on consciousness and existence in Chapter 9.

    • How it supports the text: Confirms the rigorous structural unity of Aristotle’s deduction of self-existence from the exercise of perception and thought.

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Study, Eduard (1862 – 1930)

• Die realistische Weltansicht und die Lehre vom Raume (The Realistic Worldview and the Doctrine of Space) 1914

  Notes: Trenchant philosophical treatise defending mathematical realism against conventionalism and logicism (Braunschweig: Vieweg).

  • Citation: Caput I, n. 13 (p. 131)

    • What Hoenen refers to: Study’s declaration: ‘Ausschlaggebend für die Beurtheilung der Sachlage scheint uns der Umstand zu sein, dass eine von der Analysis wirklich unabhängige Geometrie, wie das antike Ideal sie eigentlich verlangen würde, sich als eine Utopie herausgestellt hat.’

    • How it supports the text: Highlights the contemporary mathematician’s despair of saving synthetic geometry from pure analysis; Hoenen accepts Study’s historical assessment while restoring the realistic noetic foundation.

  • Citation: Caput III, n. 5 (p. 75)

    • What Hoenen refers to: Study on the reality of geometric spatial structures against pure nominalist formalism.

    • How it supports the text: Supports Hoenen’s realism against purely formalist interpretations of geometry.

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Pasch, Moritz (1843 – 1930)

• Vorlesungen über neuere Geometrie (Lectures on Modern Geometry) 1882 (2nd ed. with Max Dehn, 1926)

  Notes: Pioneering foundation of modern projective and axiomatic geometry; formulated Pasch’s Axiom of order (Berlin: Springer).

  • Citation: Caput II, n. 9 & n. 16 (pp. 5–8, 20)

    • What Hoenen refers to: Pasch’s Kernsatz IV and axioms of order: if a straight line enters a triangle through one side, it must exit through one of the other two sides.

    • How it supports the text: Hoenen shows that Pasch’s Axiom is an undeniable, immediate necessary intuition: Euclid omitted it because it is so visually and intellectually obvious. Its discovery proves that geometry relies on intuitive topological continuity rather than pure uninterpreted symbols.

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Voss, Aurel (1845 – 1931)

• Über die mathematische Erkenntnis (in Die Kultur der Gegenwart) (On Mathematical Knowledge (in The Culture of the Present)) 1914

  Notes: Epistemological treatise on mathematical cognition (Teil III, Abt. 1, Leipzig: Teubner, pp. 385–440).

  • Citation: Caput III, n. 10

    • What Hoenen refers to: Voss’s analysis of the relationship between mathematical concepts and sensory representation.

    • How it supports the text: Affirms that mathematical exactitude transcends sensory perception through an intellectual process of conceptual idealization.

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Peano, Giuseppe (1858 – 1932)

• Arithmetices principia, nova methodo exposita (The Principles of Arithmetic, Presented by a New Method) 1889

  Notes: Groundbreaking treatise introducing Peano’s axioms and modern symbolic logic (Turin: Bocca).

  • Citation: Caput I, § 6 & Caput II, § 1

    • What Hoenen refers to: Peano’s symbolic axiomatization of natural numbers and geometric foundations.

    • How it supports the text: Hoenen demonstrates that Peano’s axioms cannot be understood or applied without intuitive knowledge of the primitive notions (number, successor, equality) which they symbolically designate.

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Meyerson, Émile (1859 – 1933)

• Du cheminement de la pensée (The Progression of Thought) 1931

  Notes: Meyerson’s three-volume magnum opus on the epistemology of science and the human intellect’s demand for ontological identity (Paris: Alcan).

  • Citation: Appendix, n. 7 (Vol. II, p. 391, n. 232)

    • What Hoenen refers to: Meyerson’s observation that the human mind inherently seeks the identity of being across change and recognizes reality beyond phenomenal sensations.

    • How it supports the text: Supports Hoenen’s thesis that the mind’s grasp of existential connections is an innate, essential function of intellectual cognition.

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Pirotta, Angelo M., O.P. (1871 – 1939)

• S. Thomae Aquinatis in Aristotelis librum De Anima commentarium (St. Thomas Aquinas’s Commentary on Aristotle’s De Anima) 1936

  Notes: Standard Marietti edition with critical paragraph numbering (Turin: Marietti).

  • Citation: Caput I, § 2 (nos. 770–772, 777, 791)

    • What Hoenen refers to: Pirotta’s paragraph numbers for Aquinas’s commentary on intellectual abstraction from phantasms.

    • How it supports the text: Provides precise textual citations for the Thomistic doctrine of conversion to the phantasm in mathematical cognition.

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Heath, Sir Thomas Little (1861 – 1940)

• A History of Greek Mathematics (A History of Greek Mathematics) 1921

  Notes: The definitive two-volume history of Greek mathematics (Oxford: Clarendon Press).

  • Citation: Caput V, n. 1 (Vol. I, pp. 335 ff.)

    • What Hoenen refers to: Heath’s historical documentation that Aristotle and Greek mathematicians rigorously distinguished axioms (evident to all), hypotheses (propositions accepted by the student), and postulates (demands made without student agreement).

    • How it supports the text: Validates Hoenen’s classical division of scientific principles against the modern collapse of all principles into arbitrary uninterpreted postulates.

• The Thirteen Books of Euclid’s Elements (The Thirteen Books of Euclid’s Elements) 1908 (2nd ed. 1926)

  Notes: Standard English translation and monumental commentary on Euclid (Cambridge University Press, 3 vols.).

  • Citation: Caput I, § 1 & Caput IV, § 4

    • What Hoenen refers to: Heath’s historical notes on the fifth postulate, the definitions of line and surface, and the Eudoxian theory of Book V.

    • How it supports the text: Serves as the scholarly authority throughout Hoenen’s textual analysis of Euclidean mathematics.

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Hausdorff, Felix (1868 – 1942)

• Das Raumproblem (The Problem of Space) 1904

  Notes: Philosophical paper published in Annalen der Naturphilosophie (Vol. 3, pp. 1–23).

  • Citation: Caput IV, n. 21 (p. 3)

    • What Hoenen refers to: Hausdorff’s statement: ‘Die Mathematik hat sich vom Raume losgesagt; sie ist rein logisch geworden… Der Raum ist für sie ein Gedankending.’ (‘Mathematics has detached itself from space; it has become purely logical… Space is for it a mere mental thing.’)

    • How it supports the text: Quotes Hausdorff as an authoritative witness to modern mathematics’ abandonment of intuitive physical space, sharpening Hoenen’s critique of extreme formalism.

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Hilbert, David (1862 – 1943)

• Grundlagen der Geometrie (Foundations of Geometry) 1899 (7th ed. 1930)

  Notes: Hilbert’s revolutionary work establishing the formal axiomatic method for Euclidean geometry (Leipzig: Teubner).

  • Citation: Caput I, n. 14 (7th ed., p. 2)

    • What Hoenen refers to: Hilbert’s opening declaration: ‘Wir denken uns drei verschiedene Systeme von Dingen: die Dinge des ersten Systems nennen wir Punkte… des zweiten Systems Geraden… des dritten Systems Ebenen…’ (‘We conceive three different systems of things: the things of the first system we call points… the second straight lines… the third planes…’)

    • How it supports the text: Exposes the core thesis of modern formalism: points, lines, and planes are defined purely by implicit relations rather than intuitive essences. Hoenen demonstrates that this program cannot sustain geometry without intuitive intelligible matter.

  • Citation: Caput IV, n. 1

    • What Hoenen refers to: Hilbert’s use of intuitive ‘explanations’ (Erklärungen) interspersed among his formal axioms.

    • How it supports the text: Hoenen demonstrates a crucial inconsistency in Hilbert’s method: Hilbert smuggles intuitive geometric meaning back into his system through informal ‘explanations,’ revealing that pure formalism is impossible in practice.

  • Citation: Caput V, n. 9 & n. 10

    • What Hoenen refers to: Hilbert’s theorem on the linear order of points: ‘Sind irgendeine endliche Anzahl von Punkten einer Geraden gegeben…’ and G. H. Hardy’s critique.

    • How it supports the text: Shows that Hilbert’s proof of the linear ordering of points relies on spatial diagrams and visual inspection rather than purely mechanical deduction.

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Enriques, Federigo (1871 – 1946)

• Questioni riguardanti le matematiche elementari (Questions Regarding Elementary Mathematics) 1924 (3rd ed.)

  Notes: Influential Italian collection on geometric foundations, edited by Enriques (Bologna: Zanichelli).

  • Citation: Caput IV, n. 15 & n. 20 (Vol. I, pp. 43–44)

    • What Hoenen refers to: Articles by Enriques and Ugo Amaldi examining Euclidean postulates and the circularity of defining parallel lines via direction.

    • How it supports the text: Corroborates Hoenen’s finding that direction cannot replace Euclid’s parallel postulate without covert circularity.

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Hardy, Godfrey Harold (1877 – 1947)

• Mathematical Proof (Mathematical Proof) 1929

  Notes: Philosophical paper in Mind (New Series, Vol. 38, No. 149, pp. 1–25).

  • Citation: Caput V, n. 8 & n. 10 (pp. 12, 18)

    • What Hoenen refers to: Hardy’s candid confession: ‘I believe the prime Number Theorem because of de la Vallée-Poussin’s proof of it, but I do not believe that 2 + 2 = 4 because of a proof by Russell… If Hilbert’s axioms are to mean anything to us, we must draw figures.’

    • How it supports the text: Decisive testimonial evidence from a world-class pure mathematician: formal axiomatic deductions depend on intuitive conviction, and Hilbert’s axioms are completely sterile without imaginative diagrams.

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Geyser, Joseph (1869 – 1948)

• Die Erkenntnistheorie des Aristoteles (The Epistemology of Aristotle) 1917

  Notes: Thorough Neoscholastic epistemological study of Aristotelian noetics (Münster: Schöningh).

  • Citation: Caput I, n. 3 (chs. VI and XII)

    • What Hoenen refers to: Geyser’s analysis of how the intellect abstracts first principles and necessary propositions from sensible particulars.

    • How it supports the text: Affirms Hoenen’s peripatetic thesis: intellectual abstraction does not invent forms out of nothing, but reads necessary intelligible relations within sensible data.

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Einstein, Albert (1879 – 1955)

• Geometrie und Erfahrung (Geometry and Experience) 1921

  Notes: Expanded lecture to the Prussian Academy of Sciences on January 27, 1921 (Berlin: Springer).

  • Citation: Caput I, n. 4

    • What Hoenen refers to: Einstein’s celebrated dictum: ‘Insofern sich die Sätze der Mathematik auf die Wirklichkeit beziehen, sind sie nicht sicher, und insofern sie sicher sind, beziehen sie sich nicht auf die Wirklichkeit.’ (‘As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.’)

    • How it supports the text: Hoenen takes this as the quintessential expression of the modern crisis: if applied mathematics is purely empirical physics, its certainty vanishes; if pure mathematics is certain, it has no relation to reality. Hoenen refutes this dilemma by showing that geometry abstracts intelligible matter from the real world, retaining necessary truth that applies necessarily to real physical extension.

• Address in the journal Forum (Address in the Journal Forum) 1930

  Notes: Discussion on the concept of space and coordinate systems in modern physics (Forum, I, p. 173; cited via Cosmologia, 4th ed., p. 468).

  • Citation: Caput VI, n. 3 & Appendix, n. 17

    • What Hoenen refers to: Einstein explaining that coordinate systems in physics require physical solid bodies of reference, and that empty space without matter has no independent physical reality.

    • How it supports the text: Integrates Einstein’s relativistic physical coordinates into the Thomistic cosmology of the category ubi: coordinates describe the physical surrounding container, confirming the realistic grounding of space.

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Weyl, Hermann (1885 – 1955)

• Philosophie der Mathematik und Naturwissenschaft (Philosophy of Mathematics and Natural Science) 1927

  Notes: Treatise in the Handbuch der Philosophie (München: Oldenbourg; revised English ed., Princeton, 1949).

  • Citation: Caput IV, n. 22 (p. 18)

    • What Hoenen refers to: Weyl’s observation that modern axiomatics turns geometry into a branch of pure logic, detaching it from spatial perception.

    • How it supports the text: Demonstrates that even the foremost mathematical physicists recognize that formal axiomatics leaves the intuitive reality of geometric space behind.

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Scholz, Heinrich (1884 – 1956)

• Warum haben die Griechen die Irrationalzahlen nicht aufgebaut? (Why Did the Greeks Not Construct Irrational Numbers?) 1928

  Notes: Historical-epistemological paper in Kantstudien (Vol. 33, pp. 35–72).

  • Citation: Caput I, n. 6

    • What Hoenen refers to: Scholz’s historical investigation into why the Greeks refused to treat incommensurable geometric ratios as arithmetic fractions.

    • How it supports the text: Corroborates Hoenen’s view that ancient mathematics possessed a profound philosophical respect for the irreducible distinction between continuous geometric magnitude and discrete arithmetic number.

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Amaldi, Ugo (1875 – 1957)

• Sui concetti fondamentali della geometria (in Enriques’ Questioni) (On the Fundamental Concepts of Geometry) 1924

  Notes: Monograph on elementary geometry and parallel postulates in Enriques’ Questioni riguardanti le matematiche elementari (Vol. I, pp. 43–44).

  • Citation: Caput IV, n. 15 & n. 20

    • What Hoenen refers to: Amaldi’s critical analysis of definitions of direction and parallelism.

    • How it supports the text: Confirms that trying to define parallel lines by identity of direction is a circular definition, proving that direction cannot supersede the intuitive necessity of Euclid’s parallel postulate.

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961)

• Cosmologia (Cosmology) 1931 (4th ed. 1949; 5th ed. 1956)

  Notes: Hoenen’s standard Latin manual of the philosophy of nature at the Gregorian University (Rome: Gregorianum).

  • Citation: Caput I, n. 5 (Notes III & VII, pp. 446–455, 471–482)

    • What Hoenen refers to: Expositions of non-Euclidean geometry and physical space coordinates.

    • How it supports the text: Provides the cosmological framework establishing that physical space is not an empty absolute container but a system of relations among extended bodies.

  • Citation: Caput V, n. 12 & Caput VI, n. 2, n. 3

    • What Hoenen refers to: Physical proper attributes impeding exactitude in bodies, and the analysis of the category ubi.

    • How it supports the text: Shows how physical matter fluctuates while mathematical intelligible matter admits immutable exactitude.

  • Citation: Appendix, n. 6, n. 12, n. 15, n. 16, n. 17, n. 19, n. 20, n. 22

    • What Hoenen refers to: Detailed references to Note IV (relativity of motion, p. 456), Note VI (ubi, p. 468), Note XIII (motion as an existential act, pp. 527–530), Note XV (neo-positivism, p. 538), and the actuality of continua (p. 40).

    • How it supports the text: Supplies the foundational metaphysics for the entire Appendix: motion is an existential act (actus existentialis), extension is an actuality of continua, and the category ubi establishes real relations between physical existents.

• La théorie du jugement d’après St. Thomas d’Aquin (The Theory of Judgment According to St. Thomas Aquinas (Reality and Judgment)) 1946 (2nd ed. 1953; English trans. 1952)

  Notes: Hoenen’s epistemological masterwork in Analecta Gregoriana (Vol. XXXIX; English translation Reality and Judgment by H. F. Tiblier, Chicago: Regnery, 1952). Cited as Th. d. J. and R. a. J.

  • Citation: Praefatio, n. 2 & Caput I, n. 2

    • What Hoenen refers to: The fundamental doctrine of the two operations of the intellect: first operation = apprehension of quiddity; second operation = judgment attributing esse.

