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Bibliography & Critical Editions¶

Archival editions, ancient mathematical commentaries, and GEOMETOR companion codices referenced via the :cite: role throughout the Works and Method of Archimedes.

Critical Greek, Latin & Public-Domain English Editions¶

[heath:1897] — Archimedes of Syracuse (ed. & trans. T. L. Heath), The Works of Archimedes, edited in modern notation with introductory chapters (Cambridge: At the University Press, 1897 (clxxxvi + 326 pp.)). Primary public-domain English edition covering Sphere and Cylinder I–II, Measurement of a Circle, Conoids and Spheroids, On Spirals, Equilibrium of Planes I–II, The Sand-Reckoner, Quadrature of the Parabola, On Floating Bodies I–II, Book of Lemmas, and the Cattle Problem. Archive: https://archive.org/details/worksofarchimede00arch.
[heath:works-of-archimedes] — Archimedes of Syracuse (ed. & trans. T. L. Heath), The Works of Archimedes (Cambridge: At the University Press, 1897). Cross-corpus canonical citation key matching geometor/euclid. Archive: https://archive.org/details/worksofarchimede00arch.
[heath:1912] — Archimedes of Syracuse (ed. & trans. T. L. Heath), The Method of Archimedes, Recently Discovered by Heiberg: A Supplement to The Works of Archimedes, 1897 (Cambridge: At the University Press, 1912 (51 pp.)). Public-domain Cambridge supplement translating Archimedes’ Palimpsest treatise On Mechanical Theorems Addressed to Eratosthenes (Ephodos) from Heiberg’s 1907 Greek transcription. Archive: https://archive.org/details/methodofarchimed00archiala.
[heath:method-of-archimedes] — Archimedes of Syracuse (ed. & trans. T. L. Heath), The Method of Archimedes, Recently Discovered by Heiberg (Cambridge: At the University Press, 1912). Cross-corpus canonical citation key matching geometor/euclid. Archive: https://archive.org/details/methodofarchimed00archiala.
[heiberg:1880] — Archimedes of Syracuse (ed. Johan Ludvig Heiberg), Archimedis Opera Omnia cum commentariis Eutocii, Vol. I (Leipzig: B. G. Teubner, 1880 (2nd rev. ed. 1910)). Critical Teubner Greek text of De Sphaera et Cylindro I–II, Dimensio Circuli, and De Conoidibus et Sphaeroidibus. Archive: https://archive.org/details/archimedisoperao01arch.
[heiberg:1881] — Archimedes of Syracuse (ed. Johan Ludvig Heiberg), Archimedis Opera Omnia cum commentariis Eutocii, Vol. II (Leipzig: B. G. Teubner, 1881 (2nd rev. ed. 1913)). Critical Teubner text of De Lineis Spiralibus, De Planorum Aequilibriis I–II, Arenarius, Quadratura Parabolae, De Corporibus Fluitantibus, Stomachion, Ephodos (Methodus, added in 1913 2nd ed., pp. 425–507), and Liber Assumptorum (pp. 426–445 / 510–525). Archive: https://archive.org/details/archimedisoperao02arch.
[heiberg:archimedis-opera] — Archimedes of Syracuse (ed. Johan Ludvig Heiberg), Archimedis Opera Omnia cum commentariis Eutocii (Vols. I–III) (Leipzig: B. G. Teubner, 1880–1881 (2nd ed. 1910–1915)). Cross-corpus canonical Teubner citation key matching geometor/euclid. Archive: https://archive.org/details/archimedisoperao01arch.
[heiberg:1907] — Johan Ludvig Heiberg, Eine neue Archimedeshandschrift (Hermes: Zeitschrift für classische Philologie 42 (1907), pp. 235–303). Editio princeps of the Greek text of Archimedes’ Method deciphered from the 10th-century Constantinople Palimpsest (Codex C) in 1906.
[venatorius:1544] — Thomas Gechauff Venatorius (ed.), Ἀρχιμήδους τοῦ Συρακουσίου τὰ μέχρι νῦν σωζόμενα ἅπαντα (Archimedis Syracusani Philosophi ac Geometrae Excellentissimi Opera, Editio Princeps) (Basel: Ioannes Hervagius, 1544). First printed Greek and Latin edition of Archimedes and Eutocius’s commentaries.
[ecchellensis-borelli:1661] — Abraham Ecchellensis & Giovanni Alfonso Borelli (eds.), Archimedis Liber Assumptorum, interprete Thebit Ben-Kora exponente Almochtasso (Florence: Ex Typographia Stellae, 1661 (appended to Apollonii Pergaei Conicorum Lib. V–VII)). First Latin edition of Archimedes’ fifteen Lemmas translated from Thābit ibn Qurra’s Arabic version.

