Index Nominum (Persons)

Prosopographical register of geometers, philosophers, commentators, and editors appearing in Proclus’s Commentary (including all twenty-three geometers of the Eudemian Summary, Friedlein pp. 64–70) and in the textual transmission of the Codex.

Pre-Euclidean & Classical Geometers and Philosophers

Thales of Miletus (Θαλῆς ὁ Μιλήσιος) — c. 624–546 BC

First brought geometry from Egypt to Hellas; credited via Eudemus with bisecting the circle by its diameter (Def. 17), equality of isosceles base angles (I.5), equality of vertical angles (I.15), and ASA congruence for ship distances at sea (I.26) Friedlein loci: 65, 157, 250, 299, 352.

Mamercus (Ameristus) (Μάμερκος) — 6th cent. BC

Brother of the poet Stesichorus; remembered in the Eudemian Summary for acquiring great fame through his zeal for geometry Friedlein loci: 65.

Pythagoras of Samos (Πυθαγόρας) — c. 570–495 BC

Transformed geometry into a liberal philosophical discipline, investigating first principles intellectually and discovering cosmic figures and proportionals; credited by tradition with I.47 Friedlein loci: 35, 65, 426–428.

Anaxagoras of Clazomenae (Ἀναξαγόρας) — c. 500–428 BC

Touched upon many questions belonging to geometry after Pythagoras, according to the Eudemian Summary Friedlein loci: 65.

Oenopides of Chios (Οἰνοπίδης ὁ Χῖος) — fl. c. 450 BC

Slightly younger than Anaxagoras; first investigated dropping a perpendicular (I.12, calling it kata gnomona) and copying a rectilinear angle (I.23), and distinguished theorems from problems Friedlein loci: 65–66, 80, 283, 333.

Protagoras of Abdera (Πρωταγόρας) — c. 490–420 BC

Argued against geometers that a physical circle touches a straightedge along a line rather than at a single point; refuted by Proclus and cited by Hoenen Friedlein loci: 139–140.

Hippocrates of Chios (Ἱπποκράτης ὁ Χῖος) — fl. c. 440 BC

Discovered the quadrature of lunes, pioneered geometric reduction (apagoge, reducing cube duplication to two mean proportionals), and was the first recorded composer of Elements Friedlein loci: 66, 213.

Theodorus of Cyrene (Θεόδωρος ὁ Κυρηναῖος) — c. 465–398 BC

Eminent in geometry alongside Hippocrates of Chios; famed for proving the irrationality of non-square surds up to 17 Friedlein loci: 66.

Hippias of Elis (Ἱππίας ὁ Ἠλεῖος) — 5th cent. BC

Invented the quadratrix (tetragonizousa) curve used for trisecting rectilinear angles and squaring the circle Friedlein loci: 272, 356.

Plato (Πλάτων) — c. 428–348 BC

Catalyzed the greatest advance in mathematics and geometry; formulated the Divided Line, recollection, analytical method (transmitted to Leodamas), optical straight-line definition, and even-number right-triangle rule Friedlein loci: 3–46, 66, 109, 211, 428.

Leodamas of Thasos (Λεωδάμας ὁ Θάσιος) — fl. c. 380 BC

Contemporary of Archytas and Theaetetus; received the method of geometric analysis from Plato, discovering many things in geometry Friedlein loci: 66, 211.

Archytas of Tarentum (Ἀρχύτας ὁ Ταραντῖνος) — c. 428–347 BC

Increased the number of theorems and brought them into a more scientific arrangement alongside Leodamas and Theaetetus Friedlein loci: 66.

Theaetetus of Athens (Θεαίτητος ὁ Ἀθηναῖος) — c. 417–369 BC

Co-architect of Book X irrationals and Book XIII cosmic polyhedra; honored in the Eudemian Summary Friedlein loci: 66–67.

Neoclides (Νεοκλείδης) — fl. c. 375 BC

Younger than Leodamas and teacher of Leon; added many discoveries to those of his predecessors Friedlein loci: 66.

Leon (Λέων) — fl. c. 370 BC

Pupil of Neoclides who composed more careful Elements and discovered diorismoi determining when a sought problem is possible or impossible Friedlein loci: 66–67.

Speusippus (Σπεύσιππος) — c. 408–339 BC

Maintained against Menaechmus that all geometric propositions should be called ‘theorems’ rather than ‘problems’ because eternal objects have no temporal generation Friedlein loci: 77–78, 179, 181, 200.

Eudoxus of Cnidus (Εὔδοξος ὁ Κνίδιος) — c. 390–337 BC

Associate of Plato’s circle; first increased the number of general theorems, added three proportions, and extended Plato’s inquiries on ‘the section’ using analysis Friedlein loci: 67.

Xenocrates of Chalcedon (Ξενοκράτης) — c. 396–314 BC

Advocated indivisible lines (atomoi grammai), whose geometric impossibility Proclus demonstrates from Prop. I.10 (bisection of every finite segment) Friedlein loci: 277–279.