    • How it supports the text: The epistemological matrix of De Noetica Geometriae: mathematical knowledge begins in apprehension of quiddities in intelligible matter, but culminates in affirmative judgments of necessary existence.

  • Citation: Caput II, n. 6, n. 13, n. 15, n. 17

    • What Hoenen refers to: Analysis of the sensory datum as ‘determinative’ rather than ‘motive’ of judgment; virtual judgments; and the material and formal nexus (chs. III–IV).

    • How it supports the text: Solves the Problem of Necessity: the sensory phantasm determines the occasion of judgment, but the intellect itself is the active motive force perceiving formal necessity.

  • Citation: Appendix, n. 1, n. 25, n. 26, n. 27, n. 29, n. 30

    • What Hoenen refers to: The Cogito as immediate judgment (ch. XII); comparison with Franz Brentano (ch. II, § 4); definition of realism (pp. 190–194); and determination of the agent intellect by accepted data (pp. 25–26).

    • How it supports the text: Underpins the metaphysics of the Appendix: validates the concept of being (ratio essendi) and proves that the second operation of the intellect directly grasps the existential act of realism.

• Filosofia della natura inorganica (Philosophy of Inorganic Nature) 1949

  Notes: Italian treatise on inorganic natural philosophy (Brescia: Morcelliana).

  • Citation: Caput VI, n. 2 & Appendix, n. 16, n. 17 (pp. 110, 112, 220)

    • What Hoenen refers to: The philosophical definition of physical space, coordinate bodies, and the critique of relativistic positivism.

    • How it supports the text: Reinforces the realistic interpretation of coordinate frames and spatial extension in physical nature.

• De origine formae materialis (On the Origin of Material Form) 1951 (2nd ed.)

  Notes: Latin textbook compiling classical Thomistic texts on the eduction of material forms (Rome: Gregorianum).

  • Citation: Appendix, n. 22

    • What Hoenen refers to: The twofold function of material form: quidditative (constituting essence) and existential (determining the mode of being).

    • How it supports the text: Demonstrates that form does not merely define what a thing is, but determines how it exercises its existential act of being.

• Articles in Gregorianum and Commemorative Volumes (Scholarly Papers in Gregorianum and Festschriften) 1933–1953

  Notes: Major peer-reviewed research papers in Gregorianum and international philosophy congresses.

  • Citation: Praefatio, n. 1 (Gregorianum 1938, 1939, 1943, 1951)

    • What Hoenen refers to: The four-part series ‘De philosophia scholastica cognitionis geometricae’ and the reply to Freudenthal.

    • How it supports the text: The primary journal papers that formed the initial drafts of the chapters of De Noetica Geometriae.

  • Citation: Caput II, n. 1 & Caput I, n. 3 (Gregorianum 1933, pp. 153–184)

    • What Hoenen refers to: ‘De origine primorum principiorum scientiae’ (On the Origin of the First Principles of Science).

    • How it supports the text: Presents the foundational epistemology of how first principles are abstracted intuitively from sensible phantasms.

  • Citation: Caput II, n. 12, n. 14 & Appendix, n. 1 (Cartesio, 1937, pp. 457–471)

    • What Hoenen refers to: ‘Le « cogito ergo sum » comme intuition et comme mouvement de la pensée’.

    • How it supports the text: Establishes the Thomistic interpretation of the Cartesian Cogito as an intellectual intuition of existential actuality.

  • Citation: Caput II, n. 8 & Caput V, n. 11 (10th Phil. Congress 1948; Gregorianum 1950, pp. 126–132)

    • What Hoenen refers to: ‘Pour une philosophie de la connaissance de l’étendue physique’.

    • How it supports the text: Addresses how the intellect abstracts exact mathematical continuity from physical perceptions of extended bodies.

  • Citation: Caput V, n. 2 (Gregorianum 1951, pp. 263–268)

    • What Hoenen refers to: ‘De fontibus geometriae: Responsio ad Cl. H. Freudenthal’.

    • How it supports the text: Direct defense of the intuitive origin of geometry against Hans Freudenthal’s formalist critique.

  • Citation: Caput VI, n. 5 & Appendix, n. 14, n. 32 (Gregorianum 1953, pp. 1–31)

    • What Hoenen refers to: ‘De duratione successiva et de quaestionibus connexis’.

    • How it supports the text: Establishes that successive duration is fluent existential extension (esse fluens), distinct from permanent geometric extension.

  • Citation: Caput VI, n. 7 & Caput VII, n. 3 (Gregorianum 1953, pp. 603–639)

    • What Hoenen refers to: ‘De connexionibus necessariis inter actus existentiales’.

    • How it supports the text: The extensive study that was directly incorporated with additions as the Appendix of this monograph.

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Vallée-Poussin, Charles-Jean de la (1866 – 1962)

• Recherches analytiques sur la théorie des nombres premiers (Analytical Researches on the Theory of Prime Numbers) 1896

  Notes: Landmark memoir proving the Prime Number Theorem; published in Annales de la Société scientifique de Bruxelles.

  • Citation: Caput V, n. 8

    • What Hoenen refers to: G. H. Hardy’s reference to de la Vallée-Poussin’s proof of the Prime Number Theorem.

    • How it supports the text: Contrasts a long deductive proof (which compels belief through an intricate chain of syllogisms) with immediate intuitive arithmetic truths (such as 2 + 2 = 4).

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Hadamard, Jacques (1865 – 1963)

• La géométrie (in Encyclopédie Française, Tome I) (Geometry (in French Encyclopedia, Vol. I: Mental Tools)) 1937

  Notes: Survey essay on geometric intuition and displacement in Encyclopédie Française (Section I-52-10).

  • Citation: Caput IV, n. 11 & n. 22

    • What Hoenen refers to: Hadamard’s observation that geometric displacement and motion cannot be eradicated from spatial understanding.

    • How it supports the text: Confirms from a leading French mathematician that geometric congruence is fundamentally tied to spatial displacement.

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Russell, Bertrand (1872 – 1970)

• The Principles of Mathematics (The Principles of Mathematics) 1903 (2nd ed. 1937)

  Notes: Russell’s foundational logicist masterpiece (London: Allen & Unwin).

  • Citation: Caput IV, n. 3, n. 4, n. 5 (nos. 390 ff., pp. 405–407)

    • What Hoenen refers to: Russell’s scathing critique of Euclid’s superposition proof: ‘It has no logical validity, and strikes every intelligent child as a juggle… to speak of motion implies that our triangles are not spatial but material.’

    • How it supports the text: Hoenen uses Russell’s objection to make a crucial distinction: physical superposition of material bodies indeed cannot prove geometric equality, but mental translation of figures within intelligible matter (materia intelligibilis) is an authentic intellectual operation that grounds congruence.

  • Citation: Caput IV, n. 28 (pp. 404 ff.)

    • What Hoenen refers to: Russell’s critique of empiricism: ‘There is no evidence whatever that the circles which we are supposed to observe are true circles… geometry is not based upon observation of empirical shapes.’

    • How it supports the text: Enlists Russell’s logicist critique to demolish sensory empiricism: mathematical figures are never found in physical sensation, confirming their status as abstract intelligible entities.

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Maier, Anneliese (1905 – 1971)

• An der Grenze von Scholastik und Naturwissenschaft (On the Border of Scholasticism and Natural Science) 1943

  Notes: Groundbreaking historical study of late medieval natural philosophy and 14th-century Parisian and Oxonian physics (Rome: Edizioni di Storia e Letteratura).

  • Citation: Appendix, n. 33 (pp. 312 ff.)

    • What Hoenen refers to: Maier’s historical documentation of Nicole Oresme’s doctrine of configurations of qualities and motions.

    • How it supports the text: Hoenen utilizes Maier’s scholarly findings while offering a philosophical correction: Maier treated Oresme’s doctrine primarily as a mathematical precursor to coordinate geometry, whereas Hoenen shows that it represents a profound metaphysical insight into the qualitative configuration of fluent existential acts (esse fluens).

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Ross, Sir William David (1877 – 1971)

• Aristotle’s Metaphysics, Physics, and Analytics (Oxford Critical Editions and Commentaries on Aristotle) 1924, 1936, 1949

  Notes: The premier 20th-century critical Greek texts and English commentaries on Aristotle’s works (Oxford: Clarendon Press).

  • Citation: Caput I, n. 3 & Caput IV, n. 7

    • What Hoenen refers to: Ross’s general monograph Aristotle (pp. 38–41, 54, 217) and critical edition of Physics IV.

    • How it supports the text: Standard scholarly authority for peripatetic abstraction and natural philosophy.

  • Citation: Appendix, n. 3, n. 5, n. 13 (Metaphysics II, pp. 245, 264, 401)

    • What Hoenen refers to: Ross’s recension and English translation of Metaphysics IX, 3 (‘The word actuality, which we connect with complete reality…’), and his textual reading of ἔστιν (estin, with paroxytone accent indicating existence).

    • How it supports the text: Decisive philological support: reading ἔστιν confirms that Aristotle is treating actual existence in time rather than a mere copula, proving that the mover must already actually exist.

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Stammler, Gerhard (1898 – 1977)

• Begriff, Urteil, Schluss (Concept, Judgment, Inference) 1928

  Notes: Epistemological investigation into the foundations of logic and judgment (Halle: Niemeyer).

  • Citation: Caput V, n. 7 (pp. 229, 245)

    • What Hoenen refers to: Stammler’s demonstration that inference requires a synthetic apprehension of the relation between concepts.

    • How it supports the text: Confirms that logical inference cannot be reduced to mechanical algorithmic manipulation without intellectual insight.

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Gilson, Étienne (1884 – 1978)

• L’être et l’essence & Being and Some Philosophers (Being and Essence (1948) & Being and Some Philosophers (1949)) 1948, 1949

  Notes: Gilson’s landmark treatises establishing existential Thomism and distinguishing it from essentialism (Paris: Vrin / Toronto: PIMS).

  • Citation: Appendix, § 7 and n. 23, n. 27 (L’être et l’essence, p. 248)

    • What Hoenen refers to: Gilson’s thesis opposing ‘existential’ and ‘essential’ metaphysics, and his claim that esse itself is not conceptualizable (‘un centre d’obscurité qu’il nous faut traverser pour atteindre l’existence’).

    • How it supports the text: Hoenen’s pivotal critique: he praises Gilson for recovering the Thomistic primacy of esse, but demonstrates that Gilson goes too far in declaring esse completely unconceptualizable. Hoenen shows from St. Thomas that the intellect forms a true apprehensive concept of being (ratio essendi) following judgment, preserving the harmony between essence and existence.

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Hasse, Helmut (1898 – 1979)

• Die Grundlagenkrisis der griechischen Mathematik (The Foundational Crisis of Greek Mathematics) 1928

  Notes: Historical-mathematical paper co-authored with Heinrich Scholz in Kantstudien (Vol. 33, pp. 4–34).

  • Citation: Caput I, n. 6

    • What Hoenen refers to: Hasse and Scholz’s analysis of the crisis caused by the discovery of incommensurable magnitudes in Pythagorean geometry.

    • How it supports the text: Documents that the crisis of foundations in Greek geometry was resolved geometrically by Eudoxus rather than arithmetically.

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Lonergan, Bernard, S.J. (1904 – 1984)

• The Concept of Verbum in the Writings of St. Thomas Aquinas (The Concept of Verbum in the Writings of St. Thomas Aquinas) 1946–1947

  Notes: Five seminal articles in Theological Studies (Vols. 7 & 8); later published as Verbum: Word and Idea in Aquinas (Notre Dame, 1967).

  • Citation: Appendix, § 7 and n. 24 (Theological Studies 1946, pp. 349–392; 1947, pp. 35–79, 404–444; esp. Vol. I, p. 353)

    • What Hoenen refers to: Lonergan’s demonstration that for St. Thomas, the term conceptio / conceptus is used not only for the definition produced in the first operation, but also for the interior word (verbum mentis) produced in judgment (the second operation).

    • How it supports the text: Provides decisive contemporary Thomistic backing for Hoenen’s thesis against Gilson: St. Thomas explicitly recognizes that judgment produces an interior conception, proving that esse is conceptualizable in the second operation of the intellect.

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Freudenthal, Hans (1905 – 1990)

• De fontibus geometriae (On the Sources of Geometry) 1951

  Notes: Critical Latin article published in Gregorianum (Vol. 32, pp. 252–262) disputing Hoenen’s scholastic philosophy of geometry.

  • Citation: Praefatio, n. 1 & Caput V, n. 2

    • What Hoenen refers to: The debate between Freudenthal and Hoenen regarding whether axiomatic geometry can be constituted independently of intuitive abstraction.

    • How it supports the text: Serves as the vital contemporary sparring partner: Freudenthal defended modern formal axiomatics, prompting Hoenen to elaborate his ‘semi-axiomatic’ analysis and prove that axioms cannot function without semantic reference to intelligible matter.

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Alvarez Laso, José, C.M.F. (1910 – 1993)

• La Filosofía de las Matemáticas en Santo Tomás (The Philosophy of Mathematics in Saint Thomas) 1952

  Notes: Monograph on Thomistic philosophy of mathematics (Mexico: Editorial Jus, pp. 2–6).

  • Citation: Caput VII, n. 1

    • What Hoenen refers to: Alvarez Laso’s exposition of Aquinas’s commentary on Posterior Analytics I, 1 regarding triangle as subject vs. attribute.

    • How it supports the text: Presents scholarly confirmation that St. Thomas’s noetics of mathematics hinges on the intellectual activity that constructs figures in intelligible matter.

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Summary Statistics

• Total Authors Catalogued: 64 authors spanning 24 centuries (c. 355 BC to 1993 AD).

• Chronological Span:

  • Ancient Greek & Classical Foundations (c. 355 BC – 560 AD): Eudoxus, Plato, Aristotle, Euclid, Alexander of Aphrodisias, Themistius, Proclus, Boethius, Simplicius.

  • Medieval Scholastic Synthesis (1274 – 1382 AD): St. Thomas Aquinas, St. Albert the Great, Nicole Oresme.

  • Early Modern Epistemology (1650 – 1804 AD): Descartes, Locke, Leibniz, Kant.

  • 19th-Century Mathematics, Logic, & Philology (1864 – 1928 AD): Waitz, Möbius, Trendelenburg, Mill, Bonitz, Weierstrass, Hamelin, Poincaré, Couturat, Dedekind, Brentano, Cantor, Wellstein, Killing, Baeumker, Riehl, Klein, Hessenberg, Carteron, Burnet.

  • 20th-Century Axiomatics, Physics, & Neo-Scholasticism (1930 – 1993 AD): Study, Pasch, Voss, Peano, Meyerson, Pirotta, Heath, Hausdorff, Hilbert, Enriques, Hardy, Geyser, Einstein, Weyl, Scholz, Amaldi, Hoenen, de la Vallée-Poussin, Hadamard, Russell, Maier, Ross, Stammler, Gilson, Hasse, Lonergan, Freudenthal, Alvarez Laso.

• Footnote Census: All 130 footnotes across the 9 sections of De Noetica Geometriae are cross-referenced to their respective author, work, and textual function.

Additional Cited Authors & Commentators

John Philoponus (c. 490 – c. 570 AD)

• In Aristotelis Analytica Posteriora & Physica Commentaria (*Commentaries on Aristotle’s Posterior Analytics and Physics*) c. 520–530 AD

  Notes: Alexandrian Neoplatonic and Christian commentator on Aristotle; edited by M. Wallies and H. Vitelli in Commentaria in Aristotelem Graeca (CAG Vols. XIII, XVI–XVII, Berlin: Reimer, 1887–1909).

