Bibliography & Primary Sources¶
Critical register of primary editions, translations, ancient mathematical authorities cited by Proclus, and modern GEOMETOR companion treatises. Every :cite: reference in the Codex resolves directly to its entry below.
Primary Editions & Translations of Proclus¶
- Franciscus Barocius (Francesco Barozzi) — Procli Diadochi Lycii in primum Euclidis Elementorum librum commentariorum ad universam mathematicam disciplinam principium eruditionis tradentium libri IIII (Padua: Gratiosus Perchacinus, 1560) [1560]
Key:
barocius:1560Renaissance Latin translation collated from superior Greek manuscripts in Venice and Crete, supplying crucial lacunae of the 1533 Basel Greek text.
- Proclus Diadochus (ed. Gottfried Friedlein) — Procli Diadochi in primum Euclidis Elementorum librum commentarii (Leipzig: B. G. Teubner, 1873) [1873]
Key:
friedlein:1873Standard critical Teubner Greek edition (pp. 1–436, Indices pp. 437–507; CTS URN urn:cts:greekLit:tlg4036.tlg011.opp-grc1) providing canonical page-and-line numbering. Provenance: https://archive.org/details/friedlein-procli-diadochi-in-primum-euclidis-elementorum-librum-commentarii-gr-1873
- Simon Grynaeus (ed.) — Εὐκλείδου Στοιχείων βιβλ. ιε΄ … Procli in primum Euclidis Elementorum librum commentariorum libri IIII (Editio Princeps) (Basel: Johann Herwagen, 1533) [1533]
Key:
grynaeus:1533Editio princeps of the Greek text of Euclid and Proclus’s Commentary, whose pagination appears in the left margin of Friedlein and was used by Thomas Taylor.
- Thomas Taylor (trans.) — The Philosophical and Mathematical Commentaries of Proclus, on the First Book of Euclid’s Elements, Vol. I (London, 1788 / 1792 (Project Gutenberg #74253)) [1788/1792]
Key:
taylor:1788First English translation, Volume I covering Prologue Book I, Prologue Book II, and Definitions. Provenance: https://www.gutenberg.org/ebooks/74253
- Thomas Taylor (trans.) — The Philosophical and Mathematical Commentaries of Proclus, on the First Book of Euclid’s Elements, Vol. II (London, 1789 / 1792 (Project Gutenberg #79455)) [1789/1792]
Key:
taylor:1789First English translation, Volume II covering Petitions/Postulates, Axioms, and Propositions I.1–I.48. Provenance: https://www.gutenberg.org/ebooks/79455
Ancient Philosophical & Mathematical Sources Cited by Proclus¶
- Aristotle — Posterior Analytics (I.1–2, I.4–5, I.10 (71a–77a)) [c. 335 BC]
Key:
aristotle:anal-post:I.1-10Theory of apodictic science, first principles (axioms, hypotheses, postulates), and universal commensurately-first (katholou proton) demonstration (Friedlein 75–76, 178–183, 206, 381–383).
- Aristotle — De Anima (I.4 (409a4), III.4–8 (429a–432a)) [c. 330 BC]
Key:
aristotle:de-anima:III.4-8Motion of a point generating a line (97), soul as ‘place of forms’ (topos eidon, 16), and passive intellect / phantasia (51–52).
- Aristotle — De Caelo (I.5, 271b28–30) [c. 335 BC]
Key:
aristotle:de-caelo:I.5Lemma invoked by Proclus (Friedlein 371, 10) in his attempted proof of Postulate 5: two straight lines diverging from one point separate beyond any finite distance.
- Aristotle — Metaphysics (A.1 (981b20), B.2 (997b35), M.3 (1078a)) [c. 330 BC]
Key:
aristotle:met:981b-1078aEgyptian leisure of the priestly caste (64–65), Protagoras’s critique of geometric tangency (139–140), intelligible matter (hyle noete, 48–53), and mathematical beauty (26–27).
- Claudius Ptolemy — That Straight Lines Produced from Angles Less Than Two Right Angles Meet (fragments) (apud Proclum, Friedlein 191, 362–368) [2nd cent. AD]
Key:
ptolemy:parallel-linesLost monograph attempting to demonstrate Euclid’s Fifth Postulate; preserved solely in Proclus’s Commentary on Prop. I.29.