Amyclas of Heraclea (Ἀμύκλας ὁ Ἡρακλεώτης) — 4th cent. BC

Associate of Plato who collaborated in the Academy to perfect geometric science Friedlein loci: 67.

Menaechmus (Μέναιχμος) — fl. c. 350 BC

Analyzed the dual meaning of ‘element’ (stoicheion), defended ‘problems’ alongside ‘theorems’, and developed the theory of geometric conversion Friedlein loci: 67, 72–73, 78, 181, 254.

Aristotle (Ἀριστοτέλης) — 384–322 BC

Formulated the epistemology of axioms, postulates, and hypotheses, commensurately universal demonstration, and ‘intelligible matter’; critiqued by Proclus on abstraction Friedlein loci: 12–16, 48–53, 64, 75–76, 139, 178–183, 371, 381.

Dinostratus (Δεινόστρατος) — fl. c. 350 BC

Applied the quadratrix to the squaring of the circle and perfected geometry in the Academy Friedlein loci: 67.

Amphinomus (Ἀμφίνομος) — 4th cent. BC

Joined Speusippus on theorems vs. problems and collaborated with Menaechmus on the logic of convertible theorems Friedlein loci: 77, 181, 200, 202, 254.

Theudius of Magnesia (Θεύδιος ὁ Μάγνης) — 4th cent. BC

Arranged the Elements admirably and generalized many partial propositions Friedlein loci: 67.

Athenaeus of Cyzicus (Ἀθήναιος ὁ Κυζικηνός) — 4th cent. BC

Lived in the Academy with Eudoxus’s successors and became eminent in geometry and the other mathematical sciences Friedlein loci: 67.

Hermotimus of Colophon (Ἑρμότιμος ὁ Κολοφώνιος) — 4th cent. BC

Pursued the investigations begun by Eudoxus and Theaetetus, discovered many elements, and composed treatises on Loci Friedlein loci: 67.

Philippus of Medma (Mende) (Φίλιππος ὁ Μεδμαῖος) — fl. c. 340 BC

Carried out geometric investigations according to Plato’s instructions; marks the endpoint of Eudemus’s chronicle Friedlein loci: 67–68, 307.

Eudemus of Rhodes (Εὔδημος ὁ Ῥόδιος) — c. 370–300 BC

Pupil of Aristotle whose lost History of Geometry is Proclus’s primary source for pre-Euclidean geometry, Thales, Oenopides, the Pythagorean angle-sum proof, and application of areas Friedlein loci: 64–70, 125, 157, 250, 299, 333, 352, 379, 419.

Euclid & Hellenistic Mathematicians and Critics

Euclid (Εὐκλείδης) — fl. c. 300 BC

Synthesized the Elements under Ptolemy I, bringing to irrefutable demonstration what predecessors had proved loosely; revered by Proclus as Platonic by philosophical conviction Friedlein loci: 68–84, 208–432.

Archimedes of Syracuse (Ἀρχιμήδης) — c. 287–212 BC

Synchronism with Eratosthenes noted at p. 68; cited for shortest-path straight line definition, spirals, Equilibria of Planes, and crown hydrostatics Friedlein loci: 63, 68, 104, 110, 181, 272.

Eratosthenes of Cyrene (Ἐρατοσθένης) — c. 276–194 BC

Cited as contemporary of Archimedes and critic of the nature of proportion as the bond of mathematics Friedlein loci: 7, 43, 68.

Philo of Byzantium (Φίλων ὁ Βυζάντιος) — c. 280–220 BC

Devised a celebrated direct three-case proof of SSS triangle congruence (Prop. I.8) bypassing Euclid’s Prop. I.7 Friedlein loci: 266–268.

Nicomedes (Νικομήδης) — 3rd cent. BC

Invented the conchoidal lines (konchoeideis), cited by Geminus and Proclus both for angle trisection and as asymptotic curves that approach a line forever without meeting Friedlein loci: 111, 177, 272.

Apollonius of Perga (Ἀπολλώνιος ὁ Περγαῖος) — c. 240–190 BC

Transferred Pythagorean application-of-areas terms (parabola, hyperbola, ellipse) to conic sections; proposed alternative proofs for Common Notion 1 and Props. I.10, I.11, I.23 Friedlein loci: 71, 100, 183, 194, 279, 282, 335, 419.

Perseus (Περσεύς) — 2nd cent. BC

Investigated the three plane sections of the torus (speira), commemorated in an epigram preserved by Proclus Friedlein loci: 111–112.

Zeno of Sidon (Ζήνων ὁ Σιδώνιος) — c. 150–75 BC

Accepted Euclid’s principles solely to argue that Prop. I.1 still fails unless one also postulates that two straight lines (or circles) cannot share a common segment Friedlein loci: 199–200, 214–218.