  • What Hoenen refers to: Philoponus’s commentary on Aristotle’s Posterior Analytics and Physics regarding the nature of mathematical abstraction, spatial extension, and the pre-existence of moving causes.

  • How it supports the text: Provides late-antique Greek textual witness confirming the peripatetic understanding of mathematical abstraction and existential prerequisites of motion.

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Newton, Sir Isaac (1642 – 1727)

• Philosophiae Naturalis Principia Mathematica & Tractatus de Quadratura Curvarum (*Mathematical Principles of Natural Philosophy & Treatise on the Quadrature of Curves*) 1687, 1704

  Notes: Foundational treatises of classical mechanics and the method of fluxions, conceiving continuous geometric magnitudes as generated by continuous motion.

  • What Hoenen refers to: Newton’s cinematic generation of lines and surfaces by the local motion of points and lines (fluxions), following the classical geometric tradition commented on by St. Thomas in In I De Caelo.

  • How it supports the text: Demonstrates that the generation of continuous figures through imagined motion in intelligible extension belongs to the perennial mainstream of mathematical thought.

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Hegel, Georg Wilhelm Friedrich (1770 – 1831)

• Wissenschaft der Logik & Enzyklopädie der philosophischen Wissenschaften (*Science of Logic & Encyclopedia of the Philosophical Sciences*) 1812–1817

  Notes: Foundational treatises of German absolute idealism analyzing quantity, the mathematical infinite, and the philosophy of nature.

  • What Hoenen refers to: Hegel’s critique of the Cartesian Cogito and his dialectical treatment of quantity and mathematical demonstration.

  • How it supports the text: Contrasted by Hoenen with the realistic Aristotelian-Thomistic intuition of existential acts and continuous quantity.

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Gauss, Carl Friedrich (1777 – 1855)

• Disquisitiones generales circa superficies curvas & Briefwechsel (*General Investigations of Curved Surfaces & Mathematical Correspondence*) 1827

  Notes: Landmark differential-geometric memoir and foundational correspondence on non-Euclidean geometry and the concept of number.

  • What Hoenen refers to: Gauss’s investigations into intrinsic surface curvature, non-Euclidean parallel theory, and the foundations of number and continuous magnitude (as analyzed by Gerhard Stammler).

  • How it supports the text: Marks the historical turning point toward non-Euclidean geometry and the modern critical examination of Euclid’s Fifth Postulate.

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Helmholtz, Hermann von (1821 – 1894)

• Über die Tatsachen, die der Geometrie zum Grunde liegen (*On the Facts Underlying Geometry*) 1868

  Notes: Seminal memoir in Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen grounding Riemannian metrics in the free mobility of rigid bodies.

  • What Hoenen refers to: Helmholtz’s analysis of congruence and spatial measurement through the transport and superposition of rigid bodies.

  • How it supports the text: Hoenen examines Helmholtz’s empiricist appeal to physical rigid bodies to distinguish physical mechanics from the pure intellectual translation of figures in intelligible matter.

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Christ, Wilhelm von (1831 – 1906)

• Aristotelis Metaphysica (*Critical Teubner Edition of Aristotle’s Metaphysics*) 1886 (rev. ed. 1895)

  Notes: Standard critical Greek edition of Aristotle’s Metaphysics published by B. G. Teubner (Leipzig).

  • What Hoenen refers to: Christ’s critical apparatus and textual readings in Metaphysics V and IX alongside Bonitz and Ross.

  • How it supports the text: Provides philological verification of Aristotle’s Greek text on actuality (energeia) and metaphysical diversity.

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Mercier, Désiré-Joseph, Cardinal (1851 – 1926)

• Critériologie générale ou Théorie générale de la certitude (*General Criteriology or General Theory of Certitude*) 1899 (8th ed. 1923)

  Notes: Foundational Louvain neo-scholastic treatise on epistemology and the criterion of truth (Louvain: Institut Supérieur de Philosophie).

  • What Hoenen refers to: Mercier’s Louvain criteriology separating purely ideal judgments (connecting abstract concepts) from existential judgments of reality.

  • How it supports the text: Critiqued in the Appendix: Hoenen shows that necessary synthetic connections exist not only between abstract quidditative concepts, but directly between concrete existential acts.

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Hölder, Otto (1859 – 1937)

• Die mathematische Methode & Anschauung und Denken in der Geometrie (*The Mathematical Method & Intuition and Thought in Geometry*) 1900, 1924

  Notes: Influential epistemological studies on geometric intuition, axiomatic deduction, and measurement (Leipzig: Teubner).

  • What Hoenen refers to: Hölder’s analysis of the interplay between spatial intuition (Anschauung) and deductive logical thought in geometric proofs.

  • How it supports the text: Supports Hoenen’s thesis that deductive chains in geometry continuously rely on the structural intuition of spatial configurations.

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Brunschvicg, Léon (1869 – 1944)

• Les étapes de la philosophie mathématique (*The Stages of Mathematical Philosophy*) 1912

  Notes: Comprehensive historical and critical study of the philosophy of mathematics from Greek antiquity to modern logicism (Paris: Alcan).

  • What Hoenen refers to: Brunschvicg’s historical interpretation of Aristotelian syllogistics, Cartesian analytic geometry, and modern mathematical idealism.

  • How it supports the text: Engaged by Hoenen to defend the authentic realist meaning of Aristotelian and Thomistic mathematical abstraction against idealist reconstructions.

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Taylor, Alfred Edward (1869 – 1945)

• A Commentary on Plato’s Timaeus & Plato: The Man and His Work (*Commentary on Plato’s Timaeus & Plato*) 1928

  Notes: Monumental British philological and philosophical studies on Plato and Pythagorean mathematics (Oxford: Clarendon Press).

  • What Hoenen refers to: Taylor’s analysis of Platonic mathematical intermediates, Pythagorean geometry, and the divided line in the Republic.

  • How it supports the text: Clarifies the historical divergence between Platonic mathematical idealism and Aristotle’s doctrine of abstraction from sensible phantasms.

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Reichenbach, Hans (1891 – 1953)

• Philosophie der Raum-Zeit-Lehre (*The Philosophy of Space and Time*) 1928

  Notes: Logical empiricist treatise on the epistemology of geometry, coordinative definitions, and general relativity (Berlin: Walter de Gruyter).

  • What Hoenen refers to: Reichenbach’s positivist critique of spatial intuition and his claim that geometric visualization is merely subjective and conventional.

  • How it supports the text: Refuted by Hoenen through the distinction between variable sensory images and the universal formal relations intuited by the intellect in intelligible matter.

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Becker, Oskar (1889 – 1964)

• Mathematische Existenz & Grundlagen der Mathematik in geschichtlicher Entwicklung (*Mathematical Existence & Foundations of Mathematics in Historical Development*) 1927, 1954

  Notes: Phenomenological and historical investigations into Greek mathematics, Eudoxian proportion theory, and intuitionism (Halle: Niemeyer).

  • What Hoenen refers to: Becker’s studies on the ontology of mathematical objects and the Greek theory of incommensurables.

  • How it supports the text: Corroborates the irreducible role of intuitive construction in both ancient Greek geometry and modern foundational research.

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Brouwer, L. E. J. (1881 – 1966)

• Intuitionism and Formalism & Begründung der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten (*Foundational Papers on Mathematical Intuitionism*) 1912, 1918

  Notes: Seminal Dutch mathematical treatises founding intuitionistic mathematics in opposition to Hilbertian formalism.

  • What Hoenen refers to: Brouwer’s insistence on primordial mathematical intuition over uninterpreted formalist symbol manipulation.

  • How it supports the text: Hoenen notes that while modern intuitionism rightly rejects empty formalism, it must be grounded in realistic Thomistic abstraction of continuous extension rather than Kantian subjective time-intuition.

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Complete Concordance of Cited Loci (412 Citations)

Every inline :cite: reference across the Latin and English editions of De Noetica Geometriae resolves directly to its canonical locus entry below. Each entry links upward to the author’s main bibliographic commentary, to their biographical entry in the Index Nominum, and directly back (LA · EN) to every occurrence in the text.

Albert the Great, St., O.P. (c. 1200 – 1280) — Commentaria in Analytica Priora

• Apparatus Links: Author Commentary · Biographical Entry (Albert the Great, St., O.P.)

• I.1.9 (albertus:anal-prior:I.1.9) — « S. ALBERTUS MAGNUS, Anal. Prior. I tract. I cap. 9 (in ed. Jammy, 1651, I pag. 298 a) » — Caput IV: n. 29 (LA · EN)

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Alexander of Aphrodisias (fl. c. 200 AD) — In Aristotelis Metaphysica Commentaria

• Apparatus Links: Author Commentary · Biographical Entry (Alexander of Aphrodisias)

• 573.16 (alexander:met:573.16) — « i. h. l. » — Appendix: § 1. (LA · EN), n. 4 (LA · EN)

• 573.24 (alexander:met:573.24) — « loc. cit. lin. 24 sqq. » — Appendix: § 1. (LA · EN), n. 4 (LA · EN)

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Alvarez Laso, José, C.M.F. (1910 – 1993) — La Filosofía de las Matemáticas en Santo Tomás (1952)

• Apparatus Links: Author Commentary · Biographical Entry (José Alvarez Laso, C.M.F.)

• filosofia:2-6 (alvarez-laso:1952:filosofia:2-6) — « La Filosofia de las Matemáticas en Santo Tomás Mexico, 1952, pagg. 2-6 » — Caput VII: n. 1 (LA · EN)

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Amaldi, Ugo (1875 – 1957) — Sui concetti di retta e di piano (Questioni riguardanti le matematiche elementari)

• Apparatus Links: Author Commentary · Biographical Entry (Ugo Amaldi)

• **** (amaldi:concetti-retta-piano) — « U. Amaldi « sui concetti di retta e di piano » » — Caput IV: n. 15 (LA · EN)

• p46 (amaldi:concetti-retta-piano:p46) — « op. cit. § 3 pag. 46 » — Caput IV: n. 20 (LA · EN)

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Aristotle (384 – 322 BC) — Analytica Posteriora (Posterior Analytics)

• Apparatus Links: Author Commentary · Biographical Entry (Aristotle)

• **** (aristotle:anal-post) — « Posteriorum » — Caput IV: Animadversiones praeviae. (LA · EN) | Caput V: 2. (LA · EN)

• 1.12:77b30 (aristotle:anal-post:1.12:77b30) — « Anal. Post. I 12 77 b 30-33 » — Caput V: C) (LA · EN)

• 2.19 (aristotle:anal-post:2.19) — « Analyticorum » — Caput V: C) (LA · EN)

• I.1.71a14 (aristotle:anal-post:I.1.71a14) — « Anal. Post. I cap. 1, 71 a 14 sq. » — Caput VII: n. 1 (LA · EN)

• I.10 (aristotle:anal-post:I.10) — « 10 » — Caput IV: § 7. (LA · EN)

• I.10.76b23 (aristotle:anal-post:I.10.76b23) — « 76 b 23 » — Caput IV: § 7. (LA · EN)

• I.10.76b27 (aristotle:anal-post:I.10.76b27) — « 76 b 27 » — Caput IV: § 7. (LA · EN)

• I.10.76b28 (aristotle:anal-post:I.10.76b28) — « ibid. 28 » — Caput IV: § 7. (LA · EN)

• I.12.77b30 (aristotle:anal-post:I.12.77b30) — « Anal. Post. I 12, 77 b 30 » — Caput I: § 2. (LA · EN)

• I.2 (aristotle:anal-post:I.2) — « Anal. Post. I cap. 2 » — Caput I: § 1. (LA · EN) | Caput IV: § 7. (LA · EN)

• I.31 (aristotle:anal-post:I.31) — « Analyt. Post. I 31 » — Caput III: A) (LA · EN)

• I.31.87b35 (aristotle:anal-post:I.31.87b35) — « 87 b 35 » — Caput III: n. 1 (LA · EN)

• II.19 (aristotle:anal-post:II.19) — « Analyticorum Posteriorum » — Caput II: 2. (LA · EN), 2. (LA · EN) | Caput VII: 1. (LA · EN), 2. (LA · EN)

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Aristotle (384 – 322 BC) — Analytica Priora (Prior Analytics)

• Apparatus Links: Author Commentary · Biographical Entry (Aristotle)

• 1.4.25b37 (aristotle:anal-prior:1.4.25b37) — « Anal. Priora I, 4 25 b 37-39 » — Caput V: n. 3 (LA · EN)

• 46a17 (aristotle:anal-prior:46a17) — « (Anal. Pri. I, 30, 46 a 17) » — Caput II: 5. (LA · EN), 2. (LA · EN)

• I.4.25b37 (aristotle:anal-prior:I.4.25b37) — « Anal. Prior. I 4, 25 b 37-39 » — Caput IV: n. 30 (LA · EN)

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Aristotle (384 – 322 BC) — De Anima (On the Soul)

• Apparatus Links: Author Commentary · Biographical Entry (Aristotle)

• 431b2 (aristotle:de-anima:431b2) — « (De Anim. III 7, 431 b 2) » — Caput II: 4. (LA · EN), 2. (LA · EN)

• III.6.431a14 (aristotle:de-anima:III.6.431a14) — « De Anim. III 6, 431 a. 140 » — Caput III: A) (LA · EN)

• III.7.431a14-b2 (aristotle:de-anima:III.7.431a14-b2) — « ibid. III 7, 431a 14-16 ; 431 b 2 » — Caput I: § 2. (LA · EN)

• III.8.432a5-9 (aristotle:de-anima:III.8.432a5-9) — « De An. III 8, 432 a 5-9 » — Caput I: § 2. (LA · EN)

• b1-c4-409a (aristotle:de-anima:b1-c4-409a) — « De Anim. I 4, 409 a 3-5 » — Caput IV: § 2. (LA · EN)

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Aristotle (384 – 322 BC) — Ethica Nicomachea (Nicomachean Ethics)

• Apparatus Links: Author Commentary · Biographical Entry (Aristotle)

• IX.9.1170a31 (aristotle:eth-nic:IX.9.1170a31) — « Eth. Nic. (IX 9 1170 a 31 sqq.) » — Appendix: § 1. (LA · EN)

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Aristotle (384 – 322 BC) — Metaphysica (Metaphysics)

• Apparatus Links: Author Commentary · Biographical Entry (Aristotle)

• 1.1 (aristotle:met:1.1) — « Met. I, 1 » — Appendix: § 7. (LA · EN)

• 1018a9 (aristotle:met:1018a9) — « V 9, 1018 a 9-14 » — Appendix: § 7. (LA · EN)

• 1051a32 (aristotle:met:1051a32) — « Met. IX 1051 a 32 » — Appendix: § 5. (LA · EN)

• 1054b23 (aristotle:met:1054b23) — « Met. X 3, 1054 b 23-26 » — Appendix: § 7. (LA · EN)

• I.1 (aristotle:met:I.1) — « Metaphysicorum » — Caput VII: 2. (LA · EN)

• III.2.997b35 (aristotle:met:III.2.997b35) — « Met. III 2, 997 b 35 » — Caput III: n. 1 (LA · EN)

• IX.3.1047a30 (aristotle:met:IX.3.1047a30) — « loc. cit. 1047 a 30-b 2 » — Appendix: § 1. (LA · EN)

• IX.3.1047a32 (aristotle:met:IX.3.1047a32) — « 1047 a 32 » — Appendix: § 1. (LA · EN)

• IX.6.1048b18 (aristotle:met:IX.6.1048b18) — « Met. IX 6 1048 b 18 sq. » — Appendix: § 4. (LA · EN)

• IX.8.1049b18 (aristotle:met:IX.8.1049b18) — « Met. IX c. 8, inde a lin. 1049 b 18 » — Appendix: § 3. (LA · EN)

