Prosopography of the Conic Tradition

Chronological register of ancient Greek geometers, Pergamene dedicatees, Alexandrian commentators, ninth-century Baghdad translators, seventeenth-century projective and analytic pioneers, and modern critical editors referenced via :person: across the codex.

Menaechmus (c. 380–320 BCE)

  • Original Name / Form: Μέναιχμος

  • Role: Discoverer of the conic sections

  • Heath (1896) Loci: pp. xvii–xxx

  • Contribution: Pupil of Eudoxus and associate of Plato; discovered the triad of conic sections (section of a right-angled, acute-angled, and obtuse-angled right cone cut perpendicular to a generator) while solving the Delian problem of two mean proportionals (x² = ay, y² = bx, xy = ab).

Aristaeus the Elder (fl. c. 330 BCE)

  • Original Name / Form: Ἀρισταῖος ὁ Πρεσβύτερος

  • Role: Author of the Five Books on Solid Loci

  • Heath (1896) Loci: pp. xxxi–xxxvi, lxxvi

  • Contribution: Composed the foundational Five Books concerning Solid Loci (Τόποι στερεοί) connected with the three conic sections prior to Euclid; Pappus records that Aristaeus retained the pre-Apollonian triad names based on three species of right cones.

Euclid of Alexandria (fl. c. 300 BCE)

  • Original Name / Form: Εὐκλείδης

  • Role: Author of the Elements, Conics (4 Books), and Surface Loci

  • Heath (1896) Loci: pp. xxxi–xl, lxxvii, lxxxvii–xcvi

  • Contribution: Compiled a lost four-book treatise on Conics subsequently absorbed and generalized by Books I–IV of Apollonius; furnished the exact geometrical-algebraic machinery (Elements Books II, III, V, VI, XII) upon which Apollonius grounds every symptom and proportion.

Archimedes of Syracuse (c. 287–212 BCE)

  • Original Name / Form: Ἀρχιμήδης ὁ Συρακούσιος

  • Role: Geometer of Quadrature of the Parabola and On Conoids and Spheroids

  • Heath (1896) Loci: pp. xli–lxvii, lxxxii

  • Contribution: Mastered extensive properties of conic sections prior to Apollonius using the pre-Apollonian names (‘section of a right-angled/acute-angled/obtuse-angled cone’), including oblique circular cones, subcontrary sections, and the two-abscissa proportion y² : x·x₁ = const.

Conon of Samos (c. 280–220 BCE)

  • Original Name / Form: Κόνων ὁ Σάμιος

  • Role: Court astronomer at Alexandria and precursor on intersecting conics

  • Heath (1896) Loci: pp. lxxii–lxxiii

  • Contribution: Friend of Archimedes and predecessor of Apollonius in investigating how many points two conic sections or a conic and a circle can have in common (Preface to Book IV), later critiqued by Nicoteles of Cyrene.

Nicoteles of Cyrene (fl. c. 230 BCE)

  • Original Name / Form: Νικοτέλης ὁ Κυρηναῖος

  • Role: Polemical critic of Conon on conic intersections

  • Heath (1896) Loci: pp. lxxii–lxxiii

  • Contribution: Addressed polemical replies to Conon of Samos concerning the number of intersections of conics; Apollonius notes in the Preface to Book IV that Nicoteles hinted at how the double-branch hyperbola meets another conic without supplying rigorous demonstrations.

Naucrates the Geometer (fl. c. 210 BCE)

  • Original Name / Form: Ναυκράτης ὁ Γεωμέτρης

  • Role: Instigator of the first draft of Apollonius’s Conics

  • Heath (1896) Loci: p. lxix

  • Contribution: Visiting geometer in Alexandria at whose request Apollonius hurriedly committed the initial unrevised eight-book draft of the Conics to writing before Naucrates set sail.

