Bibliography & Editions

Critical Greek Editions, Oxford Translations, Classical Treatises & Commentaries

Authoritative editions, translations, classical mathematical propositions, and commentaries cited across the primary apparatus and analytical notes of Loci Geometrici et Noetici.

Bekker, Immanuel (ed.) — Aristotelis Opera, edidit Academia Regia Borussica, Vols. I–II (Berlin: Georg Reimer, 1831; Oxford repr. 1837)

  • Citation Key: bekker:1831 | Locus: 1a–1462b

  • Significance: Canonical Greek critical text defining universal Bekker page, column (a/b), and line coordinates.

Ross, Sir William David (ed.) — Aristotle’s Metaphysics: A Revised Text with Introduction and Commentary, 2 vols. (Oxford: Clarendon Press, 1924)

  • Citation Key: ross:metaphysics:1924 | Locus: 980a–1093b

  • Significance: Standard critical Greek edition and commentary for Liber V of this Codex.

Ross, Sir William David (ed.) — Aristotle’s Physics: A Revised Text with Introduction and Commentary (Oxford: Clarendon Press, 1936)

  • Citation Key: ross:physics:1936 | Locus: 184a–267b

  • Significance: Standard critical commentary on Aristotle’s abstraction, infinite, place, and continuum treatises.

Ross, Sir William David (ed.) — Aristotle’s Prior and Posterior Analytics: A Revised Text with Introduction and Commentary (Oxford: Clarendon Press, 1949)

  • Citation Key: ross:analytics:1949 | Locus: 24a–100b

  • Significance: Comprehensive philological and logical commentary on the Analytics.

Waitz, Theodor (ed.) — Aristotelis Organon Graece, 2 vols. (Leipzig: Hahn, 1844–1846)

  • Citation Key: waitz:organon:1844 | Locus: Vols. I–II

  • Significance: Nineteenth-century critical edition and Latin commentary cited throughout Heath and Hoenen.

Bonitz, Hermann — Index Aristotelicus, Aristotelis Opera Vol. V (Berlin: Georg Reimer, 1870)

  • Citation Key: bonitz:index:1870 | Locus: pp. 1–878

  • Significance: Exhaustive lexicon of Aristotle’s Greek philosophical and mathematical terminology.

Smith, J. A., and W. D. Ross (eds.) — The Works of Aristotle Translated into English, Vols. I–III, VIII (Oxford: Clarendon Press, 1908–1931)

  • Citation Key: oxford:works:1908 | Locus: Vols. I, II, III, VIII

  • Significance: Public-domain Oxford English translations by Edghill, Jenkinson, Mure, Pickard-Cambridge, Hardie & Gaye, Stocks, Smith, and Ross staged in this Codex.

Heath, Sir Thomas Little — The Thirteen Books of Euclid’s Elements, 2nd ed., 3 vols. (Cambridge University Press, 1926) [geometor/euclid]

  • Citation Key: heath:euclid:1926 | Locus: Vols. I–III

  • Significance: Contains 145 distinct Aristotelian locus citations reconstructing pre-Euclidean definitions, postulates, and proofs.

Heath, Sir Thomas Little — Mathematics in Aristotle (Oxford: Clarendon Press, 1949)

  • Citation Key: heath:math-aristotle:1949 | Locus: pp. 1–291

  • Significance: Systematic treatise-by-treatise mathematical commentary on every geometrical and arithmetical passage in the Aristotelian corpus.

Hoenen, Petrus Hubertus Jacobus, S.J. — De Noetica Geometriae: Origine Theoriae Cognitionis, Analecta Gregoriana Vol. 56 (Rome: Pontificia Universitas Gregoriana, 1952) [geometor/hoenen]

  • Citation Key: hoenen:noetica:1952 | Locus: Cap. I–VII & Appendix

  • Significance: Contains 64 Aristotelian locus keys developing the noetics of intellectual intuition in the phantasm and intelligible matter.

Pacioli, Fra Luca, O.F.M. — De Divina Proportione (Venice: Paganino Paganini, 1509) [geometor/pacioli]

  • Citation Key: pacioli:divina:1509 | Locus: Compendio Cap. I–V & Architectura

  • Significance: Renaissance treatise citing Aristotle on mathematical certitude, subalternation of perspective/music, and the five regular solids.

Euclid of Alexandria — Elements (Στοιχεῖα, ed. J. L. Heiberg, Leipzig, 1883–1888)

  • Citation Key: euclid:elements | Locus: Books I–XIII

  • Significance: The canonical Greek synthesis of definitions, postulates, common notions, plane geometry, Eudoxian proportion, irrationals, and stereometry.

Euclid of Alexandria — Elements, Book I, Proposition 5 (Pons Asinorum)

  • Citation Key: euclid:I.5 | Locus: I.5

  • Significance: Equality of base angles in an isosceles triangle; contrasted with Aristotle’s older mixed-angle proof in Prior Analytics I.24 (41b13–22).

Euclid of Alexandria — Elements, Book I, Postulate 5 & Proposition 29 (Theory of Parallels)

  • Citation Key: euclid:I.29 | Locus: Post. 5; I.27–29

  • Significance: Euclid’s resolution of the circularity in parallel-line proofs diagnosed by Aristotle in Prior Analytics II.16 (65a4–9).