• IX.8.1049b23 (aristotle:met:IX.8.1049b23) — « 1049 b 23-27 » — Appendix: § 3. (LA · EN)

• IX.8.1050a21 (aristotle:met:IX.8.1050a21) — « Met. IX 8 1050 a 21-23 » — Appendix: n. 5 (LA · EN)

• IX.8.1050a7 (aristotle:met:IX.8.1050a7) — « Met. (IX 1050 a 7-9) » — Appendix: § 4. (LA · EN)

• IX.9.1051a32 (aristotle:met:IX.9.1051a32) — « Met. IX 9, 1051 a 32 » — Caput VII: § 1. (LA · EN)

• X.1.1052b20 (aristotle:met:X.1.1052b20) — « 1052 b 20 » — Caput VI: 1. (LA · EN)

• X.1.1053a25 (aristotle:met:X.1.1053a25) — « Met. X c. 1 1053 a 25 » — Caput VI: 1. (LA · EN)

• XI.11 (aristotle:met:XI.11) — « Met. XI c. 11 » — Appendix: § 1. (LA · EN)

• XI.11.1067b29 (aristotle:met:XI.11.1067b29) — « 1067b 29 sq. » — Appendix: § 1. (LA · EN)

• XI.3 (aristotle:met:XI.3) — « Met. XI c. 3 » — Appendix: § 1. (LA · EN)

• XII.6.1071b28 (aristotle:met:XII.6.1071b28) — « libro XII metaphysicorum (cap. 6 1071 b 28) » — Appendix: § 3. (LA · EN)

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Aristotle (384 – 322 BC) — De Interpretatione (Peri Hermeneias)

• Apparatus Links: Author Commentary · Biographical Entry (Aristotle)

• 1 (aristotle:periherm:1) — « « principio Perihermeneias » » — Appendix: § 7. (LA · EN)

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Aristotle (384 – 322 BC) — Physica (Physics)

• Apparatus Links: Author Commentary · Biographical Entry (Aristotle)

• 219a11 (aristotle:phys:219a11) — « Phys. IV 11 219 a 11 » — Appendix: Additiones (LA · EN)

• 251a10 (aristotle:phys:251a10) — « lin. 10 » — Appendix: § 6. (LA · EN)

• 251a8 (aristotle:phys:251a8) — « Phys. VIII cap. 1, 251 a 8-16 » — Appendix: § 6. (LA · EN)

• 3 (aristotle:phys:3) — « lib. III » — Appendix: § 6. (LA · EN)

• 4.1 (aristotle:phys:4.1) — « Phys. IV c. 1-2 » — Caput V: 2. (LA · EN)

• III (aristotle:phys:III) — « libro III » — Appendix: § 1. (LA · EN)

• IV.1 (aristotle:phys:IV.1) — « Phys. IV 1, 4 » — Caput VI: B) (LA · EN) | Appendix: § 2. (LA · EN)

• IV.1.208b1 (aristotle:phys:IV.1.208b1) — « c. 1 208 b 1 » — Appendix: § 2. (LA · EN)

• IV.2.209b24 (aristotle:phys:IV.2.209b24) — « c. 2 (209 b 24-30) » — Appendix: § 2. (LA · EN)

• IV.2.210a12 (aristotle:phys:IV.2.210a12) — « 210 a 12 » — Appendix: § 2. (LA · EN)

• IV.4.211a12 (aristotle:phys:IV.4.211a12) — « c. 4, 211 a 12-17 » — Appendix: § 2. (LA · EN)

• IV.5.212a31 (aristotle:phys:IV.5.212a31) — « c. 5, 212 a 31 sq. » — Appendix: § 2. (LA · EN)

• IV.5.212b14 (aristotle:phys:IV.5.212b14) — « ibid. 212 b 14 sqq. » — Appendix: § 2. (LA · EN)

• V (aristotle:phys:V) — « Phys. V » — Appendix: § 1. (LA · EN)

• V.1 (aristotle:phys:V.1) — « Phys. V 1 » — Appendix: § 1. (LA · EN)

• V.1.225a25 (aristotle:phys:V.1.225a25) — « Phys. V 1 (225 a 25 sqq.) » — Appendix: § 1. (LA · EN), § 1. (LA · EN), § 1. (LA · EN)

• V.1.225a31 (aristotle:phys:V.1.225a31) — « 225 a 31-32 » — Appendix: § 1. (LA · EN)

• VIII.1 (aristotle:phys:VIII.1) — « Phys. VIII c. 1. » — Appendix: § 1. (LA · EN)

• VIII.7.261a13 (aristotle:phys:VIII.7.261a13) — « Phys. VIII 7, 261 a 13 » — Appendix: § 4. (LA · EN)

• b4-c11-219a (aristotle:phys:b4-c11-219a) — « Phys. IV 11, 219 a 10-18 » — Caput IV: § 2. (LA · EN)

• b4-c11-219b (aristotle:phys:b4-c11-219b) — « ibid. b 15 sqq. et cap. 12, 220 b 24 sqq. » — Caput IV: n. 7 (LA · EN)

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Baeumker, Clemens (1853 – 1924) — Das Problem der Materie in der griechischen Philosophie (1890)

• Apparatus Links: Author Commentary · Biographical Entry (Clemens Baeumker)

• p422 (baeumker:1890:p422) — « Cl. BAEUMKER, Das Problem der Materie in der Griechischen Philosophie pagg. 422 sqq. » — Caput III: n. 2 (LA · EN)

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Becker, Oskar (1889 – 1964) — Beiträge zur phänomenologischen Begründung der Geometrie (1923)

• Apparatus Links: Author Commentary · Biographical Entry (Oskar Becker)

• p90 (becker:1923:p90) — « Beiträge zur phaenomenologischen Begründung der Geometrie und ihrer physikalischen Anwendungen (in Jahrbuch fur Philos. und phaenomenologische Forschung VI 1923) pagg. 90-93 » — Caput III: C) (LA · EN)

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Bonitz, Hermann (1814 – 1888) — Aristotelis Metaphysica: Commentarius (1848–1849)

• Apparatus Links: Author Commentary · Biographical Entry (Hermann Bonitz)

• II.387 (bonitz:met:II.387) — « in comm. in locum ex Met. IX 3) II pag. 387 » — Appendix: n. 5 (LA · EN)

• II.401 (bonitz:met:II.401) — « commentario (II pag. 401) » — Appendix: n. 13 (LA · EN)

• IX.8.1049b27 (bonitz:met:IX.8.1049b27) — « Bonitz » — Appendix: n. 13 (LA · EN)

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Brouwer, L. E. J. (1881 – 1966) — Over de grondslagen der wiskunde (1907)

• Apparatus Links: Author Commentary · Biographical Entry (Luitzen Egbertus Jan Brouwer)

• p8 (brouwer:1907:p8) — « Over de grondslagen der wiskunde 1907 pag. 8 » — Caput III: B) (LA · EN)

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Brunschvicg, Léon (1869 – 1944) — Les étapes de la philosophie mathématique (1912)

• Apparatus Links: Author Commentary · Biographical Entry (Léon Brunschvicg)

• p338 (brunschvicg:etapes:p338) — « Les étapes de la philosophie mathématique pag. 338 » — Caput III: C) (LA · EN)

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Carteron, Henri (1891 – 1927) — Aristote: Physique (ed. Budé, 1926)

• Apparatus Links: Author Commentary · Biographical Entry (Henri Carteron)

• I.134 (carteron:phys:I.134) — « Aristote Physique ed. Budé I pag. 134 » — Appendix: n. 10 (LA · EN)

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Christ, Wilhelm von (1831 – 1906) — Aristotelis Metaphysica (ed. Teubner)

• Apparatus Links: Author Commentary · Biographical Entry (Wilhelm von Christ)

• IX.8.1049b27 (christ:met:IX.8.1049b27) — « Christ (Teubner) » — Appendix: n. 13 (LA · EN)

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Couturat, Louis (1868 – 1914) — La philosophie des mathématiques de Kant (Revue de Métaphysique et de Morale, 1904)

• Apparatus Links: Author Commentary · Biographical Entry (Louis Couturat)

• 339 (couturat:1904:339) — « Rev. Mét. et Mor. 1904 pag. 339 » — Caput II: n. 3 (LA · EN)

• p810 (couturat:1904:p810) — « COUTURAT, Revue de Métaph. et de Morale 1904 pag. 810 » — Caput III: n. 8 (LA · EN)

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Descartes, René (1596 – 1650) — Œuvres de Descartes (ed. Adam & Tannery)

• Apparatus Links: Author Commentary · Biographical Entry (René Descartes)

• 5.164 (descartes:at:5.164) — « colloquio cum Burman Oeuvres ed. Adam et Tannery V pag. 164 » — Appendix: Additiones (LA · EN)

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Descartes, René (1596 – 1650) — Œuvres de Descartes (ed. Adam & Tannery)

• Apparatus Links: Author Commentary · Biographical Entry (René Descartes)

• VI.32 (descartes:discours:VI.32) — « Discours de la Méthode (A. et T. VI 32, 17) » — Appendix: § 1. (LA · EN)

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Descartes, René (1596 – 1650) — Œuvres de Descartes (ed. Adam & Tannery)

• Apparatus Links: Author Commentary · Biographical Entry (René Descartes)

• II.64 (descartes:principia:II.64) — « Principia Philos. II n. 64 » — Caput II: n. 7 (LA · EN)

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Descartes, René (1596 – 1650) — Œuvres de Descartes (ed. Adam & Tannery)

• Apparatus Links: Author Commentary · Biographical Entry (René Descartes)

• VII.140 (descartes:resp2:VII.140) — « In secundis responsionibus (ed. Adam et Tannery VII) 140, 18-141, 2 » — Appendix: n. 2 (LA · EN)

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Einstein, Albert (1879 – 1955) — Geometrie und Erfahrung (1921)

• Apparatus Links: Author Commentary · Biographical Entry (Albert Einstein)

• forum (einstein:1930:forum) — « Forum I 1930 pag. 173 » — Caput VI: n. 3 (LA · EN)

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Einstein, Albert (1879 – 1955) — Geometrie und Erfahrung (1921)

• Apparatus Links: Author Commentary · Biographical Entry (Albert Einstein)

• 1921 (einstein:geometrie-und-erfahrung:1921) — « A. EINSTEIN, Geometrie und Erfahrung, Berlin 1921 » — Caput I: n. 4 (LA · EN)

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Enriques, Federigo (1871 – 1946) — Questioni riguardanti le matematiche elementari

• Apparatus Links: Author Commentary · Biographical Entry (Federigo Enriques)

• **** (enriques:quaestioni) — « Quaestioni riguardanti le matematiche elementari » — Caput IV: n. 15 (LA · EN)

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Euclid of Alexandria (fl. c. 300 BC) — Elementa (The Thirteen Books of the Elements)

• Apparatus Links: Author Commentary · Biographical Entry (Euclid of Alexandria)

• 1.def.4 (euclid:elements:1.def.4) — « Def. IV Elementa ed. Heiberg I pagg. 2 et 3 » — Caput IV: 4. (LA · EN)

• 1.def.7 (euclid:elements:1.def.7) — « Def. VII, in ed. Heiberg pagg. 2 et 3 » — Caput IV: 5. (LA · EN)

• I.1 (euclid:elements:I.1) — « Heiberg (pagg. 11 sq.) » — Caput IV: n. 28 (LA · EN)

• I.1,I.46 (euclid:elements:I.1,I.46) — « I 1 et 46 » — Caput VII: § 1. (LA · EN)

• I.29 (euclid:elements:I.29) — « 29 » — Caput IV: 9. (LA · EN)

• I.30 (euclid:elements:I.30) — « propositione 30 » — Caput IV: 9. (LA · EN)

• I.cn.1 (euclid:elements:I.cn.1) — « κ. ἔνν. 1 » — Caput IV: n. 28 (LA · EN)

• I.def.23 (euclid:elements:I.def.23) — « Def. XXIII » — Caput IV: 9. (LA · EN)

• I.post1-3 (euclid:elements:I.post1-3) — « Heiberg » — Caput VII: § 1. (LA · EN)

• V (euclid:elements:V) — « Elementorum Euclidis » — Caput I: § 4. (LA · EN)

• b1-p4 (euclid:elements:b1-p4) — « ed. Heiberg pagg. 16-19 » — Caput IV: § 2. (LA · EN)

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Freudenthal, Hans (1905 – 1990) — De fontibus geometriae in intuitione et abstractione quaerendis (Gregorianum, 1951)

• Apparatus Links: Author Commentary · Biographical Entry (Hans Freudenthal)

• p425 (freudenthal:1951:p425) — « H. FR., De fontibus geometriae in intuitione et abstractione quaerendis pagg. 425-433 » — Caput V: n. 2 (LA · EN)

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Gauss, Carl Friedrich (1777 – 1855) — Werke

• Apparatus Links: Author Commentary · Biographical Entry (Carl Friedrich Gauss)

• IV.p365 (gauss:werke:IV.p365) — « Gauss’ Werke IV S. 365 » — Caput IV: n. 19 (LA · EN)

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Geyser, Joseph (1869 – 1948) — Die Erkenntnistheorie des Aristoteles (1917)

• Apparatus Links: Author Commentary · Biographical Entry (Joseph Geyser)

• VI-XII (geyser:erkenntnistheorie:VI-XII) — « GEYSER, Die Erkenntnistheorie des Aristoteles, cap. VI et XII » — Caput I: n. 3 (LA · EN)

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Gilson, Étienne (1884 – 1978) — L’être et l’essence (1948) / Being and Some Philosophers (1949)

• Apparatus Links: Author Commentary · Biographical Entry (Étienne Gilson)

• **** (gilson:1948) — « E. Gilson, L’être et l’essence, Paris Vrin 1948 » — Appendix: n. 23 (LA · EN)

• 248 (gilson:1948:248) — « L’être et l’essence pag. 248 » — Appendix: § 7. (LA · EN)

• 284 (gilson:1948:284) — « Gilson, L’être et l’essence, pag. 284 » — Appendix: § 7. (LA · EN)

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Gilson, Étienne (1884 – 1978) — L’être et l’essence (1948) / Being and Some Philosophers (1949)

• Apparatus Links: Author Commentary · Biographical Entry (Étienne Gilson)

• **** (gilson:1949) — « Being and some philosophers Toronto 1949 » — Appendix: n. 23 (LA · EN)

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Hadamard, Jacques (1865 – 1963) — Encyclopédie Française, Tome I: L’Outillage Mental (1937)

• Apparatus Links: Author Commentary · Biographical Entry (Jacques Hadamard)

• 1-52-7 (hadamard:1937:1-52-7) — « J. HADAMARD, Encycl. Franç I (1937) I-52-7 » — Caput IV: n. 22 (LA · EN)

• i-52-10 (hadamard:1937:i-52-10) — « Encyclopédie Française I 1937, I-52-10 » — Caput IV: n. 11 (LA · EN)

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Hamelin, Octave (1856 – 1907) — Le Système d’Aristote (1920)

• Apparatus Links: Author Commentary · Biographical Entry (Octave Hamelin)

• 258 (hamelin:systeme-aristote:258) — « O. HAMELIN, Le Système d’Aristote, pagg. 258 sq., 234 sq. » — Caput I: n. 3 (LA · EN)

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Hardy, Godfrey Harold (1877 – 1947) — Mathematical Proof (Mind, 1929)

• Apparatus Links: Author Commentary · Biographical Entry (Godfrey Harold Hardy)

• p12 (hardy:1929:p12) — « Mind 38 pag. 12 » — Caput V: n. 10 (LA · EN)