Eudemus of Pergamum (fl. c. 205 BCE)

  • Original Name / Form: Εὔδημος ὁ Περγαμηνός

  • Role: Scholarly dedicatee of Books I–III of the Conics

  • Heath (1896) Loci: pp. lxviii–lxxii

  • Contribution: Philosopher and mathematician at Pergamum to whom Apollonius addressed the Prefatory Letters of Books I and II (and originally Book III) before Eudemus’s death, sending Book II via Apollonius’s son of the same name.

Attalus of Pergamum (fl. c. 200 BCE)

  • Original Name / Form: Ἄτταλος

  • Role: Dedicatee of Books IV–VIII of the Conics

  • Heath (1896) Loci: pp. lxxii–lxxv

  • Contribution: Recipient of Apollonius’s Prefatory Letters to Books IV, V, VI, and VII following the death of Eudemus of Pergamum (traditionally identified either with King Attalus I Soter of Pergamum, r. 241–197 BCE, or a Pergamene mathematical patron).

Apollonius of Perga (c. 240–190 BCE)

  • Original Name / Form: Ἀπολλώνιος ὁ Περγαῖος

  • Role: ‘The Great Geometer’ (ὁ μέγας γεωμέτρης); author of the Conics

  • Heath (1896) Loci: pp. lxviii–clxx, 1–254

  • Contribution: Born at Perga in Pamphylia and educated at Alexandria under the pupils of Euclid; unified the theory of conics by cutting all three curves and the opposite branches from a single arbitrary oblique double cone, coining the enduring names parabola, ellipse, and hyperbola via application of areas.

Philonides of Laodicea (c. 200–130 BCE)

  • Original Name / Form: Φιλωνίδης

  • Role: Epicurean philosopher and geometer

  • Heath (1896) Loci: p. lxxii

  • Contribution: Commended to Eudemus by Apollonius at the close of the Preface to Book II (‘if Philonides the geometer whom I introduced to you in Ephesus should ever happen to visit the neighbourhood of Pergamum, communicate it to him also’); attested independently in Herculaneum papyrus PHerc. 1044.

Diocles (c. 240–180 BCE)

  • Original Name / Form: Διοκλῆς

  • Role: Author of On Burning Mirrors and discoverer of the focus-directrix property of the parabola

  • Heath (1896) Loci: pp. 113–118

  • Contribution: Contemporaneous Hellenistic geometer whose treatise On Burning Mirrors (preserved in Arabic) explicitly established the focal reflection property and focus-directrix construction of the parabola omitted from Book III of Apollonius.

Geminus of Rhodes (c. 110–40 BCE)

  • Original Name / Form: Γεμῖνος

  • Role: Historian and philosopher of Greek mathematics

  • Heath (1896) Loci: pp. lxviii, lxxvii

  • Contribution: Author of the lost Theory of the Mathematical Sciences quoted by Eutocius, preserving the testimony that contemporaries styled Apollonius ‘The Great Geometer’ for proving that every cone—right or scalene—yields all three conic sections.

Pappus of Alexandria (c. 290–350 CE)

  • Original Name / Form: Πάππος ὁ Ἀλεξανδρεύς

  • Role: Author of the Synagoge (Mathematical Collection)

  • Heath (1896) Loci: pp. xxxi–xxxvi, lxviii, lxxvii, cxxxviii–cl

  • Contribution: Preserved in Book VII of his Collection (Domain of Analysis, Τόπος ἀναλυόμενος) the sole surviving analytical syllabus, proposition counts, and 180+ auxiliary lemmas for Apollonius’s Conics and six lost analytic treatises (Tangencies, Plane Loci, Cutting Off of a Ratio, Cutting Off of an Area, Determinate Section, Inclinations), together with the focus-directrix theorem.

Hypatia of Alexandria (c. 355–415 CE)

  • Original Name / Form: Ὑπατία

  • Role: Neoplatonic philosopher, astronomer, and commentator on Apollonius

  • Heath (1896) Loci: p. lxviii

  • Contribution: Daughter of Theon of Alexandria; according to the Suda lexicon, composed a learned commentary on Apollonius’s Conics alongside commentaries on Diophantus and Ptolemy’s Handy Tables.