Ancient & Medieval Mathematical Witnesses¶

[archimedes:sphere-and-cylinder] — Archimedes of Syracuse, On the Sphere and Cylinder (Περὶ σφαίρας καὶ κυλίνδρου, Books I–II) (Heiberg I, 1–255; Heath 1897, pp. 1–90). Establishes convexity assumptions, Archimedes’ Lemma, and the 2:3 sphere-to-cylinder volume and surface theorem.
[archimedes:sphere-and-cylinder:ii-2] — Archimedes of Syracuse, On the Sphere and Cylinder, Book II, Prop. 2 (Heiberg I, 194–203; Heath 1897, pp. 59–62). Cubature of any spherical segment reduced to an equivalent cone.
[archimedes:conoids-and-spheroids] — Archimedes of Syracuse, On Conoids and Spheroids (Περὶ κωνοειδέων καὶ σφαιροειδέων) (Heiberg I, 272–499; Heath 1897, pp. 99–150). Quadrature of the ellipse and cubature of paraboloids, hyperboloids, and ellipsoids of revolution.
[archimedes:equilibrium-of-planes:i-7] — Archimedes of Syracuse, On the Equilibrium of Planes (Ἐπιπέδων ἰσορροπιῶν), Book I, Prop. 7 (Heiberg II, 154–159; Heath 1897, pp. 193–194). Proof of the Law of the Lever for incommensurable magnitudes via Eudoxean approximation.
[archimedes:quadrature-of-parabola] — Archimedes of Syracuse, Quadrature of the Parabola (Τετραγωνισμὸς παραβολῆς) (Heiberg II, 294–353; Heath 1897, pp. 233–252). Dual mechanical (Props. 1–17) and geometric exhaustion (Props. 18–24) proof that a parabolic segment equals 4/3 of its inscribed triangle.
[archimedes:liber-assumptorum] — Archimedes of Syracuse (tr. Thābit ibn Qurra), Book of Lemmas (Liber Assumptorum / Kitāb al-Maʾkhūdhāt) (Heiberg II, 426–445; Heath 1897, pp. 301–318). Fifteen planar lemmas preserving the Arbelos, Twin Circles, Neusis Trisection, Salinon, and golden-ratio pentagon/decagon secants.
[archimedes:methodus] — Archimedes of Syracuse, The Method of Mechanical Theorems Addressed to Eratosthenes (Ἔφοδος) (Heiberg II (2nd ed.), 426–507; Heath 1912, pp. 12–51). Palimpsest treatise unveiling Archimedes’ analytic mechanical slice method and proving the cubature of the cylindrical ungula and bicylinder.
[euclid:elements] — Euclid of Alexandria, Elements (Στοιχεῖα, Books I–XIII) (Heath ed. 1908 (geometor/euclid & geometor/elements)). Axiomatic foundation presupposed throughout Archimedes’ canon: especially I.47 (Pythagoras), III.31 & III.35 (chords & semicircles in Arbelos/Salinon), V.Def.4 (Eudoxean ratio), VI.3 (angle bisector in Measurement Prop. 3), X.1 (exhaustion lemma), and XII.2, 7, 10, 18 (circles, pyramids, cones, spheres).
[eutocius:in-archimedem] — Eutocius of Ascalon, Commentarii in libros De Sphaera et Cylindro, In Dimensionem Circuli, In libros De Planorum Aequilibriis (Heiberg Vol. III (Teubner, 1881 / 1915)). Sole ancient Greek commentary on Archimedes: supplies explicit numerical multiplications for Measurement Prop. 3, preserves Archimedes’ lost cubic-section lemma for Sphere and Cylinder II.4, and records twelve classical solutions to two mean proportionals.
[pappus:synagoge:iv] — Pappus of Alexandria, Mathematical Collection (Συναγωγή), Book IV (Props. 14–25 & 36–44 (ed. Hultsch, Vol. I, 1876)). Preserves the ‘ancient proposition’ on the infinite chain of tangent circles in the Arbelos (cn = n·dn), studies the Archimedean spiral, and classifies solid vs. neusis angle trisections.
[pappus:synagoge:v] — Pappus of Alexandria, Mathematical Collection (Συναγωγή), Book V, Prop. 19 (Hultsch Vol. I, pp. 350–358 (1876)). Primary ancient witness recording the exact face counts and polygon species of all thirteen Semi-Regular Solids discovered by Archimedes.
[pappus:synagoge:viii] — Pappus of Alexandria, Mathematical Collection (Συναγωγή), Book VIII (Hultsch Vol. III, pp. 1022–1147 (1878)). Extends Archimedes’ theory of centers of gravity (κέντρα βαρῶν) and leads directly to the Pappus–Guldin centroid theorem.
[heron:metrica] — Heron of Alexandria, Metrica (Μετρικά, Books I–III) (ed. Hermann Schöne (Teubner, 1903)). Explicitly quotes Archimedes’ Measurement of a Circle, Sphere and Cylinder, Equilibrium, and The Method (ungula and bicylinder).
[proclus:in-euclidem] — Proclus Diadochus, Commentary on the First Book of Euclid’s Elements (Friedlein pp. 63, 110 (geometor/proclus)). Cites Archimedes’ postulate that the straight line is the shortest of lines having the same extremities (Friedlein 110) and Hiero’s crown/ship narratives (Friedlein 63).

