Index Nominum (Persons)

Prosopographical register of geometers, astronomers, philosophers, commentators, medieval translators, and critical editors connected with Hero of Alexandria’s mathematical corpus.

Classical Geometers & Philosophers

Eupalinus of Megara (Εὐπαλῖνος ὁ Μεγαρεύς) — fl. c. 530 BCE

Excavated the 1,036-meter two-portal aqueduct tunnel through Mount Kastro on Samos from both hillsides simultaneously; Hero’s Dioptra Ch. 15 preserves the classical Hellenistic geometric solution to the two-portal mountain-tunneling problem. Loci: Dioptra Ch. 15 (historical engineering archetype).

Plato (Πλάτων) — 427–347 BCE

Named by Hero in Metrica II.15–19 as eponym of the Five Platonic Solids (cube, pyramid/tetrahedron, octahedron, icosahedron, dodecahedron) from the Timaeus, and echoed in Metrica III’s Prooemium on proportional distributive justice (Laws VI 757b–c). Loci: Metrica II.15 (Schöne p. 132), III Preface (Schöne p. 140).

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

Architect of the theory of quadratic irrationals (Elements X) and exact edge-to-circumradius constructions of the five regular solids (Elements XIII), which Hero translates into explicit edge-to-volume algorithms in Metrica II.16–19. Loci: Metrica II.16–19 (Schöne pp. 132–138).

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

Explicitly credited in Hero’s Preface to Metrica Book II (together with Archimedes) as demonstrating before Archimedes that every cylinder is triple the cone on the same base and equal height, and every prism triple the pyramid. Loci: Metrica II Preface (Schöne p. 90–92).

Aristotle of Stagira (Ἀριστοτέλης ὁ Σταγειρίτης) — 384–322 BCE

Formulates proportional distributive justice in Nicomachean Ethics V.3 (echoed in Hero’s Metrica III Prooemium) and the teleological principle ‘nature does nothing in vain’ invoked in Olympiodorus’s Commentary on Meteorology III.2 preserving Hero’s Catoptrica shortest-path proof. Loci: Metrica III Preface; Catoptrica Greek Fragment.

Hellenistic Mathematicians & Astronomers

Euclid of Alexandria (Εὐκλείδης ὁ Ἀλεξανδρεύς) — fl. c. 300 BCE

Provides the deductive backbone of Hero’s geometric analyses (‘given in magnitude and form’ via the Data, angle bisectors and cyclic quadrilaterals in Books III–IV, golden-section pentagon ratios in Book XIII, and area/solid divisions extending Euclid’s lost On Divisions of Figures in Metrica Book III). Loci: Metrica I.5–8, I.18, I.23, II.16–19, III.1–19; Definitiones passim.

Archimedes of Syracuse (Ἀρχιμήδης ὁ Συρακούσιος) — c. 287–212 BCE

Hero’s supreme mathematical authority throughout Books I and II of the Metrica; Hero cites Measurement of a Circle, On the Sphere and Cylinder, Quadrature of the Parabola, On Conoids and Spheroids, the lost Plinthides and Cylinders, and—uniquely before the 1906 Archimedes Palimpsest discovery—the Mechanical Method (Ἐφοδικόν). Arabic witnesses (al-Bīrūnī) also credit Archimedes with discovering the triangle area theorem proved in Metrica I.8. Loci: Metrica I.26, I.31–32, I.35, I.37–39; II.11–12, II.14–15 (Method), II.20 (hydrostatic crown/bath displacement).

Dionysodorus of Caunos (or Melos) (Διονυσόδωρος) — fl. c. 200 BCE

Hellenistic geometer whose lost treatise On the Torus (Περὶ τῆς σπείρας) is preserved solely through Hero’s citation in Metrica II.13, establishing that the volume of a torus equals a cylinder on the centroid radius scaled by the ratio of the generating circle to half its meridian rectangle (V = 2π²Rr²). Loci: Metrica II.13 (Schöne pp. 126–130).

Hipparchus of Nicaea (Ἵππαρχος ὁ Νικαεύς) — c. 190–120 BCE

Pioneer of the treatise On Chords in a Circle (Περὶ τῶν ἐν κύκλῳ εὐθειῶν), the chord-table tradition invoked by Hero in Metrica I.22 and I.24 to compute the regular enneagon (9-gon) and hendecagon (11-gon). Loci: Metrica I.22, I.24 (Schöne pp. 58–62); Dioptra Ch. 35.

Posidonius of Apamea (Ποσειδώνιος ὁ Ἀπαμεύς) — c. 135–51 BCE

Source for several kinematic and physical-conceptual supplements in Hero’s Definitiones and Proclus’s Commentary on Book I, defending Euclidean postulates and classifying quadrilaterals and parallels. Loci: Definitiones §§1–14, §§50–65.

Roman Imperial Geometers & Physicists

Hero (Heron) of Alexandria (Ἥρων ὁ Ἀλεξανδρεύς) — fl. c. 60 CE

Author of the Metrica, Dioptra, Mechanica, Pneumatica, Automata, Catoptrica, and Definitiones; dated securely via the lunar eclipse of 13 March 62 CE recorded in Dioptra Ch. 35. Unified Euclidean synthetic demonstration with Archimedean exhaustion and Babylonian-Egyptian numerical calculation. Loci: Metrica I–III passim; Dioptra Chs. 1–38; Catoptrica Prop. 4 (Schmidt pp. 324–329, 368–372); Definitiones §§1–138.

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

Paired with Hero by Olympiodorus as co-witness of the shortest-path reflection demonstration in Optics and Catoptrica, and successor to the chord-table tradition cited in Metrica I.22–24. Loci: Catoptrica Greek Fragment (Schmidt p. 368).