Euclid of Alexandria — Elements, Book I, Proposition 32 (Interior Angles of a Triangle = 2R)

  • Citation Key: euclid:I.32 | Locus: I.32

  • Significance: Proved via the parallel through the vertex; cited in Posterior Analytics I.5 (74a25–32), I.31 (87b35), and Metaphysics Θ.9 (1051a24–26).

Euclid of Alexandria — Elements, Book III, Proposition 31 (Angle in a Semicircle is Right)

  • Citation Key: euclid:III.31 | Locus: III.31

  • Significance: Proved in Metaphysics Θ.9 (1051a26–29) and Posterior Analytics II.11 (94a28–34) by erecting the radius from the center of the diameter.

Euclid of Alexandria / Eudoxus of Cnidus — Elements, Book V, Definition 5 & Proposition 16 (General Proportion & Alternation)

  • Citation Key: euclid:V.def.5 | Locus: V.Def.5; V.16

  • Significance: General Eudoxian theory of proportion heralded in Posterior Analytics I.5 (74a17–25) as superseding separate proofs for numbers, lines, solids, and times.

Euclid of Alexandria / Theaetetus — Elements, Book X, Propositions 2–3 (Anthyphairetic Criterion of Incommensurability)

  • Citation Key: euclid:X.2 | Locus: X.2–3

  • Significance: Geometric preservation of reciprocal subtraction (antanairesis), attested in Topics VIII.3 (158b29–35).

Plato — Meno

  • Citation Key: plato:meno | Locus: 80d–86c

  • Significance: Meno’s paradox of inquiry and the geometric doubling of the square, explicitly answered in Posterior Analytics I.1 (71a29).

Plato — Republic, Books VI–VII (Divided Line & Quadrivium)

  • Citation Key: plato:republic | Locus: 509d–511e, 525a–534d

  • Significance: Distinction between discursive mathematical dianoia from hypotheses and dialectical noēsis.

Plato — Timaeus

  • Citation Key: plato:timaeus | Locus: 48e–56c

  • Significance: Identification of receptacle space (chōra) with matter and construction of physical bodies out of elementary plane triangles—critiqued in Physics IV.2 and De Caelo III.7–8.

Proclus Diadochus — In Primum Euclidis Elementorum Librum Commentarii (ed. G. Friedlein, Leipzig, 1873)

  • Citation Key: proclus:in-euclidem | Locus: pp. 48–84, 178–207

  • Significance: Preserves the Eudemian summary of Greek geometry and compares Aristotelian axioms, postulates, and hypotheses with Euclid’s Elements.

Alexander of Aphrodisias — In Aristotelis Metaphysica Commentaria (ed. M. Hayduck, CAG I, Berlin, 1891)

  • Citation Key: alexander:in-metaph | Locus: CAG I

  • Significance: Classical Peripatetic commentary on Metaphysics A–Δ (with pseudo-Alexander / Michael of Ephesus on E–N).

Simplicius of Cilicia — In Aristotelis Physicorum Libros Commentaria (ed. H. Diels, CAG IX–X, Berlin, 1882–1895)

  • Citation Key: simplicius:in-physica | Locus: CAG IX–X

  • Significance: Essential source on Antiphon, Bryson, Hippocrates of Chios, and Zeno’s continuum arguments.

John Philoponus — In Aristotelis Analytica Priora et Posteriora Commentaria (ed. M. Wallies, CAG XIII.2–3, Berlin, 1905–1909)

  • Citation Key: philoponus:in-anal-post | Locus: CAG XIII.2–3

  • Significance: Preserves ancient reconstructions of Aristotle’s geometric examples in the Analytics.

Thomas Aquinas, St., O.P. — Expositio Libri Posteriorum Analyticorum (Leonine ed., Vol. I*2, Rome, 1989)

  • Citation Key: aquinas:in-anal-post | Locus: Lib. I–II

  • Significance: Scholastic exposition of demonstrative science, axioms vs. postulates, subalternation, and intuitive epagōgē.

Thomas Aquinas, St., O.P. — Super Boethium De Trinitate (Leonine ed., Vol. L, Rome, 1992)

  • Citation Key: aquinas:in-boeth-trin | Locus: qq. 5–6

  • Significance: Locus classicus on the three degrees of theoretical distinction/abstraction and the termination of mathematical judgment in the imagination (ad imaginationem).

Averroes (Ibn Rushd) — Aristotelis Metaphysicorum Libri XIIII cum Averrois Cordubensis in eosdem Commentariis (Venice: Junta, 1562)

  • Citation Key: averroes:in-metaph | Locus: Lib. II, comm. 14–16

  • Significance: Classical Peripatetic-Arabic exposition of Metaphysics α.3 (995a14–17) on mathematical exactitude (akribeia) and abstraction from sensible matter.

Hilbert, David — Grundlagen der Geometrie (Leipzig: Teubner, 1899)

  • Citation Key: hilbert:grundlagen:1899 | Locus: Chs. I–II

  • Significance: Modern formalist axiomatization contrasted with Aristotelian intuitive first principles in the Codex commentary.