GEOMETOR Ecosystem & Modern Axiomatic Concordances¶

[geometor:euclid] — Sir Thomas Little Heath / GEOMETOR, GEOMETOR • euclid & elements: The Thirteen Books of Euclid’s Elements (geometor/euclid & geometor/elements). Sister Digital Scriptorium edition of Heath’s Euclid and computable G-Index dependency DAG.
[geometor:etc] — Clark Kimberling / GEOMETOR, GEOMETOR • etc: Encyclopedia of Triangle Centers (X(2) Centroid & Homogeneous Barycentric Coordinates (geometor/etc)). Archimedes’ On the Equilibrium of Planes I.13–14 provides the foundational synthetic proof of X(2) (intersection of medians) and homogeneous barycentric coordinates (1 : 1 : 1).
[geometor:pacioli] — Luca Pacioli / GEOMETOR, GEOMETOR • pacioli: De Divina Proportione (1509) (geometor/pacioli). Renaissance reconstruction of the truncated and semi-regular Archimedean polyhedra illustrated by Leonardo da Vinci.
[geometor:pappus] — Pappus of Alexandria / GEOMETOR, GEOMETOR • pappus: Projective & Classical Configurations from the Synagoge (geometor/pappus). Companion constructive repository linking Pappus’s Collection (harmonic conjugates, circle chains, and semi-regular polyhedra) to Archimedes.
[geometor:wildberger] — N. J. Wildberger / GEOMETOR, GEOMETOR • wildberger: Divine Proportions & Rational Trigonometry (Archimedes’ Function / Quadrea A(Q1, Q2, Q3) (geometor/wildberger)). Formalizes Archimedes’ algebraic invariant A(Q1, Q2, Q3) = (Q1 + Q2 + Q3)^2 - 2(Q1^2 + Q2^2 + Q3^2) = 16·Area^2 governing collinearity, Heron/Archimedes triangle area, and rational circle tangency.
[hilbert:1899] — David Hilbert / GEOMETOR, Grundlagen der Geometrie (Foundations of Geometry) (Axiom Group V: Axiom of Continuity / Archimedes’ Axiom (geometor/hilbert)). Elevates Archimedes’ Lemma (Sphere and Cylinder I Assump. 5) into Axiom V 1 of modern axiomatic geometry and demonstrates non-Archimedean ordered fields.