Late Antique & Medieval Commentators and Translators

Pappus of Alexandria (Πάππος ὁ Ἀλεξανδρεύς) — fl. c. 320–340 CE

Preserves extensive testimony to Hero’s Mechanics in Synagoge Book VIII and generalizes the torus centroid principle anticipated by Hero’s ‘unrolled cylinder’ proof in Metrica II.13 into the Pappus-Guldin Centroid Theorem (Synagoge VII.42). Loci: Metrica II.13 (centroid unrolling parallel).

Proclus Diadochus (Πρόκλος ὁ Διάδοχος) — 412–485 CE

Repeatedly cites ‘Heron the Mechanician’ (Ἥρων ὁ μηχανικός) in his Commentary on Euclid Book I—recording Hero’s proofs without reductio ad absurdum, his kinematic constructs, and his Economy of Postulates reducing Euclid’s postulates to three. Loci: Proclus In Euclidem Friedlein pp. 196, 305, 323–326, 340–346, 429.

Eutocius of Ascalon (Εὐτόκιος ὁ Ἀσκαλωνίτης) — c. 480–540 CE

Attests explicitly in his commentary on Archimedes’ Measurement of a Circle that Hero explained the extraction of approximate square roots of non-square numbers in his Metrica. Loci: Metrica I.8 (square-root iteration testimony).

Olympiodorus the Younger (Ὀλυμπιόδωρος) — c. 495–570 CE

In his Commentary on Aristotle’s Meteorology III.2, Olympiodorus preserves verbatim the original Greek text of Hero’s variational shortest-path proof of the Law of Reflection from Hero’s Catoptrica. Loci: Catoptrica Greek Fragment (Schmidt pp. 368–372).

Abū Rayḥān al-Bīrūnī — 973–1048 CE

In his Book on the Finding of Chords in the Circle, al-Bīrūnī preserves the medieval Islamic geometric tradition attributing the triangle area rule Δ = √(s(s−a)(s−b)(s−c)) originally to Archimedes, whose earliest surviving Greek proof is Hero’s Metrica I.8. Loci: Metrica I.8; Dioptra Ch. 30.

William of Moerbeke — c. 1215–1286 CE

Translated Hero’s Catoptrica (under the title De speculis, long attributed to Ptolemy) and Archimedes’ treatises into Latin at Viterbo in 1269, preserving the full proposition sequence of the Catoptrica alongside Olympiodorus’s Greek fragment. Loci: Catoptrica Prop. 4 (Schmidt pp. 316–365).

Modern Philologists, Historians & Mathematicians

Friedrich Otto Hultsch — 1833–1906

Edited Heronis Alexandrini Geometricorum et Stereometricorum Reliquiae (Berlin: Weidmann, 1864), establishing the first critical Greek edition of the Definitiones and the Byzantine metrological compilations (Geometrica, Stereometrica, Geodaesia) before the rediscovery of the authentic Metrica. Loci: Definitiones §§1–138 (Hultsch 1864).

Richard Schöne — 1840–1922

Identified the lost Metrica of Hero of Alexandria in 1896 inside Codex Constantinopolitanus Palatii Veteris 1 in Constantinople and entrusted its editio princeps to his son Hermann Schöne. Loci: Codex Constantinopolitanus 1 rediscovery (1896).

Wilhelm Schmidt — 1862–1905

Edited Vols. I and II.1 of the Teubner Opera omnia of Hero of Alexandria (Pneumatica, Automata, Mechanica, and Catoptrica, 1899–1900), decisively restoring the Catoptrica (De speculis) from pseudo-Ptolemy to Hero. Loci: Catoptrica (Teubner Vol. II.1, 1900).

Hermann Schöne — 1870–1941

Following Richard Schöne’s and Paul Tannery’s identification of the unique 11th-century Constantinople manuscript (Codex Constantinopolitanus Palatii Veteris 1) in 1896, Hermann Schöne published the landmark 1903 Teubner editio princeps of Hero’s Metrica and critical text of the Dioptra. Loci: Metrica I–III & Dioptra (Teubner Vol. III, 1903).

Johan Ludvig Heiberg — 1854–1928

Edited Teubner Hero Vols. IV–V (Definitiones, Geometrica, Stereometrica, 1912–1914) and discovered the Archimedes Palimpsest in Constantinople in 1906, confirming every quotation from Archimedes’ Method (Ἐφοδικόν) preserved in Hero’s Metrica I–II. Loci: Definitiones (Teubner Vol. IV, 1912); Metrica citations of Archimedes’ Method.

Sir Thomas Little Heath — 1861–1940

Synthesized Hero’s mathematical corpus across The Thirteen Books of Euclid’s Elements (1908, preserved in geometor/euclid) and A History of Greek Mathematics Vol. II (1921, pp. 298–354). Loci: geometor/euclid Heath commentary; History of Greek Mathematics II.298–354.

Otto Neugebauer — 1899–1990

Established the definitive chronological anchor for Hero of Alexandria in 1938 by proving that the lunar eclipse observed simultaneously at Alexandria and Rome in Dioptra Ch. 35 occurred on 13 March 62 CE, and traced the Babylonian root-extraction background of Metrica I.8. Loci: Dioptra Ch. 35 eclipse dating (62 CE); Metrica I.8.

Norman J. Wildberger — b. 1955

Formulates Archimedes’ Function / Quadrea A = 16Δ² = (Q₁ + Q₂ + Q₃)² − 2(Q₁² + Q₂² + Q₃²) and rational spread/quadrance laws over arbitrary fields without square roots or transcendental functions, directly illuminating the algebraic core of Hero’s Metrica I.8. Loci: geometor/wildberger W.07 (Archimedes’ Function / Quadrea).