• p17 (hardy:1929:p17) — « G. H. HARDY, Mathematical proof in periodico Mind 38 (1929) pag. 17 » — Caput V: n. 8 (LA · EN)

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Hasse, Helmut & Scholz, Heinrich — Die Grundlagenkrisis der griechischen Mathematik (Kant-Studien, 1928)

• Apparatus Links: Author Commentary

• 4-34 (hasse-scholz:1928:4-34) — « H. HASSE und H. SCHOLZ, Die Grundlagenkrisis der Griechischen Mathematik in Kantstudien (1928) pagg. 4-34 » — Caput I: n. 6 (LA · EN)

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Hausdorff, Felix (1868 – 1942) — Das Raumproblem (Annalen der Naturphilosophie, 1904)

• Apparatus Links: Author Commentary · Biographical Entry (Felix Hausdorff)

• p3 (hausdorff:1904:p3) — « F. HAUSDORF, Das Raumproblem in Annalen der Naturphilosophie III (1904) pag. 3 » — Caput IV: n. 21 (LA · EN)

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Heath, Sir Thomas Little (1861 – 1940) — The Thirteen Books of Euclid’s Elements / A History of Greek Mathematics

• Apparatus Links: Author Commentary · Biographical Entry (Sir Thomas Little Heath)

• v1:p335 (heath:1921:v1:p335) — « Th. Heath in suo opere famoso A History of Greek Mathematics, Oxford 1921, I pagg. 335 sqq. » — Caput V: n. 1 (LA · EN)

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Hegel, Georg Wilhelm Friedrich (1770 – 1831) — Wissenschaft der Logik (Werke, 1834)

• Apparatus Links: Author Commentary · Biographical Entry (Georg Wilhelm Friedrich Hegel)

• p142 (hegel:1834:p142) — « HEGEL , Wissenschaft der Logik II I k. 3 Anmerkung. Werke (ed. 1834) pagg. 142 sq. » — Caput V: n. 5 (LA · EN)

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Helmholtz, Hermann von (1821 – 1894) — Schriften zur Erkenntnistheorie (ed. Hertz & Schlick, 1921)

• Apparatus Links: Author Commentary · Biographical Entry (Hermann von Helmholtz)

• p141 (helmholtz:1921:p141) — « Schriften zur Erkenntnistheorie ed. P. Hertz et M. Schlick 1921 pag. 141 » — Caput IV: n. 13 (LA · EN)

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Hessenberg, Gerhard (1874 – 1925) — Kritik und System in Mathematik und Philosophie (1908)

• Apparatus Links: Author Commentary · Biographical Entry (Gerhard Hessenberg)

• 102-106 (hessenberg:1908:102-106) — « Kritik und System in Mathematik und Philosophie in Abhandlungen der Friesschen Schule II pagg. 102-106 » — Caput II: n. 10 (LA · EN)

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Hilbert, David (1862 – 1943) — Grundlagen der Geometrie (Foundations of Geometry, 1899 / 1930)

• Apparatus Links: Author Commentary · Biographical Entry (David Hilbert)

• **** (hilbert:grundlagen) — « Grundlagen der Geometrie » — Caput IV: n. 1 (LA · EN), n. 11 (LA · EN)

• 1930 (hilbert:grundlagen:1930) — « Die Grundlagen der Geometrie » — Caput I: § 6. (LA · EN)

• 1930:p2 (hilbert:grundlagen:1930:p2) — « Op. cit. ed. 7 (1930) pag. 2 » — Caput I: n. 14 (LA · EN)

• p5 (hilbert:grundlagen:p5) — « in ed. 7 pag. 5-8 » — Caput V: A) (LA · EN)

• p8 (hilbert:grundlagen:p8) — « HILBERT, Grundlagen der Geometrie ed. 7 (1930) pag. 8 » — Caput V: n. 9 (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — De origine primorum principiorum scientiae (Gregorianum XIV, 1933, pp. 153–184)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• 153-184 (hoenen:1933:153-184) — « De origine primorum principiorum scientiae in Gregorianum XIV (1933) pagg. 153-184 » — Caput I: n. 3 (LA · EN) | Caput II: 5. (LA · EN), 2. (LA · EN), 2. (LA · EN), n. 1 (LA · EN)

• 159 (hoenen:1933:159) — « De origine principiorum pag. 159 » — Caput II: 2. (LA · EN)

• 21 (hoenen:1933:21) — « R. a. J. pag. 21 » — Appendix: n. 30 (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — Le « Cogito ergo sum » comme intuition et comme mouvement de la pensée (1937)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• **** (hoenen:1937) — « Le « cogito ergo sum » comme intuition et comme mouvement de la pensée in fasciculo commemorativo periodici Riv. di Filos. Neoscolastica 1937 Cartesio nel terzo centenario del « Discorso del Metodo » pagg. 457-471 » — Appendix: n. 1 (LA · EN)

• 457-471 (hoenen:1937:457-471) — « Cartesio (1937) cui titulus Le « Cogito ergo sum » comme intuition et comme mouvement de la pensée pagg. 457-471 » — Caput II: n. 12 (LA · EN), n. 14 (LA · EN)

• 470 (hoenen:1937:470) — « Le cogito ergo sum etc. pagg. 470 sqq. » — Appendix: § 1. (LA · EN)

• acta:367-374 (hoenen:1937:acta:367-374) — « Acta 2ⁱ congr. thom. Romae 1937 pagg. 367-374 » — Caput VI: A) (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — De philosophia scholastica cognitionis geometricae (Gregorianum XIX, 1938, pp. 498–514)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• 498-514 (hoenen:1938:498-514) — « 1938, 498-514, De philosophia scholastica cognitionis geometricae » — Praefatio: n. 1 (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — De problemate necessitatis geometricae (Gregorianum XX, 1939, pp. 19–54)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• 19-54 (hoenen:1939:19-54) — « 1939, 19-54, De problemate necessitatis geometricae » — Praefatio: n. 1 (LA · EN)

• 321-350 (hoenen:1939:321-350) — « 1939, 321-350, De problemate exactitudinis geometricae I » — Praefatio: n. 1 (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — De Noetica Geometriae / La théorie du jugement / Cosmologia

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• 171-234 (hoenen:1943:171-234) — « 1943, 171-234, De problemate exactitudinis geometricae II » — Praefatio: n. 1 (LA · EN)

• p234 (hoenen:1943:p234) — « anni 1943 pag. 234 » — Praefatio: PRAEFATIO (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — Recherches de logique formelle (Rome: Gregorian University, 1947)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• **** (hoenen:1947) — « Recherches de logique formelle » — Caput V: B) (LA · EN), n. 3 (LA · EN)

• greg:171 (hoenen:1947:greg:171) — « Gregor. 1947 pag. 171 » — Appendix: n. 33 (LA · EN)

• p315 (hoenen:1947:p315) — « op. cit. pag. 315 » — Caput V: B) (LA · EN)

• reality:269 (hoenen:1947:reality:269) — « R. a. J. pagg. 269 resp. 223 » — Caput VII: 3. (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — Gregorianum XXIX (1948), pp. 295–303

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• gregorianum (hoenen:1948:gregorianum) — « Gregorianum, 1948, pagg. 295-303 » — Caput VI: n. 4 (LA · EN)

• gregorianum:295-303 (hoenen:1948:gregorianum:295-303) — « Gregor., 1948, pagg. 295-303 » — Caput VII: 3. (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — Pour une philosophie de la connaissance de l’étendu physique (Gregorianum XXX, 1949)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• **** (hoenen:1949) — « Filosofia della natura inorganica » — Caput V: 2. (LA · EN)

• 193-203 (hoenen:1949:193-203) — « Pour une philosophie de la connaissance de l’étendu physique in Gregorianum 1949 pagg. 193-203 » — Caput II: n. 8 (LA · EN)

• 195 (hoenen:1949:195) — « Gregorianum XXX, 1949, pagg. 195 sq. » — Appendix: § 1. (LA · EN)

• filosofia-natura (hoenen:1949:filosofia-natura) — « Filosof. della nat. inorg. pagg. 131 sqq. » — Caput VI: B) (LA · EN), B) (LA · EN), B) (LA · EN), n. 2 (LA · EN), n. 3 (LA · EN)

• filosofia-natura:214-222 (hoenen:1949:filosofia-natura:214-222) — « Filos. d. nat. inorg. pagg. 214-222 » — Caput VI: A) (LA · EN)

• filosofia-natura:221 (hoenen:1949:filosofia-natura:221) — « Filos. d. nat. inorg. pagg. 221 sq. » — Caput VI: C) (LA · EN)

• filosofia-natura:p207 (hoenen:1949:filosofia-natura:p207) — « Filosofia della natura inorganica, Brescia, 1949, p. 207 » — Caput VI: 1. (LA · EN)

• gregorianum (hoenen:1949:gregorianum) — « Gregor. 1949, 448 » — Caput VI: 1. (LA · EN)

• p193 (hoenen:1949:p193) — « Pour une philosophie de la connaissance de l’étendue physique in Gregorianum, 1949, pagg. 193-203 » — Caput V: n. 11 (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — De noetica geometriae (Gregorianum XXXII, 1951, pp. 434–452)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• 434-452 (hoenen:1951:434-452) — « Gregorianum, 1951, 434-452, De noetica geometriae, responsum ad animadversiones clmi. H. Freudenthal » — Praefatio: n. 1 (LA · EN)

• gregorianum (hoenen:1951:gregorianum) — « Gregorianum, 1951, pagg. 432 et 451 » — Caput VI: § 1. (LA · EN), B) (LA · EN), 1. (LA · EN)

• origine (hoenen:1951:origine) — « De origine formae materialis (ed. 2 1951) » — Appendix: n. 22 (LA · EN)

• p434 (hoenen:1951:p434) — « Gregor. 1951, pag. 434 sq. » — Caput V: 2. (LA · EN), n. 2 (LA · EN)

• p449 (hoenen:1951:p449) — « Gregorianum 1951 pagg. 449 sq. » — Caput IV: n. 6 (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — De connexionibus necessariis inter actus existentiales (Gregorianum XXXIV, 1953)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• **** (hoenen:1953) — « Th. du Jug. passim » — Appendix: § 1. (LA · EN)

• 148 (hoenen:1953:148) — « Op. cit. pagg. 148, 267-268, resp. 145, 264-265, resp. 132, 224-225 » — Appendix: § 7. (LA · EN)

• 193 (hoenen:1953:193) — « Th. du J. pagg. 193-194 in ed. 2 pagg. 190-191, in vers. Anglic. pagg. 165-166 » — Appendix: n. 27 (LA · EN)

• 243 (hoenen:1953:243) — « Th. du Jug. Ch. VII § 7 ed. 1 pagg. 246 sq., ed. 2, 243 sq. » — Appendix: § 3. (LA · EN)

• 25 (hoenen:1953:25) — « Th. du J. pagg. 25-26 » — Appendix: n. 30 (LA · EN)

• 300 (hoenen:1953:300) — « op. cit. pag. 300, ed. 2 pag. 296, in vers. Angl. pag. 251 » — Appendix: § 5. (LA · EN), § 5. (LA · EN)

• 314 (hoenen:1953:314) — « Th. du Jug. Ch. XI § 3 n. 3 B ed. 1 pagg. 318-324, 2 pagg. 314-318 » — Appendix: § 3. (LA · EN)

• 603-639 (hoenen:1953:603-639) — « De connexionibus necessariis inter actus existentiales ex periodico Gregorianum 1953 pag. 603-639 » — Praefatio: PRAEFATIO (LA · EN)

• 69 (hoenen:1953:69) — « Th. du J. pagg. 69-70, resp. 68-69, resp. 61-62 » — Appendix: § 7. (LA · EN)

• ch10.5 (hoenen:1953:ch10.5) — « Théorie du Jugement (Ch. X » — Appendix: § 5. (LA · EN), § 5. (LA · EN)

• ch12 (hoenen:1953:ch12) — « id. cap. in Th. du. J. » — Appendix: § 1. (LA · EN), § 7. (LA · EN), n. 1 (LA · EN)

• ch2 (hoenen:1953:ch2) — « Th. du J. Ch. II » — Appendix: n. 25 (LA · EN)

• ch2.4 (hoenen:1953:ch2.4) — « Th. du J. Ch. II § 4 » — Appendix: n. 26 (LA · EN)

• ch2.5 (hoenen:1953:ch2.5) — « Op. cit. Ch. II § 5 » — Appendix: § 7. (LA · EN)

• ch3 (hoenen:1953:ch3) — « Th. du Jug. ch. III et IV » — Appendix: § 1. (LA · EN), n. 29 (LA · EN)

• ch9 (hoenen:1953:ch9) — « cap. IX-XI » — Appendix: § 7. (LA · EN)

• greg:1 (hoenen:1953:greg:1) — « Gregor. (1953 pagg. 1-31) articulum nostrum De duratione successiva et de quaestionibus connexis » — Appendix: n. 32 (LA · EN)

• greg:3 (hoenen:1953:greg:3) — « artic. supra cit. ex Gregor. 1953 » — Appendix: § 5. (LA · EN), n. 14 (LA · EN)

• greg:6 (hoenen:1953:greg:6) — « Gregorianum, 1953, pagg. 6-16 » — Appendix: § 5. (LA · EN), § 5. (LA · EN)

• gregorianum (hoenen:1953:gregorianum) — « Gregorianum, 1953, pag. 3-31 De duratione successiva et de quaestionibus connexis » — Caput VI: n. 5 (LA · EN) | Caput VII: A) (LA · EN)

• gregorianum:23 (hoenen:1953:gregorianum:23) — « Gregorianum 1953 pag. 23 » — Caput VII: 3. (LA · EN)

• gregorianum:3-19 (hoenen:1953:gregorianum:3-19) — « Gregorianum, 1953, pagg. 3-19 » — Caput VII: 3. (LA · EN)

• gregorianum:30 (hoenen:1953:gregorianum:30) — « Gregorianum 1953 pag. 30 » — Caput VII: 3. (LA · EN)

• gregorianum:603-631 (hoenen:1953:gregorianum:603-631) — « De connexionibus necessariis inter actus existentiales in Gregorianum 1953 pagg. 603-31, praesertim pagg. 635, 637 » — Caput VI: n. 7 (LA · EN)

• gregorianum:603-639 (hoenen:1953:gregorianum:603-639) — « Gregorianum 1953 pagg. 603-639 De connexionibus necessariis inter actus existentiales » — Caput VII: n. 3 (LA · EN)

• gregorianum:617-619 (hoenen:1953:gregorianum:617-619) — « Gregor. 1953 pagg. 617-619 » — Caput VII: 2. (LA · EN)

• p3 (hoenen:1953:p3) — « Gregorianum 1953 pagg. 3-31 » — Caput V: 2. (LA · EN)

• theorie (hoenen:1953:theorie) — « Théorie du Jugement, Introduction, ch. V § 2, § 5, in ed. 2 pagg. 1, 164, 188 » — Caput VI: B) (LA · EN)

• theorie:1,25,164,188,227 (hoenen:1953:theorie:1,25,164,188,227) — « Th. du Jug. Introduction, I § 3 B, V § 3, 5, VII § 5, in ed. 2 pagg. 1, 25, 164, 188, 227 » — Caput VII: 1. (LA · EN)

• theorie:214 (hoenen:1953:theorie:214) — « Th. du Jug. Ch. VII § 1 ed. 2 pagg. 214 sq. » — Caput VII: 2. (LA · EN)

• theorie:319 (hoenen:1953:theorie:319) — « Th. du Jug. Ch. XI § 3 B et Ch. IX § 3 in ed. 2 pagg. 319 resp. 262-263 ; ed. 1 323 resp. 265-266 » — Caput VII: 3. (LA · EN)