- Euclid — Elements (Στοιχεῖα), Book I (Defs. 1–23, Posts. 1–5, CN 1–5, Props. I.1–I.48) [c. 300 BC]
Key:
euclid:elementsThe canonical treatise expounded throughout Proclus’s Commentary; cross-linked via GEOMETOR :just: to geometor/euclid and geometor/elements.
- Eudemus of Rhodes — History of Geometry (Γεωμετρικὴ Ἱστορία, fragments) (apud Proclum, Friedlein 64–70, 125, 157, 250, 299, 333, 352, 379, 419) [c. 320 BC]
Key:
eudemus:history-of-geometryLost Peripatetic history of Greek geometry whose priceless fragments—the Eudemian Summary and attributions to Thales, Oenopides, Hippocrates, and the Pythagoreans—survive almost solely through Proclus.
- Geminus of Rhodes — Theory of the Mathematical Sciences / Philokalia (fragments) (apud Proclum, Friedlein 38–42, 105, 111, 126, 176–177, 181–192, 241, 251) [1st cent. BC]
Key:
geminus:philokaliaEncyclopedic Stoic-mathematical treatise on the classification of sciences, curves (homoeomeric, spiric, cissoid, conchoid), asymptotic lines, and postulates.
- Pappus of Alexandria — Mathematical Collection & Commentary on Euclid (apud Proclum, Friedlein 189, 197, 249–250) [c. 320 AD]
Key:
pappus:collectioSource of the famous zero-construction symmetry proof of Prop. I.5 (pons asinorum) and critical notes on Postulate 4 and the Common Notions.
- Plato — Meno (81e–85d) [c. 385 BC]
Key:
plato:meno:81e-85dRecollection (anamnesis) demonstrated by Socrates eliciting the doubling of the square from an untaught boy, proving mathematical logoi are innate in the soul (Friedlein 45).
- Plato — Parmenides (137e) [c. 370 BC]
Key:
plato:parmenides:137ePlato’s optical definition of the straight line as ‘that of which the middle covers both extremities’ (Friedlein 109–110).
- Plato — Philebus (16c–26d) [c. 355 BC]
Key:
plato:philebus:16c-26dMetaphysics of Limit (peras) and the Unlimited (apeiron) as cosmic principles generating all mathematical harmony and figure (Friedlein 5–7).
- Plato — Republic (VI, 509d–511e (The Divided Line)) [c. 375 BC]
Key:
plato:rep:VI.510b-511dFoundational Platonic text establishing dianoia and mathematical objects as intermediate (metaxy) between sensibles and pure intelligibles (Friedlein 3–4, 10, 42).
- Plato — Republic (VII, 525a–534e (Curriculum of the Quadrivium & Dialectic)) [c. 375 BC]
Key:
plato:rep:VII.525a-534eMathematics as the ‘prelude’ awakening the eye of the soul and Dialectic as the ‘coping-stone’ (thrigkos) of the sciences (Friedlein 20–29, 42–44).
- Plato — Timaeus (31c–36d, 53c–56c) [c. 360 BC]
Key:
plato:timaeus:31c-36dHarmonic composition of the World-Soul and construction of the five regular cosmic polyhedra—identified by Proclus as the ultimate skopos of Euclid’s Elements (Friedlein 16, 62, 70–71).
Companion GEOMETOR & Modern Critical Works¶
- Petrus H. J. Hoenen, S.J. — De Noetica Geometriae: Origine Theoriae Cognitionis (Rome: Analecta Gregoriana Vol. 63, 1954 (geometor/hoenen)) [1954]
Key:
hoenen:1954Companion GEOMETOR treatise engaging Proclus on sensible inexactitude, phantasia and intelligible matter (Friedlein 12, 49, 97, 139–140, 185), and the epistemology of Postulate 5 (Friedlein 191, 365–373).
- Sir Thomas Little Heath — The Thirteen Books of Euclid’s Elements (2nd ed., 3 vols.) (Cambridge University Press, 1926 (geometor/euclid)) [1926]
Key:
heath:1926Primary modern critical commentary on Euclid in geometor/euclid, citing Proclus across 156 distinct Friedlein loci.