Eutocius of Ascalon (c. 480–540 CE)

  • Original Name / Form: Εὐτόκιος ὁ Ἀσκαλωνίτης

  • Role: Editor and commentator of Books I–IV of the Conics

  • Heath (1896) Loci: pp. xiii, lxviii, lxxvii

  • Contribution: Prepared the canonical late-antique Greek recension and commentary on Books I–IV of Apollonius dedicated to Anthemius of Tralles (architect of Hagia Sophia), ensuring the survival of the first four Books in Byzantine Greek manuscripts.

Banū Mūsā (Ahmad & al-Hasan ibn Shākir) (9th cent. CE (Baghdad))

  • Original Name / Form: Banū Mūsā

  • Role: Patrons and editors of the Arabic Conics Books I–VII

  • Heath (1896) Loci: pp. xiii, lxviii, lxxiv

  • Contribution: Commissioned the 9th-century Baghdad recovery and translation of Books I–VII of Apollonius’s Conics; Ahmad ibn Musa discovered a Damascus manuscript of Eutocius’s Books I–IV allowing the decipherment of the corrupt seven-book Arabic archetype.

Thābit ibn Qurra (836–901 CE)

  • Original Name / Form: Thābit ibn Qurra al-Ḥarrānī

  • Role: Translator into Arabic of Books V–VII of Apollonius’s Conics

  • Heath (1896) Loci: pp. xiii, lxviii, lxxiv

  • Contribution: Sabian mathematician and astronomer of Harran and Baghdad who translated Books V–VII of the Conics into Arabic (while Hilal ibn Abi Hilal al-Himsi translated Books I–IV) under the patronage of the Banu Musa—the sole textual channel through which Books V–VII survived.

Ibn al-Haytham (Alhazen) (c. 965–1040 CE)

  • Original Name / Form: Abū ʿAlī al-Ḥasan ibn al-Haytham

  • Role: Geometer of the Completion of the Conics

  • Heath (1896) Loci: p. lxviii

  • Contribution: Studied Thabit’s Arabic Conics deeply (copying a complete manuscript in his own hand in 1024 CE, MS Aya Sofya 2762) and authored Maqāla fī Tamām Kitāb al-Makhrūṭāt, reconstructing the lost Book VIII via determinate conic problems.

François Viète (1540–1603)

  • Original Name / Form: Franciscus Vieta

  • Role: Author of Apollonius Gallus (1600)

  • Heath (1896) Loci: p. lxviii

  • Contribution: Reconstructed Apollonius’s lost treatise On Tangencies (Περὶ ἐπαφῶν) in his Apollonius Gallus (1600), solving the Problem of Apollonius (CCC: constructing a circle tangent to three given circles) by pure Euclidean compass-and-straightedge reductions.

Johannes Kepler (1571–1630)

  • Original Name / Form: Ioannes Keplerus

  • Role: Coined the term focus (1604) and discovered elliptical planetary orbits (1609)

  • Heath (1896) Loci: pp. 113–118

  • Contribution: Turned Apollonius’s pure geometry into celestial mechanics in Astronomia Nova (1609) and introduced in Ad Vitellionem Paralipomena (1604) both the modern name ‘foci’ (burning points) for Apollonius’s ‘points arising from the application’ and the principle of projective continuity uniting all conics.

René Descartes (1596–1650)

  • Original Name / Form: Renatus Cartesius

  • Role: Founder of analytic coordinate geometry via Pappus’s Three- and Four-Line Locus

  • Heath (1896) Loci: pp. cxxxviii–cl, 119–125

  • Contribution: Made the Apollonian-Pappus Three-Line and Four-Line Locus (Book III Props. 53–56; Pappus Book VII) the centerpiece test problem of La Géométrie (1637), proving algebraically that every three- or four-line locus is a quadratic curve and launching symbolic algebraic geometry.