• theorie:IV.4,X.1 (hoenen:1953:theorie:IV.4,X.1) — « Th. du Jug. Ch. IV § 4 et Ch. X § 1 » — Caput VII: 3. (LA · EN)

• theorie:VII (hoenen:1953:theorie:VII) — « Th. du Jug. Ch. VII » — Caput VII: 2. (LA · EN)

• theorie:VIII-XII (hoenen:1953:theorie:VIII-XII) — « Théorie du Jugement Ch. VIII-XII » — Caput VII: 3. (LA · EN), 3. (LA · EN)

• theorie:X.4-5 (hoenen:1953:theorie:X.4-5) — « Th. du Jug. ch. X § 4, 5 » — Caput VII: § 1. (LA · EN)

• theorie:X.5 (hoenen:1953:theorie:X.5) — « Th. du Jug. ch. X § 5 » — Caput VII: A) (LA · EN), 3. (LA · EN)

• theorie:XI.3 (hoenen:1953:theorie:XI.3) — « Th. du Jug. Ch. XI § 3 n. 2 et n. 3 C et D » — Caput VII: 3. (LA · EN), 3. (LA · EN)

• theorie:ch4.5 (hoenen:1953:theorie:ch4.5) — « Théorie du Jugement Ch. IV § 5 » — Caput VI: C) (LA · EN)

• theorie:ch6.5 (hoenen:1953:theorie:ch6.5) — « Théorie du Jugement ch. VI praesertim § 5 » — Caput VI: C) (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — De Noetica Geometriae: Origine Theoriae Cognitionis (1954 — Internal Cross-Reference)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• 253 (hoenen:1954:253) — « pag. 253 » — Appendix: § 7. (LA · EN)

• 256 (hoenen:1954:256) — « casum supra expositum de « extensione » pagg. 256 sq. » — Appendix: n. 28 (LA · EN)

• VI.2B (hoenen:1954:VI.2B) — « VI § 2 B pag. 206 sq. » — Appendix: n. 17 (LA · EN)

• VI.3 (hoenen:1954:VI.3) — « VI § 3 » — Appendix: n. 32 (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — Cosmologia (4th ed., Rome: Gregorian University, 1949)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• **** (hoenen:cosmologia) — « Cosmologia » — Caput II: 2. (LA · EN) | Caput V: 2. (LA · EN) | Caput VI: B) (LA · EN), 1. (LA · EN), 1. (LA · EN), n. 2 (LA · EN), n. 3 (LA · EN) | Caput VII: B) (LA · EN), 3. (LA · EN), 3. (LA · EN), 3. (LA · EN) | Appendix: § 5. (LA · EN), § 7. (LA · EN)

• 152 (hoenen:cosmologia:152) — « Cosmologiam nn. 152, 161 not. XIII « de motu ut est actus existentialis » in ed. 4 pagg. 527-530 » — Appendix: n. 20 (LA · EN)

• 155 (hoenen:cosmologia:155) — « Cosmologia late exponebamus de motu et eius propriis, praesertim, pro hac nostra consideratione, ea quae habentur nn. 155, 158, 161, et notas XIII (de motu ut est actus existentialis) et XIV (de motu, actu imperfecto, et operatione, actu perfecto) in ed. 4 pagg. 527-532 » — Appendix: § 4. (LA · EN)

• 158 (hoenen:cosmologia:158) — « Cosmologia n. 158 » — Appendix: § 4. (LA · EN)

• 161 (hoenen:cosmologia:161) — « Cosmologiam nostram ed. 4 n. 161 sq. et not. XIII (pagg. 527-530) » — Appendix: n. 6 (LA · EN)

• 257-259,532-541 (hoenen:cosmologia:257-259,532-541) — « Cosmologia ed. 4 pagg. 257-259 ; 532-541 » — Caput VI: A) (LA · EN)

• 259 (hoenen:cosmologia:259) — « Cosmolog. ed. 4 pag. 259 » — Caput VI: C) (LA · EN)

• 40 (hoenen:cosmologia:40) — « Cosmologia ed. 4 pag. 40 nota » — Appendix: n. 19 (LA · EN)

• 471-474 (hoenen:cosmologia:471-474) — « Cosmologiam ed. 4, pagg. 471-474 » — Caput II: 4. (LA · EN)

• 516 (hoenen:cosmologia:516) — « passum cit. ex Cosmologia ed. 4. pagg. 516 sq. » — Appendix: Additiones (LA · EN), n. 33 (LA · EN)

• 58 (hoenen:cosmologia:58) — « Cosmologia nn. 58-63 de praedicamento « ubi », insuper n. 45, et notam De ubi in ed. 4 pagg. 467-470 » — Appendix: n. 15 (LA · EN)

• 98 (hoenen:cosmologia:98) — « Cosmologiam nn. 98-99, 214-218 » — Appendix: n. 22 (LA · EN)

• ed4 (hoenen:cosmologia:ed4) — « Cosmologiam nostram ed. 4 not. III pagg. 446-455, VII pagg. 471-482 » — Caput I: n. 5 (LA · EN)

• not.XI (hoenen:cosmologia:not.XI) — « Cosmologiam ed. 4 Not. XI de sensibilibus propriis » — Caput VII: 3. (LA · EN)

• not4 (hoenen:cosmologia:not4) — « Notam IV de relativitate motus n. 1 ed. 4 pag. 456, notam XV de principio neo-positivismi n. 3 pag. 538 » — Appendix: n. 16 (LA · EN)

• not6 (hoenen:cosmologia:not6) — « Cosmologia in nota VI de « ubi » ed. 4 pag. 468 » — Appendix: n. 17 (LA · EN)

• not8 (hoenen:cosmologia:not8) — « Cosmologia ed. 4 not. VIII de historia notionis impetus, not. IX De Principio inertiae » — Appendix: § 3. (LA · EN)

• nota-XI (hoenen:cosmologia:nota-XI) — « ed. 4 notam XI » — Caput VII: B) (LA · EN)

• p184-203 (hoenen:cosmologia:p184-203) — « Cosmologia cap. « De mensura qualitatum » ed. 4 pagg. 184-203, 518-527 » — Caput IV: § 2. (LA · EN)

• p27-40 (hoenen:cosmologia:p27-40) — « Cosmologiam ed. 4 pagg. 27-40 » — Caput III: A) (LA · EN)

• p35-36 (hoenen:cosmologia:p35-36) — « Cosmologia nostra, ed. 4, pagg. 35-36 » — Caput III: A) (LA · EN)

• p40 (hoenen:cosmologia:p40) — « Cosmologiam ed. 4 pag. 40 » — Caput V: B) (LA · EN)

• p438 (hoenen:cosmologia:p438) — « Cosmologia in nota « de ente extenso physico » in ed. 4 pagg. 438-445 » — Caput V: n. 12 (LA · EN)

• p451 (hoenen:cosmologia:p451) — « Cosmologiam pag. 451 » — Caput III: B) (LA · EN)

• p451-455 (hoenen:cosmologia:p451-455) — « Cosmologia ed. 4 pagg. 451-455 » — Caput III: B) (LA · EN)

• p455 (hoenen:cosmologia:p455) — « Cosmologiam nostram pag. 455 » — Caput IV: n. 19 (LA · EN)

• p471-474 (hoenen:cosmologia:p471-474) — « Cosmologiam ed. 4 pagg. 471-474 » — Caput III: 3. (LA · EN)

• p508 (hoenen:cosmologia:p508) — « Cosmologia ed. 4 notam de sensibilibus propriis pagg. 508-517 » — Caput VI: n. 4 (LA · EN)

• p593 (hoenen:cosmologia:p593) — « Cosmologiam ed. 4 pagg. 593 sq. » — Caput VI: C) (LA · EN)

• ubi (hoenen:cosmologia:ubi) — « Cosmologiam de « ubi » » — Appendix: n. 12 (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — Filosofia della natura inorganica (Milan, 1949)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• 110 (hoenen:filosofia-natura:110) — « Filosofia della natura inorganica pag. 110 » — Appendix: n. 17 (LA · EN)

• 112 (hoenen:filosofia-natura:112) — « Filosofia della natura inorganica pagg. 112, 220 » — Appendix: n. 16 (LA · EN)

• 126 (hoenen:filosofia-natura:126) — « Filosofia della natura inorganica pagg. 126-128 » — Appendix: § 3. (LA · EN)

• p176-186 (hoenen:filosofia-natura:p176-186) — « Filosofia della natura inorganica pagg. 176-186 » — Caput IV: § 2. (LA · EN)

• p57-72 (hoenen:filosofia-natura:p57-72) — « Filosofia della natura inorganica, pagg. 57-72 » — Caput III: A) (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — Reality and Judgment According to St. Thomas (Chicago: Regnery, 1952)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• **** (hoenen:reality-and-judgment) — « Reality and Judgment according to St. Thomas Chicago 1952 » — Appendix: n. 1 (LA · EN)

• 1952 (hoenen:reality-and-judgment:1952) — « Reality and Judgment according to St. Thomas, Chicago 1952 » — Praefatio: n. 2 (LA · EN)

• 206 (hoenen:reality-and-judgment:206) — « R. a. J. pagg. 206 sq. » — Appendix: § 3. (LA · EN)

• 264 (hoenen:reality-and-judgment:264) — « R. a. J. pagg. 264-269 » — Appendix: § 3. (LA · EN)

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Hoenen, Petrus Hubertus Jacobus, S.J. (1880 – 1961) — La théorie du jugement d’après St. Thomas d’Aquin (1946; 2nd ed. 1953)

• Apparatus Links: Author Commentary · Biographical Entry (Petrus Hubertus Jacobus Hoenen, S.J.)

• **** (hoenen:theorie-du-jugement) — « La théorie du jugement d’après St. Thomas d’Aquin » — Caput I: n. 2 (LA · EN) | Caput II: n. 15 (LA · EN)

• 1946 (hoenen:theorie-du-jugement:1946) — « La théorie du jugement d’après St. Thomas d’Aquin ed. 1, 1946 » — Praefatio: n. 2 (LA · EN)

• 1953 (hoenen:theorie-du-jugement:1953) — « ed. 2 aucta et emendata, 1953 » — Praefatio: n. 2 (LA · EN) | Caput I: n. 3 (LA · EN)

• 214-215 (hoenen:theorie-du-jugement:214-215) — « Théorie du Jugement ed. 2 pagg. 214-215 » — Caput II: n. 11 (LA · EN)

• 25 (hoenen:theorie-du-jugement:25) — « Théorie du Jug. ed. 2 pagg. 25 sqq. » — Caput II: n. 13 (LA · EN)

• c10 (hoenen:theorie-du-jugement:c10) — « Théorie du Jug. ch. X » — Caput V: B) (LA · EN)

• c1:s4 (hoenen:theorie-du-jugement:c1:s4) — « Théorie du Jug. Ch. I § 4 pagg. 37 sq. » — Caput V: C) (LA · EN)

• c2:s5 (hoenen:theorie-du-jugement:c2:s5) — « Théorie du Jugement Ch. II § 5 » — Caput V: n. 4 (LA · EN)

• c4:s3 (hoenen:theorie-du-jugement:c4:s3) — « Théorie du jugem. ch. IV § 3 B » — Caput V: 1. (LA · EN)

• c6:s4 (hoenen:theorie-du-jugement:c6:s4) — « Théorie du Jugem. Ch. VI § 4 » — Caput V: B) (LA · EN), B) (LA · EN)

• c7:s6 (hoenen:theorie-du-jugement:c7:s6) — « Théorie du jugement, Ch. VII § 6 » — Caput V: § 2. (LA · EN), 1. (LA · EN)

• c9:s3 (hoenen:theorie-du-jugement:c9:s3) — « Théorie du Jug. Ch. IX § 3 » — Caput V: A) (LA · EN)

• ch3-4 (hoenen:theorie-du-jugement:ch3-4) — « Théor. du jug. ch. III et IV » — Caput II: n. 17 (LA · EN)

• p242 (hoenen:theorie-du-jugement:p242) — « Théorie du Jug. 2ª ed. pagg. 242-244 » — Caput V: Nota de neo-positivismo. (LA · EN)

• p32 (hoenen:theorie-du-jugement:p32) — « Th. d. J. pag. 32 » — Caput III: n. 11 (LA · EN)

• passim (hoenen:theorie-du-jugement:passim) — « La théorie du jugement d’après St. Thomas d’Aquin passim » — Caput II: n. 6 (LA · EN)

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Hölder, Otto (1859 – 1937) — Die mathematische Methode (1924)

• Apparatus Links: Author Commentary · Biographical Entry (Otto Hölder)

• p120 (hoelder:1924:p120) — « Hölder, Die mathematische Methode pag. 120 » — Caput IV: n. 19 (LA · EN)

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John Philoponus (c. 490 – c. 570 AD) — In Aristotelis Physicorum Libros Commentaria (ed. Vitelli)

• Apparatus Links: Author Commentary · Biographical Entry (John Philoponus)

• 501.16 (philoponus:phys:501.16) — « i. h. l. ed. Vitelli 501, 16-19 » — Appendix: § 2. (LA · EN)

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Kant, Immanuel (1724 – 1804) — Kritik der reinen Vernunft (Critique of Pure Reason, 2nd ed. 1787)

• Apparatus Links: Author Commentary · Biographical Entry (Immanuel Kant)

• B14-15 (kant:krv:B14-15) — « Criticae rationis purae » — Caput II: 5. (LA · EN), n. 4 (LA · EN)

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Kant, Immanuel (1724 – 1804) — Prolegomena zu einer jeden künftigen Metaphysik (1783)

• Apparatus Links: Author Commentary · Biographical Entry (Immanuel Kant)

• 27 (kant:prolegomena:27) — « Prolegomena Vorrede et § 27 » — Appendix: § 2. (LA · EN)

• 2c.2 (kant:prolegomena:2c.2) — « Proleg. § 2 c n. 2 » — Caput II: n. 4 (LA · EN)

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Killing, Wilhelm (1847 – 1923) — Einführung in die Grundlagen der Geometrie (1893–1898)

• Apparatus Links: Author Commentary · Biographical Entry (Wilhelm Killing)

• **** (killing:1893) — « W. KILLING, Einführung in die Grundlagen der Geometrie, Münster I (1893) II (1898) » — Caput IV: n. 16 (LA · EN)

• I.p5 (killing:1893:I.p5) — « T. I § 3 pagg. 5 sqq. » — Caput IV: n. 16 (LA · EN), n. 17 (LA · EN)

• I.p6 (killing:1893:I.p6) — « loc. cit. pag. 6 » — Caput IV: n. 18 (LA · EN), n. 19 (LA · EN)

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Klein, Felix (1849 – 1925) — Anwendung der Differential- und Integralrechnung auf Geometrie: Eine Revision der Prinzipien (2nd ed. 1907)

• Apparatus Links: Author Commentary · Biographical Entry (Felix Klein)

• **** (klein:1907) — « Anwendung der Differential- und Integralrechnung. Eine Revision der Prinzipien » — Caput I: § 4. (LA · EN)

• p11 (klein:1907:p11) — « op. cit. pag. 11 » — Caput I: n. 8 (LA · EN)

• p39 (klein:1907:p39) — « Anwendung der Differential- und Integralrechnung (neuer Abdruck 1907) pagg. 39 sq., 51 sq., 78 sq., 83-102 » — Caput III: C) (LA · EN)

• p7 (klein:1907:p7) — « Op. cit. in ed. 2 (Leipzig 1907) pag. 7 » — Caput I: n. 7 (LA · EN)

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Klein, Felix (1849 – 1925) — Elementarmathematik vom höheren Standpunkte aus, Band II: Geometrie (3rd ed. 1925)

• Apparatus Links: Author Commentary · Biographical Entry (Felix Klein)

• II.p189 (klein:1925:II.p189) — « F. KLEIN, Elementarmathematik vom höheren Standpunkte aus (II ed. 3 1925) pagg. 189 sq. » — Caput IV: n. 23 (LA · EN)

• II.p192 (klein:1925:II.p192) — « op. cit. pagg. 192-194 » — Caput IV: n. 24 (LA · EN)

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Leibniz, Gottfried Wilhelm (1646 – 1716) — Nouveaux Essais sur l’entendement humain (1704)

• Apparatus Links: Author Commentary · Biographical Entry (Gottfried Wilhelm Leibniz)

• IV.7.10 (leibniz:nouveaux-essais:IV.7.10) — « Nouveaux Essais sur l’entendement L. IV Ch. VII § 10 » — Caput II: n. 2 (LA · EN)

• p458 (leibniz:nouveaux-essais:p458) — « Nouveaux Essais ap. Gerhardt V pagg. 458 sqq. » — Caput V: n. 5 (LA · EN)

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Locke, John (1632 – 1704) — An Essay Concerning Human Understanding (1690)

• Apparatus Links: Author Commentary · Biographical Entry (John Locke)

• b4:c17:s4 (locke:1690:b4:c17:s4) — « J. LOCKE, An essay concerning human understanding Bk. IV ch. 17 § 4 (in ed. Fraser II pagg. 390 sqq.) » — Caput V: n. 5 (LA · EN)

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Lonergan, Bernard, S.J. (1904 – 1984) — The Concept of Verbum in the Writings of St. Thomas Aquinas (1946–1949)

• Apparatus Links: Author Commentary · Biographical Entry (Bernard Lonergan, S.J.)

