Bibliography & Critical Editions

Critical Greek Texts, Public-Domain Translations, Euclidean Propositions & Commentaries

Authoritative editions, Euclidean propositions, ancient commentaries, and modern mathematical histories (30 entries) cited across Loci Mathematici et Geometrici.

Burnet, John (ed.) — Platonis Opera, recognovit brevique adnotatione critica instruxit Ioannes Burnet, Tomi I–V (Oxford: Clarendon Press, 1900–1907)

  • Citation Key: burnet:opera:1900 | Locus: Tomi I–V

  • Significance: Authoritative Oxford Classical Text staged verbatim in the Greek (el) track via Perseus Canonical GreekLit TEI-XML.

Jowett, Benjamin (trans.) — The Dialogues of Plato, Translated into English with Analyses and Introductions, 3rd ed., 5 vols. (Oxford: Clarendon Press, 1892)

  • Citation Key: jowett:dialogues:1892 | Locus: Vols. I–V

  • Significance: Public-domain English translation staged in the English (en) track with exact mathematical philology notes.

Estienne, Henri (Henricus Stephanus, ed.) — Platonis opera quae extant omnia, 3 vols. (Geneva, 1578)

  • Citation Key: stephanus:1578 | Locus: Vols. I–III (a–e sections)

  • Significance: Universal pagination and five-section column standard (a–e) governing all Platonic references.

Euclid of Alexandria — Στοιχεῖα — The Thirteen Books of Euclid’s Elements (ed. Heiberg 1883–1888; trans. Heath 1926)

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

  • Significance: Deductive culmination of the fourth-century Academic curriculum (geometor/euclid & geometor/elements).

Euclid — Elements, Book I, Definitions 4 & 15 (Straight Line & Circle)

  • Citation Key: euclid:I.def.4 | Locus: I, Defs. 4, 15

  • Significance: Euclidean counterpart to Plato’s optical straightness and equidistant roundness in Parmenides 137e.

Euclid — Elements, Book I, Definitions 13–14 & Book XI, Definition 2 (Boundary, Figure & Solid)

  • Citation Key: euclid:I.def.13 | Locus: I, Defs. 13–14; XI, Def. 2

  • Significance: Formalizes Socrates’ definition of figure as limit (peras) in Meno 76a.

Euclid — Elements, Book I, Proposition 1 (Equilateral Triangle Construction)

  • Citation Key: euclid:I.1 | Locus: I.1

  • Significance: Constructs the cosmic equilateral face bisected into six Timaeus 1:√3:2 half-triangles.

Euclid — Elements, Book I, Propositions 11–12 (Perpendicular Lines)

  • Citation Key: euclid:I.11 | Locus: I.11–12

  • Significance: Erects orthogonal legs in Meno’s square, Theodorus’s spiral, and the Divided Line mean ordinate.

Euclid — Elements, Book I, Proposition 46 (Construction of a Square)

  • Citation Key: euclid:I.46 | Locus: I.46

  • Significance: Constructs the given square ABCD and diagonal square BHKD in Meno 82b–85b.

Euclid — Elements, Book I, Proposition 47 (Pythagorean Theorem)

  • Citation Key: euclid:I.47 | Locus: I.47

  • Significance: General theorem generalizing Socrates’ isosceles case Q = 4 + 4 = 8 and iterating Theodorus’s spiral Q_{n+1} = Q_n + 1.

Euclid — Elements, Book II, Proposition 11 & Book VI, Proposition 30 (Extreme and Mean Ratio)

  • Citation Key: euclid:II.11 | Locus: II.11, VI.30

  • Significance: Canonical Academic ‘section’ (ἡ τομή) realizing the Divided Line under golden ratio φ.

Euclid — Elements, Book II, Proposition 14 & Book VI, Proposition 13 (Quadrature & Mean Proportional)

  • Citation Key: euclid:II.14 | Locus: II.14, VI.13

  • Significance: Semicircle ordinate construction of quadratic powers √n (Theaetetus 147d) and geometric mean √(ab) (Timaeus 32a).

Euclid (Eudoxus) — Elements, Book V, Definition 5 & Proposition 16 (General Theory of Proportion)

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

  • Significance: Proves alternation (A:B = C:D => A:C = B:D) required for the Divided Line equality |BC| = |CD| even for irrational ratios.

Euclid — Elements, Book VI, Propositions 27–28 (Elliptic Application of Areas & Diorismos)

  • Citation Key: euclid:VI.28 | Locus: VI.27–28

  • Significance: Exact Euclidean counterpart to Socrates’ hypothesis of applying an area with similar defect in Meno 87a.

Euclid — Elements, Book VII, Definitions 16–19 (Plane, Solid, Square & Oblong Numbers)

  • Citation Key: euclid:VII.def.16 | Locus: VII, Defs. 16–19

  • Significance: Preserves Theaetetus’s arithmetic distinction between equilateral square and oblong numbers (147e–148a).