Girard Desargues (1591–1661)

  • Original Name / Form: Girard Desargues

  • Role: Founder of synthetic projective conic geometry (Brouillon project, 1639)

  • Heath (1896) Loci: pp. 102–108

  • Contribution: Extended Apollonius’s oblique-cone generation and Book III harmonic pole-polar properties into universal projective geometry in his Brouillon project d’une atteinte aux événemens des rencontres du cône avec un plan (1639), introducing involutions and points at infinity.

Blaise Pascal (1623–1662)

  • Original Name / Form: Blasius Pascalis

  • Role: Author of the Essay pour les coniques (1640)

  • Heath (1896) Loci: pp. cli–clvi

  • Contribution: At age sixteen generalized Pappus’s hexagon theorem from a degenerate line-pair to any non-degenerate Apollonian conic section via central projection on the cone (Hexagrammum Mysticum).

Sir Isaac Newton (1642–1727)

  • Original Name / Form: Isaacus Newtonus

  • Role: Author of Principia Book I Sections IV–V (organic construction & five-point conics)

  • Heath (1896) Loci: pp. cxxxviii–clvi

  • Contribution: Vindicated Greek synthetic conic geometry in Principia Mathematica (1687, Book I Lemmas XVII–XXVII), praising the elegance of the Ancients’ Three- and Four-Line Locus and constructing conics from five points and tangents.

Edmond Halley (1656–1742)

  • Original Name / Form: Edmundus Halleius

  • Role: Savilian Professor of Geometry; editor of the monumental 1710 Oxford Conics

  • Heath (1896) Loci: pp. vii–xiii, lxviii

  • Contribution: Published De Sectione Rationis (1706, learning Arabic directly from Bodleian manuscripts) and the monumental folio editio princeps Apollonii Pergaei Conicorum Libri Octo (Oxford, 1710), presenting Books I–IV in Greek and Latin, Books V–VII in Latin from Thabit ibn Qurra’s Arabic MS Bodleian Marsh 667, and a conjectural Book VIII.

Hieronymus Georg Zeuthen (1839–1920)

  • Original Name / Form: H. G. Zeuthen

  • Role: Historian of Greek conic geometry (Die Lehre von den Kegelschnitten im Altertum, 1886)

  • Heath (1896) Loci: pp. vii–xiii, lxxxii, cxxxviii–cl

  • Contribution: Danish mathematician whose 1886 treatise uncovered the geometric-algebraic coordinate architecture of Apollonius and reconstructed how Book III Props. 41–56 supply the synthetic proof of the Three-Line and Four-Line Locus.

Johan Ludvig Heiberg (1854–1928)

  • Original Name / Form: I. L. Heiberg

  • Role: Critical Teubner editor of Apollonius (1891–1893), Euclid, and Archimedes

  • Heath (1896) Loci: pp. vii, xiii, lxviii

  • Contribution: Established the definitive critical Greek text of Apollonius’s Books I–IV, ancient fragments, Pappus’s lemmas, and Eutocius’s commentaries in two Teubner volumes (1891, 1893) from Codex Vaticanus Graecus 206 (12th–13th c.).

Sir Thomas Little Heath (1861–1940)

  • Original Name / Form: T. L. Heath

  • Role: Editor of the Cambridge Greek Mathematical Trilogy: Apollonius (1896), Archimedes (1897), Euclid (1908)

  • Heath (1896) Loci: pp. vii–clxx, 1–254

  • Contribution: Published at Cambridge University Press in 1896 the landmark English edition of Apollonius’s Conics (Books I–VII in 147 consolidated propositions preserving all 387 classical bracketed references, preceded by a 170-page historical and analytical introduction), launching the Cambridge trilogy completed by Archimedes (1897/1912) and Euclid (1908).