• 349 (lonergan:1946:349) — « P. B. Lonergan, The concept of « verbum » in the writings of St. Thomas Aquinas in Theological Studies 1946 pagg. 349-392, 1947 pagg. 35-79, 404-44 ; pro hoc puncto I pag. 353 » — Appendix: n. 24 (LA · EN)

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Maier, Anneliese (1905 – 1971) — An der Grenze von Scholastik und Naturwissenschaft (1943)

• Apparatus Links: Author Commentary · Biographical Entry (Anneliese Maier)

• 312 (maier:1943:312) — « Anneliese Maier, An der Grenze von Scholastik und Naturwissenschaft, 1943 pagg. 312 sqq. » — Appendix: n. 33 (LA · EN)

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Mercier, Désiré-Joseph, Cardinal (1851 – 1926) — Critériologie générale (8th ed., 1923)

• Apparatus Links: Author Commentary · Biographical Entry (Désiré-Joseph Cardinal Mercier)

• 118 (mercier:criteriologie:118) — « Critériologie n. 118 in ed. 8 pagg. 282-283 » — Caput II: B) (LA · EN)

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Meyerson, Émile (1859 – 1933) — Du cheminement de la pensée (1931)

• Apparatus Links: Author Commentary · Biographical Entry (Émile Meyerson)

• 391 (meyerson:1931:391) — « E. Meyerson, Du cheminement de la Pensée pag. 391 n. 232 » — Appendix: n. 7 (LA · EN)

• II.333-339 (meyerson:1931:II.333-339) — « Du cheminement de la pensée II pagg. 333-339, III 877-879 » — Caput II: 6. (LA · EN)

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Mill, John Stuart (1806 – 1873) — A System of Logic (5th ed., 1862)

• Apparatus Links: Author Commentary · Biographical Entry (John Stuart Mill)

• I.p255 (mill:1862:I.p255) — « J. STUART MILL, System of Logic I ed. 5 (1862) pag. 255 » — Caput III: n. 3 (LA · EN)

• I.p257 (mill:1862:I.p257) — « Ibid. pag. 257 » — Caput III: n. 4 (LA · EN)

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Newton, Sir Isaac (1642 – 1727) — Philosophiae Naturalis Principia Mathematica (1687)

• Apparatus Links: Author Commentary · Biographical Entry (Sir Isaac Newton)

• **** (newton:1687) — « Philosophiae naturalis principia mathematica » — Caput V: A) (LA · EN)

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Pasch, Moritz (1843 – 1930) — Vorlesungen über neuere Geometrie (1882; 2nd ed. 1926)

• Apparatus Links: Author Commentary · Biographical Entry (Moritz Pasch)

• **** (pasch:1882) — « Pasch (1882) » — Caput II: 4. (LA · EN)

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Pasch, Moritz (1843 – 1930) — Vorlesungen über neuere Geometrie (1882; 2nd ed. 1926)

• Apparatus Links: Author Commentary · Biographical Entry (Moritz Pasch)

• 20 (pasch:1926:20) — « Vorlesungen über neuere Geometrie » — Caput II: n. 9 (LA · EN)

• 5-8 (pasch:1926:5-8) — « pagg. 5-8, 19 sq. » — Caput II: n. 16 (LA · EN)

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Plato (428/427 – 348/347 BC) — Leges (The Laws)

• Apparatus Links: Author Commentary · Biographical Entry (Plato)

• 737e-738b (plato:leges:737e-738b) — « De Legibus (737 e - 738 b) » — Caput II: 1. (LA · EN)

• 738a (plato:leges:738a) — « (738 a) » — Caput II: 1. (LA · EN)

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Plato (428/427 – 348/347 BC) — Meno

• Apparatus Links: Author Commentary · Biographical Entry (Plato)

• 82b-85b (plato:meno:82b-85b) — « Meno 82b-85b » — Caput I: § 2. (LA · EN)

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Plato (428/427 – 348/347 BC) — Respublica (The Republic)

• Apparatus Links: Author Commentary · Biographical Entry (Plato)

• VI.510c (plato:rep:VI.510c) — « Rep. VI 510 c » — Caput I: § 1. (LA · EN)

• VII.532c (plato:rep:VII.532c) — « Rep. VII 532 c » — Caput I: § 1. (LA · EN)

• VII.533c (plato:rep:VII.533c) — « Rep. VII 533 c » — Caput I: § 1. (LA · EN)

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Poincaré, Henri (1854 – 1912) — Dernières Pensées (1913)

• Apparatus Links: Author Commentary · Biographical Entry (Henri Poincaré)

• **** (poincare:dernieres-pensees) — « Dernières Pensées » — Caput I: § 4. (LA · EN)

• p271 (poincare:dernieres-pensees:p271) — « ibid. pag. 271 » — Caput V: B) (LA · EN)

• p62 (poincare:dernieres-pensees:p62) — « POINCARÉ, Dernières Pensées pag. 62 » — Caput IV: n. 14 (LA · EN)

• p65 (poincare:dernieres-pensees:p65) — « Op. cit. pag. 65 » — Caput I: n. 11 (LA · EN), n. 12 (LA · EN)

• p93 (poincare:dernieres-pensees:p93) — « Dernières Pensées pagg. 93-95 » — Caput V: B) (LA · EN)

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Poincaré, Henri (1854 – 1912) — La Science et l’Hypothèse (1902)

• Apparatus Links: Author Commentary · Biographical Entry (Henri Poincaré)

• ch5.2.p92 (poincare:science-hypothese:ch5.2.p92) — « La science et l’hypothèse ch. V n. 2 pag. 92 » — Caput VI: A. De extensione corporum. (LA · EN)

• ch5.7.p101 (poincare:science-hypothese:ch5.7.p101) — « n. 7 pag. 101 » — Caput VI: A. De extensione corporum. (LA · EN)

• p60 (poincare:science-hypothese:p60) — « ibid. pag. 60 » — Caput IV: n. 10 (LA · EN)

• p80 (poincare:science-hypothese:p80) — « H. POINCARÉ, La science et l’hypothèse pag. 80 » — Caput IV: n. 10 (LA · EN)

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Poincaré, Henri (1854 – 1912) — Science et Méthode (1908)

• Apparatus Links: Author Commentary · Biographical Entry (Henri Poincaré)

• p212 (poincare:science-methode:p212) — « Science et Méthode pag. 212 » — Caput III: B) (LA · EN)

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Poincaré, Henri (1854 – 1912) — La Valeur de la Science (1905)

• Apparatus Links: Author Commentary · Biographical Entry (Henri Poincaré)

• p17 (poincare:valeur-science:p17) — « La valeur de la science pag. 17 » — Caput I: n. 9 (LA · EN) | Caput III: C) (LA · EN)

• p22 (poincare:valeur-science:p22) — « pagg. 22 sq. » — Caput I: n. 10 (LA · EN)

• p59 (poincare:valeur-science:p59) — « La valeur de la science pag. 59 » — Caput IV: n. 14 (LA · EN)

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Proclus Lycius Diadochus (412 – 485 AD) — In Primum Euclidis Elementorum Librum Commentarii (ed. Friedlein, 1873)

• Apparatus Links: Author Commentary · Biographical Entry (Proclus Lycius Diadochus)

• 12.14 (proclus:in-euclid:12.14) — « In Euclid. Elem. ed. Friedlein 12, 14 ; 49, 17 sqq. 140, 4 » — Caput III: A) (LA · EN)

• 12.14-22 (proclus:in-euclid:12.14-22) — « ibid. 12, 14-22 ; 49, 12-17 ; 139, 26-140, 7 etc. » — Caput III: A) (LA · EN)

• p185 (proclus:in-euclid:p185) — « In Euclid. Comment. ed. Friedlein pag. 185 » — Caput IV: 4. (LA · EN)

• p97 (proclus:in-euclid:p97) — « Proclum pag. 97, 6 » — Caput IV: n. 8 (LA · EN)

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Pseudo-Thomas Aquinas / Pseudo-Scotus — Summa Totius Logicae Aristotelis

• Apparatus Links: Author Commentary

• **** (pseudo-thomas:summa-totius-logicae) — « Summa totius logicae » — Caput IV: n. 29 (LA · EN) | Caput V: 1. (LA · EN)

• VII.2 (pseudo-thomas:summa-totius-logicae:VII.2) — « op. cit. tract. VII cap. 2 et 6 (in editione Mandonnet pagg. 102-104, pag. 111) » — Caput IV: n. 29 (LA · EN)

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Reichenbach, Hans (1891 – 1953) — Philosophie der Raum-Zeit-Lehre (1928)

• Apparatus Links: Author Commentary · Biographical Entry (Hans Reichenbach)

• p10 (reichenbach:1928:p10) — « H. REICHENBACH, Philos. der Raum-Zeit-Lehre (1928) pag. 10 » — Caput IV: n. 22 (LA · EN)

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Riehl, Alois (1844 – 1924) — Logik und Erkenntnistheorie (Die Kultur der Gegenwart, 1921)

• Apparatus Links: Author Commentary · Biographical Entry (Alois Riehl)

• p71 (riehl:1921:p71) — « A. RIEHL. Logik und Erkenntnistheorie in Kultur der Gegenwart Abt. VI ed. 3 (1921) pag. 71 » — Caput V: n. 6 (LA · EN)

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Ross, Sir William David (1877 – 1971) — Aristotle’s Metaphysics (1924) / Aristotle’s Physics (1936)

• Apparatus Links: Author Commentary · Biographical Entry (Sir William David Ross)

• **** (ross:1936) — « W. D. Ross Aristotle’s Physics » — Caput IV: n. 7 (LA · EN)

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Ross, Sir William David (1877 – 1971) — Aristotle’s Metaphysics (1924) / Aristotle’s Physics (1936)

• Apparatus Links: Author Commentary · Biographical Entry (Sir William David Ross)

• 38-41 (ross:aristotle:38-41) — « W. D. ROSS, Aristotle, pagg. 38-41, 54, 217 » — Caput I: n. 3 (LA · EN)

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Ross, Sir William David (1877 – 1971) — Aristotle’s Metaphysics (1924) / Aristotle’s Physics (1936)

• Apparatus Links: Author Commentary · Biographical Entry (Sir William David Ross)

• II.245 (ross:met:II.245) — « commentarium II pagg. 245 sq. » — Appendix: n. 3 (LA · EN)

• II.264 (ross:met:II.264) — « comm. Ross II pag. 264 » — Appendix: n. 5 (LA · EN)

• IX.8.1049b27 (ross:met:IX.8.1049b27) — « In lin. 27 cum Ross » — Appendix: n. 13 (LA · EN)

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Russell, Bertrand (1872 – 1970) — The Principles of Mathematics (1903)

• Apparatus Links: Author Commentary · Biographical Entry (Bertrand Russell)

• p404 (russell:1903:p404) — « Principles of Mathematics pagg. 404 sq. » — Caput IV: n. 28 (LA · EN)

• p405-407 (russell:1903:p405-407) — « B. RUSSELL, Principles of Mathematics 1903, ed. 2 1937, n. 390 sq., pagg. 405-407 » — Caput IV: n. 3 (LA · EN)

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Russell, Bertrand (1872 – 1970) — The Principles of Mathematics (1903)

• Apparatus Links: Author Commentary · Biographical Entry (Bertrand Russell)

• p183 (russell:1911:p183) — « Revue de Mét. et de Mor. 1911 pag. 183 » — Caput III: B) (LA · EN)

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Scholz, Heinrich (1884 – 1956) — Warum haben die Griechen die Irrationalzahlen nicht aufgebaut? (1928)

• Apparatus Links: Author Commentary · Biographical Entry (Heinrich Scholz)

• 35-72 (scholz:1928:35-72) — « H. SCHOLZ, Warum haben die Griechen die Irrazionalzahlen nich aufgebaut ? ibid. pagg. 35-72 » — Caput I: n. 6 (LA · EN)

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Simplicius of Cilicia (c. 490 – c. 560 AD) — In Aristotelis Physicorum Libros Commentaria (ed. Diels)

• Apparatus Links: Author Commentary · Biographical Entry (Simplicius of Cilicia)

• 127.9 (simplicius:phys:127.9) — « Simplicius i. h. l. (127, 9 et 14) » — Appendix: n. 21 (LA · EN)

• 520.30 (simplicius:phys:520.30) — « i. h. l. ed. Diels 520, 30-32 » — Appendix: § 2. (LA · EN)

• 817 (simplicius:phys:817) — « i. h. l. ed. Diels 817 sqq. » — Appendix: § 1. (LA · EN)

• p722 (simplicius:phys:p722) — « Simplicium Phys. (ed. Diels) pag. 722, 8 » — Caput IV: n. 8 (LA · EN)

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Stammler, Gerhard (1898 – 1977) — Begriff, Urteil, Schluss (1928) / Der Zahlbegriff seit Gauss (1926)

• Apparatus Links: Author Commentary · Biographical Entry (Gerhard Stammler)

• p229 (stammler:1928:p229) — « G. STAMMLER in Begriff, Urteil, Schlusz, Halle-Saale 1928, pagg. 229, 245 » — Caput V: n. 7 (LA · EN)

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Study, Eduard (1862 – 1930) — Die realistische Weltansicht und die Lehre vom Raume (1914)

• Apparatus Links: Author Commentary · Biographical Entry (Eduard Study)

• p131 (study:1914:p131) — « Die realistische Weltansicht und die Lehre vom Raume (Braunschweig 1914 pag. 131) » — Caput I: § 4. (LA · EN)

• p74 (study:1914:p74) — « E. STUDY, Die realistische Weltansicht und die Lehre vom Raume pagg. 74 sqq. » — Caput III: n. 5 (LA · EN)

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Taylor, Alfred Edward (1869 – 1945) — Plato: The Man and His Work (1927)

• Apparatus Links: Author Commentary · Biographical Entry (Alfred Edward Taylor)

• p506 (taylor:1927:p506) — « Plato the man and his work (ed. 2) 1927) pag. 506 » — Caput IV: n. 8 (LA · EN)