Posidonius of Apamea (Ποσειδώνιος) — c. 135–51 BC

Wrote a dedicated treatise refuting Zeno of Sidon; proposed enclosing-limit definition of figure, equidistant definition of parallels, and sevenfold classification of quadrilaterals Friedlein loci: 80, 143, 170, 176, 200, 214–218.

Geminus of Rhodes (Γεμῖνος) — 1st cent. BC

Proclus’s richest Hellenistic source on classification of sciences, curves, postulates vs. axioms, uniform flux (quoted in Greek by Hoenen), and asymptotic cautions on Postulate 5 Friedlein loci: 38–42, 105, 111, 126, 176–192, 241, 251.

Heron of Alexandria (Ἥρων ὁ Ἀλεξανδρεύς) — 1st cent. AD

Reduced authentic Common Notions to three and supplied direct and construction-sparing proofs for Props. I.19, I.20, I.24, I.25, and I.47 Friedlein loci: 41, 196, 305, 323, 340, 346, 429.

Carpus of Antioch (Κάρπος ὁ Ἀντιοχεύς) — 1st/2nd cent. AD

Defined angle as distance/divergence between lines and argued in his Astronomical Treatise that problems precede theorems in natural order Friedlein loci: 125–126, 241–243.

Menelaus of Alexandria (Μενέλαος ὁ Ἀλεξανδρεύς) — c. 70–140 AD

Author of the Sphaerica; contributed a concise direct demonstration of Prop. I.25 (converse Hinge Theorem) preserved by Proclus Friedlein loci: 345–346.

Claudius Ptolemy (Κλαύδιος Πτολεμαῖος) — c. 100–170 AD

Composed a treatise attempting to prove Euclid’s Fifth Postulate; Proclus preserves Ptolemy’s lemmas and attempted proof of I.29 while diagnosing its circularity Friedlein loci: 191, 362–368.

Late Antique & Neoplatonic Commentators

Porphyry of Tyre (Πορφύριος) — c. 234–305 AD

Furnished incisive geometric analyses, case completions, and direct proofs in Book I (Props. I.14, I.18, I.20, I.24, I.26) Friedlein loci: 56, 255, 297, 315, 323–326, 347–352.

Iamblichus of Chalcis (Ἰάμβλιχος) — c. 245–325 AD

Inspired the Athenian Academy’s synthesis of Pythagorean-Platonic mathematics in his On Pythagoreanism / De Communi Mathematica Scientia Friedlein loci: 20–47.

Pappus of Alexandria (Πάππος ὁ Ἀλεξανδρεύς) — fl. c. 320 AD

Author of the celebrated zero-construction symmetry proof of Prop. I.5 (pons asinorum) and critical remarks on Postulate 4 converses and additional axioms Friedlein loci: 189, 197, 249–250, 429.

Plutarch of Athens (Πλούταρχος ὁ Ἀθηναῖος) — c. 350–432 AD

Teacher of Syrianus and aged mentor of young Proclus; cited with reverence on the multi-categorical nature of the angle Friedlein loci: 125.

Syrianus (Συριανός) — d. c. 437 AD

Expositor of ontological projection in phantasia and the horn-angle problem, whose lectures inspired Proclus’s Commentary Friedlein loci: 123, 125, 432.

Proclus Lycius Diadochus (Πρόκλος ὁ Διάδοχος) — 412–485 AD

Head of the Athenian Academy for nearly fifty years; composed the Commentary on Book I of Euclid’s Elements uniting Neoplatonic epistemology of phantasia, Eudemian history, and rigorous axiomatic analysis Friedlein loci: 1–436.

Marinus of Neapolis (Μαρῖνος ὁ Νεαπολίτης) — c. 440–500 AD

Succeeded Proclus at Athens, wrote Vita Procli, and authored the Preface to Euclid’s Data Friedlein loci: passim.

Renaissance & Modern Editors, Translators, and Scholars

Franciscus Barocius (Francesco Barozzi) — 1537–1604

Published the 1560 Padua Latin edition from Cretan and Venetian manuscripts, healing major corruptions and lacunae of the 1533 Basel Greek editio princeps Friedlein loci: ed. 1560.

Thomas Taylor — 1758–1835

Published the two-volume English translation (1788–1789; reissued 1792) defending Platonic mathematics against modern empiricism Friedlein loci: ed. 1788–1789.

Gottfried Friedlein — 1828–1875

Edited the standard 1873 Teubner critical Greek edition from Munich, Vatican, Bologna, and Oxford manuscripts Friedlein loci: ed. 1873.

Sir Thomas Little Heath — 1861–1940

Author of the monumental three-volume commentary in geometor/euclid, citing Friedlein’s Proclus at more than 150 loci Friedlein loci: Heath I–III.

Petrus H. J. Hoenen, S.J. — 1880–1961

Professor at the Pontifical Gregorian University (geometor/hoenen), engaging Proclus on sensible inexactitude, phantasia, intelligible matter, and Postulate 5 Friedlein loci: Hoenen 1954.