Euclid — Elements, Book VIII, Propositions 11–12 (Means Between Square and Cube Numbers)

  • Citation Key: euclid:VIII.11 | Locus: VIII.11–12

  • Significance: Demonstrates Timaeus 32a–b: one mean proportional between two squares, two means between two cubes.

Euclid (Theaetetus) — Elements, Book X, Definitions 1–4 & Proposition 9 (Commensurability in Length vs. Square)

  • Citation Key: euclid:X.def.1 | Locus: X, Defs. 1–4; X.9

  • Significance: Codifies Theaetetus 147d–148b: squares have commensurable sides iff their areas have the ratio of square numbers.

Euclid (Theaetetus) — Elements, Book XIII, Propositions 13–18 (Construction & Exhaustive Comparison of the Five Cosmic Solids)

  • Citation Key: euclid:XIII.13 | Locus: XIII.13–18

  • Significance: Inscribes tetrahedron, octahedron, cube, icosahedron, and dodecahedron in a sphere and proves no sixth regular polyhedron can exist (cf. Timaeus 54d–55c).

Proclus Diadochus — In Primum Euclidis Elementorum Librum Commentarii (ed. Friedlein 1873; trans. Morrow 1970)

  • Citation Key: proclus:in-euclidem | Locus: Friedlein pp. 1–436

  • Significance: Neoplatonic mathematical synthesis linking Philebus, Republic VI–VII, Meno, Parmenides, and Timaeus to Euclid Book I (geometor/proclus).

Proclus Diadochus — In Platonis Timaeum Commentaria, ed. Ernst Diehl, 3 vols. (Leipzig: Teubner, 1903–1906)

  • Citation Key: proclus:in-timaeum | Locus: Vol. II, pp. 167–236 (on Tim. 35a–36d)

  • Significance: Preserves Crantor’s base-384 integer table and verifies the 34-pitch Timaeus World-Soul scale.

Aristotle — Analytica Posteriora, Book I (Bekker 71a1–89b20)

  • Citation Key: aristotle:anal-post | Locus: 71a29, 76b39, 77b30

  • Significance: Engages Meno’s paradox and Republic’s doctrine of mathematical hypotheses and diagrams (geometor/aristotle).

Aristotle — Metaphysica, Books A.6, B.2, M.1–3 (ed. Ross 1924)

  • Citation Key: aristotle:metaphysics | Locus: 987b14–18, 997b, 1076a–1078b

  • Significance: Primary witness for Plato’s doctrine of mathematical intermediates (ta mathēmatika) between Forms and sensibles.

Aristotle — De Caelo, Book III, Chapters 7–8 (Bekker 305b28–307b24)

  • Citation Key: aristotle:de-caelo | Locus: 306a1–307b18

  • Significance: Critiques Timaeus 53c–56c on generating three-dimensional bodies from weightless planar triangles.

Heath, Sir Thomas Little — A History of Greek Mathematics, Vol. I: From Thales to Euclid (Oxford: Clarendon Press, 1921)

  • Citation Key: heath:greek-math:1921 | Locus: Vol. I, Ch. IX ('Plato', pp. 284–315) & pp. 202–212

  • Significance: Standard reconstruction of Meno’s geometric hypothesis, Theodorus’s √3..√17 methods, and the Timaeus scale.

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

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

  • Significance: Exhaustive commentary reconciling all 21 Plato citations in geometor/euclid and geometor/elements.

Taylor, A. E. — A Commentary on Plato’s Timaeus (Oxford: Clarendon Press, 1928)

  • Citation Key: taylor:timaeus:1928 | Locus: pp. 92–164, 362–388

  • Significance: Detailed mathematical analysis of the World-Soul harmonic intervals and cosmic polyhedra.

Cornford, Francis Macdonald — Plato’s Cosmology: The Timaeus of Plato Translated with a Running Commentary (London: Routledge, 1937)

  • Citation Key: cornford:timaeus:1937 | Locus: pp. 43–93, 210–230

  • Significance: Clarifies the band construction of the Circles of the Same and the Different and the planar triangle assemblies.

Pacioli, Fra Luca — De Divina Proportione (Venice: Paganino Paganini, 1509)

  • Citation Key: pacioli:divina:1509 | Locus: Compendio Caps. V, XXV–LV

  • Significance: Renaissance synthesis of Timaeus 53c–56c and Euclid Book XIII (geometor/pacioli).

Hoenen, Petrus H. J., S.J. — De Noetica Geometriae: Origine Theoriae Cognitionis (Rome: Analecta Gregoriana 63, 1954)

  • Citation Key: hoenen:noetica:1952 | Locus: Caps. I, IV, VII

  • Significance: Scholastic-noetic analysis of Meno 82b–85b, Republic VI–VII, and Laws V 737e (geometor/hoenen).

Knorr, Wilbur Richard — The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry (Dordrecht: Reidel, 1975)

  • Citation Key: knorr:evolution:1975 | Locus: Chs. III–VIII

  • Significance: Definitive modern study of Theodorus’s stopping-point at √17 and Theaetetus’s theory of quadratic powers.