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Themistius (c. 317 – c. 388 AD) — In Aristotelis Physica Paraphrasis (ed. Schenkl)

• Apparatus Links: Author Commentary · Biographical Entry (Themistius)

• 102.3 (themistius:phys:102.3) — « ed. Schenkl 102, 3-5 » — Appendix: § 2. (LA · EN)

• 210 (themistius:phys:210) — « paraphrasin Themistii (ed. Schenkl pag. 210) » — Appendix: n. 21 (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — In Aristotelis Libros Posteriorum Analyticorum Expositio

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• **** (aquinas:anal-post) — « S. Th. » — Caput V: C) (LA · EN)

• I.1.10 (aquinas:anal-post:I.1.10) — « Anal. Post. I lect, 1 n. 10 » — Caput I: § 1. (LA · EN)

• I.10.7 (aquinas:anal-post:I.10.7) — « S. Thomas Analyt. Post. I lect. 10 n. 7 » — Caput II: 1. (LA · EN)

• I.15 (aquinas:anal-post:I.15) — « Anal. Post. I l. 15 » — Caput VII: § 1. (LA · EN)

• I.17.4 (aquinas:anal-post:I.17.4) — « lect. 17 n. 4 » — Caput I: § 1. (LA · EN)

• I.19.2 (aquinas:anal-post:I.19.2) — « S. Th. lect. » — Caput IV: § 7. (LA · EN), § 7. (LA · EN)

• I.19.4 (aquinas:anal-post:I.19.4) — « ibid. lect. 19 n. 4 » — Caput IV: § 7. (LA · EN), § 7. (LA · EN)

• I.2.5 (aquinas:anal-post:I.2.5) — « Anal. Post. I lect. 2 n. 5 » — Caput IV: § 7. (LA · EN) | Caput VII: § 1. (LA · EN)

• I.42.7 (aquinas:anal-post:I.42.7) — « lect. 42 n. 7 » — Caput III: A) (LA · EN)

• I.5.7 (aquinas:anal-post:I.5.7) — « Anal. Post. I lect. 5 n. 7 » — Caput I: § 1. (LA · EN), § 1. (LA · EN)

• I.6 (aquinas:anal-post:I.6) — « Anal. Post. I lect. 6 » — Caput I: § 1. (LA · EN)

• II.20 (aquinas:anal-post:II.20) — « Anal. Post. in ultima lectione » — Caput II: 2. (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Sentencia Libri De Anima

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 2.16 (aquinas:de-anima:2.16) — « De Anim. II l. 16 » — Appendix: Additiones (LA · EN)

• III.12.770-777 (aquinas:de-anima:III.12.770-777) — « S. Thomas lect. 12 ; Pirotta n. 770-772, n. 777 » — Caput I: § 2. (LA · EN)

• III.13.791 (aquinas:de-anima:III.13.791) — « S. Thomas lect. 13 ; Pirotta n. 791 » — Caput I: § 2. (LA · EN)

• III.8 (aquinas:de-anima:III.8) — « De anim. III lect. 8 » — Caput II: 3. (LA · EN)

• b1-l11 (aquinas:de-anima:b1-l11) — « lect. 11, ed. Pirotta n. 170 » — Caput IV: n. 8 (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — In Libros Aristotelis De Caelo et Mundo Expositio

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• b1-l2 (aquinas:de-caelo:b1-l2) — « De Caelo I lect. 2 n. 9 » — Caput IV: n. 9 (LA · EN)

• b2-l2 (aquinas:de-caelo:b2-l2) — « ibid. II lect. 2 n. 11 » — Caput IV: n. 9 (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Quaestiones Disputatae de Malo

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 6.1.ad18 (aquinas:de-malo:6.1.ad18) — « Q. D. de Malo q. 6 a. 1 ad 18 » — Caput VII: 2. (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Quaestiones Disputatae de Potentia Dei

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 7.2.ad9 (aquinas:de-potentia:7.2.ad9) — « de Pot. q. 7, a. 2, ad 9 » — Appendix: § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), Additiones (LA · EN)

• 8.1 (aquinas:de-potentia:8.1) — « de Pot. q. 8 a. 1 » — Appendix: § 7. (LA · EN), § 7. (LA · EN)

• 9.5 (aquinas:de-potentia:9.5) — « ibid. q. 9 » — Appendix: § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Expositio super Librum Boethii De Trinitate

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 5.1.ad3 (aquinas:de-trin:5.1.ad3) — « Boet. de Trin. q. 5 a. 1 ad 3 » — Caput VII: § 1. (LA · EN)

• q5-a3 (aquinas:de-trin:q5-a3) — « In Boet. de Trin. q. 5 a. 3 ad 3 » — Caput IV: n. 2 (LA · EN)

• q6.a1 (aquinas:de-trin:q6.a1) — « In Boet. de Trin. q. 6 a. 1 » — Caput V: B) (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Quaestiones Disputatae de Veritate

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 10.12.ad7 (aquinas:de-veritate:10.12.ad7) — « Q. D. de Ver. q. 10 a. 12 ad 7 » — Appendix: § 1. (LA · EN)

• 10.6.sc2 (aquinas:de-veritate:10.6.sc2) — « (Q. D. de Ver. q. 10 a. 6 sed contra 2) » — Caput II: 5. (LA · EN) | Caput VII: 1. (LA · EN)

• 4.2 (aquinas:de-veritate:4.2) — « de Ver. q. 4 a. 2 » — Appendix: § 7. (LA · EN), § 7. (LA · EN)

• q10-a6 (aquinas:de-veritate:q10-a6) — « Q. D. de Ver. q. 10 a. 6 « sed contra » 2 » — Caput IV: Animadversiones praeviae. (LA · EN)

• q12-a3 (aquinas:de-veritate:q12-a3) — « Q. D. de Ver. q. 12 a. 3 ad 2 » — Caput IV: Animadversiones praeviae. (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Sententia Libri Ethicorum

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• IX.11 (aquinas:eth-nic:IX.11) — « i. h. l. (lect. 11) » — Appendix: n. 9 (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Sententia super Metaphysicam

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 10.4.2017 (aquinas:met:10.4.2017) — « S. Th. l. 4 n. 2017 sqq. » — Appendix: § 7. (LA · EN), § 7. (LA · EN)

• 4.l4.n577 (aquinas:met:4.l4.n577) — « Met. IV lect. 4 n. 577 » — Caput V: B) (LA · EN)

• 5.12.916 (aquinas:met:5.12.916) — « S. Th. l. 12 n. 916 » — Appendix: § 7. (LA · EN)

• 5.9 (aquinas:met:5.9) — « Met. V l. 9 » — Appendix: § 7. (LA · EN)

• 5.9.890 (aquinas:met:5.9.890) — « Met. l. c. n. 290 » — Appendix: § 7. (LA · EN)

• 9.10.1894 (aquinas:met:9.10.1894) — « S. Th. lect. 10 n. 1894 » — Appendix: § 5. (LA · EN)

• 9.3.1805 (aquinas:met:9.3.1805) — « Met. IX l. 3 n. 1805 » — Appendix: § 7. (LA · EN)

• 9.3.1806 (aquinas:met:9.3.1806) — « 1806 » — Appendix: § 7. (LA · EN)

• III.7.416 (aquinas:met:III.7.416) — « S. Th. lect. 7 n. 416 » — Caput III: n. 1 (LA · EN)

• IX.3.1805 (aquinas:met:IX.3.1805) — « i. h. l. Cath. n. 1805 » — Appendix: § 1. (LA · EN)

• IX.7.1848 (aquinas:met:IX.7.1848) — « i. h. l. (n. 1848) » — Appendix: § 3. (LA · EN)

• IX.8.1857 (aquinas:met:IX.8.1857) — « i. h. l. ex Met. IX (l. 8 n. 1857) » — Appendix: § 4. (LA · EN)

• X.2.1938 (aquinas:met:X.2.1938) — « l. 2 n. 1938 » — Caput VI: 1. (LA · EN)

• XI.11.2370 (aquinas:met:XI.11.2370) — « n. 2370 » — Appendix: § 1. (LA · EN)

• b7-l10 (aquinas:met:b7-l10) — « Met. VII lect. 10 (Cath. n. 1496) » — Caput IV: n. 2 (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Expositio Libri Peryermeneias

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 1.5.17 (aquinas:periherm:1.5.17) — « ibid. n. 17 » — Appendix: § 7. (LA · EN)

• 1.5.5 (aquinas:periherm:1.5.5) — « Peri Herm. I l. 5, n. 5 » — Appendix: § 7. (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Commentaria in Octo Libros Physicorum Aristotelis

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 3.5 (aquinas:phys:3.5) — « Phys. III l. 5 » — Appendix: § 7. (LA · EN), § 7. (LA · EN), § 7. (LA · EN)

• 4.17 (aquinas:phys:4.17) — « S. Thomas l. 17 » — Appendix: Additiones (LA · EN)

• II.3 (aquinas:phys:II.3) — « In Phys. II lect. 3 » — Caput II: 3. (LA · EN)

• IV.3 (aquinas:phys:IV.3) — « S. Th. l. 3 in fine » — Appendix: § 2. (LA · EN)

• IV.7 (aquinas:phys:IV.7) — « lectionem 7 » — Appendix: § 2. (LA · EN)

• IV.7.7 (aquinas:phys:IV.7.7) — « lect. cit. n. 7 » — Appendix: § 2. (LA · EN)

• V.2.8 (aquinas:phys:V.2.8) — « i. h. l. lect. 2 n. 8 » — Appendix: § 1. (LA · EN)

• V.2.9 (aquinas:phys:V.2.9) — « l. c. n. 9 » — Appendix: § 1. (LA · EN)

• VIII.1 (aquinas:phys:VIII.1) — « lect. 1 et 2 » — Appendix: § 1. (LA · EN)

• b4-l18 (aquinas:phys:b4-l18) — « Phys. IV lect. 18 n. 4 » — Caput IV: n. 9 (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Summa contra Gentiles

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 1.26.2 (aquinas:scg:1.26.2) — « S. c. G. I 26 n. 2 » — Appendix: n. 31 (LA · EN)

• I.36 (aquinas:scg:I.36) — « S. c. G. I 36 » — Caput II: 1. (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Scriptum super Libros Sententiarum

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• 1.19.5.1.ad6 (aquinas:sent:1.19.5.1.ad6) — « Sent. I D. 19 q. 5 a. 1 ad 6 » — Appendix: § 7. (LA · EN)

• 1.2.1.3 (aquinas:sent:1.2.1.3) — « Sent. I D. 2 q. 1 a. 3 » — Appendix: § 7. (LA · EN)

• I.3.1.2 (aquinas:sent:I.3.1.2) — « I Sent. Dist. III q. 1 a. 2 » — Caput II: 2. (LA · EN)

• I.4.2.1.ad1 (aquinas:sent:I.4.2.1.ad1) — « I Sent. Dist. 4 q. 2 a. 1 ad 1 » — Caput II: 1. (LA · EN)

• III.11.1.4.ad6 (aquinas:sent:III.11.1.4.ad6) — « III Sent. Dist. 11 q. 1 a. 4 ad 6 » — Caput II: 1. (LA · EN)

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Thomas Aquinas, St., O.P. (1225 – 1274) — Summa Theologiae

• Apparatus Links: Author Commentary · Biographical Entry (St. Thomas Aquinas, O.P.)

• I.12.4.ad3 (aquinas:st:I.12.4.ad3) — « S. Th. I q. 12 a. 4 ad 3 » — Appendix: § 7. (LA · EN)

• I.13.12 (aquinas:st:I.13.12) — « S. Th. I q. 13 a. 12 » — Caput II: 1. (LA · EN)

• I.7.1 (aquinas:st:I.7.1) — « S. Th. I q. 7 a. 1 » — Appendix: n. 8 (LA · EN)

• I.75.6 (aquinas:st:I.75.6) — « S. Th. I q. 75 a. 6 » — Appendix: § 7. (LA · EN)

• I.85.1.ad2 (aquinas:st:I.85.1.ad2) — « S. Th. I q. 85 a. 1 ad 2 » — Caput II: 3. (LA · EN)

• I.85.5.ad3 (aquinas:st:I.85.5.ad3) — « q. 85 a. 5 ad 3 » — Caput II: 1. (LA · EN)

• I.q84.a6 (aquinas:st:I.q84.a6) — « S. Th. I. q. 84 a. 6 in fine » — Caput III: A) (LA · EN)

• I.q84.a6.ad3 (aquinas:st:I.q84.a6.ad3) — « resp. 3 eiusdem articuli » — Caput III: A) (LA · EN)

• II-II.24.4.ad3 (aquinas:st:II-II.24.4.ad3) — « S. Th. II, II q. 24 a. 4 ad 3 » — Appendix: Additiones (LA · EN)

• III.q11.a2.ad1 (aquinas:st:III.q11.a2.ad1) — « S. Th. III q. 11 a. 2 ad 1 » — Caput III: A) (LA · EN)

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Voss, Aurel (1845 – 1931) — Über die mathematische Erkenntnis (Die Kultur der Gegenwart, 1914)

• Apparatus Links: Author Commentary · Biographical Entry (Aurel Voss)

• p96 (voss:1914:p96) — « A. VOSS, Ueber die mathematische Erkenntnis in Die Kultur der Gegenwart III pag. E 96 » — Caput III: n. 10 (LA · EN)

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Waitz, Theodor (1821 – 1864) — Aristotelis Organon Graece (1844–1846)

• Apparatus Links: Author Commentary · Biographical Entry (Theodor Waitz)

• I.p427 (waitz:1844:I.p427) — « TH. WAITZ in suo Commentario in Anal. Priora I 23 ; in eius editione I pagg. 427-429 » — Caput IV: n. 27 (LA · EN)

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Weber, Heinrich & Wellstein, Josef — Enzyklopädie der Elementarmathematik, Band II: Elemente der Geometrie (1915 / 1925)

• Apparatus Links: Author Commentary

• II (weber-wellstein:enzyklopaedie:II) — « Weber-Wellstein Enzyklopaedie der Elementar-Mathematik II (3 ed. 1925) » — Caput III: B) (LA · EN)

• II.p10 (weber-wellstein:enzyklopaedie:II.p10) — « Op. cit. pag. 10 » — Caput III: 4. (LA · EN)

• II.p33 (weber-wellstein:enzyklopaedie:II.p33) — « Weber-Wellstein in Enzyklopaedie der Elementarmathematik II Elemente der Geometrie (ed. 3 1915) pagg. 33-62 » — Caput IV: n. 26 (LA · EN)

• II.p9 (weber-wellstein:enzyklopaedie:II.p9) — « pag. 9 » — Caput III: 1. (LA · EN), 1. (LA · EN), n. 6 (LA · EN)

• II.p9-11 (weber-wellstein:enzyklopaedie:II.p9-11) — « op. cit. pagg. 9-11 » — Caput III: 1. (LA · EN)

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Weyl, Hermann (1885 – 1955) — Philosophie der Mathematik und Naturwissenschaft (1927)

• Apparatus Links: Author Commentary · Biographical Entry (Hermann Weyl)

• p18 (weyl:1927:p18) — « H. WEYL, Philosophie der Mathematik und Naturwissenschaft (1927) pag. 18 » — Caput IV: n. 22 (LA · EN)

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Whitehead, Alfred North & Russell, Bertrand — Principia Mathematica (1910–1913)

• Apparatus Links: Author Commentary

• **** (whitehead-russell:principia) — « Principia Mathematica » — Caput V: A) (LA · EN)

• p100 (whitehead-russell:principia:p100) — « Principia Mathematica (pag. 100) » — Caput V: B) (LA · EN)

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