Works & Method of Archimedes

ΑΡΧΙΜΗΔΟΥΣ ΤΟΥ ΣΥΡΑΚΟΥΣΙΟΥ

ΤΑ ΣΩΖΟΜΕΝΑ ΑΠΑΝΤΑ ΚΑΙ ΕΦΟΔΟΣ

ARCHIMEDIS OPERA OMNIA CUM COMMENTARIIS EUTOCII

The Works of Archimedes (1897) & The Method of Archimedes (1912)

Critical Greek & Latin Edition: Johan Ludvig Heiberg (Leipzig: B. G. Teubner, 1880–1881 / 1910–1915)

Public-Domain English Edition: Sir Thomas Little Heath (Cambridge University Press, 1897 & Supplement, 1912)

“Give me a place to stand on, and I can move the earth.” (δός μοι ποῦ στῶ καὶ κινῶ τὴν γῆν.)

—Archimedes of Syracuse, preserved by Pappus of Alexandria, Synagoge VIII

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Conspectus Totius Operis

This Seven-Unit Synchronized Book Codex unites the entire classical and Palimpsest canon of Archimedes of Syracuse (c. 287–212 BC) from T. L. Heath's Cambridge editions (heath:1897, heath:1912) collated directly against 300 DPI archival scans of J. L. Heiberg's critical Teubner Greek and Latin editions (heiberg:1880, heiberg:1881). Every unit provides three synchronized reading tracks: English (folio-anchored primary translation with calibrated .euclid-graphic vector plates), Summary (deductive architecture & theorem tables), and Notes (Doric/Koine philology, Eutocian scholia, and GEOMETOR cross-corpus concordances).

• Unit 1 — Measurement of a Circle (Κύκλου μέτρησις · Heiberg I, 258–271 · Heath 1897, pp. 91–98): Measurement of a Circle (Props. 1–3) — Double exhaustion of circle area by a right triangle () and rational 96-gon bisection bounding . (English · Summary · Notes)

• Unit 2 — On the Equilibrium of Planes, Books I–II (Ἐπιπέδων ἰσορροπιῶν αʹ βʹ · Heiberg II, 142–241 · Heath 1897, pp. 189–220): On the Equilibrium of Planes I–II — Seven Postulates of static equilibrium, the commensurable and incommensurable Law of the Lever (I.6–7), the foundational synthetic proof of the triangle centroid X(2) (I.13–14, geometor:etc), and the centroid of the parabolic segment (II.8). (English · Summary · Notes)

• Unit 3 — Quadrature of the Parabola (Τετραγωνισμὸς παραβολῆς · Heiberg II, 294–353 · Heath 1897, pp. 233–252): Quadrature of the Parabola (Props. 1–24) — Epistle to Dositheus, Archimedes' Lemma, mechanical balance quadrature (Props. 1–17), and geometric exhaustion proving (Props. 18–24). (English · Summary · Notes)

• Unit 4 — Sphere and Cylinder, Spirals & Conoids (Περὶ σφαίρας καὶ κυλίνδρου · Περὶ ἑλίκων · Περὶ κωνοειδέων καὶ σφαιροειδέων · Heiberg I & II · Heath 1897, pp. 1–90, 99–188): Sphere and Cylinder, On Spirals & Conoids and Spheroids — Convexity postulates (ἐπὶ τὰ αὐτὰ κοῖλα), surface and the Tomb Theorem of the sphere and cylinder, Eutocius’s cubic intersection for II.4, kinematic spiral subtangent rectification and sector quadrature, and cubature of paraboloids, hyperboloids, and spheroids. (English · Summary · Notes)

• Unit 5 — Book of Lemmas (*Liber Assumptorum*) (Kitāb al-Maʾkhūdhāt · Heiberg II, 426–445 · Heath 1897, pp. 301–318): Book of Lemmas (Propositions 1–15) — Complete 15-proposition planar treasury preserved by Thābit ibn Qurra: the Arbelos (Prop. 4), Archimedes' Twin Circles (Prop. 5), the inscribed circle and Pappus's infinite circle chain (Prop. 6), neusis angle trisection (Prop. 8), orthogonal-chord quadrance invariant (Prop. 11), the Salinon (Prop. 14), and golden-ratio pentagon/decagon secants (Prop. 15). (English · Summary · Notes)

• Unit 6 — The Method of Mechanical Theorems (*Ephodos*) (Περὶ τῶν μηχανικῶν θεωρημάτων πρὸς Ἐρατοσθένην ἔφοδος · Heiberg 1907 / II², 426–507 · Heath 1912, pp. 12–51): The Method Addressed to Eratosthenes (Props. 1–15) — Recovered by Heiberg from the Constantinople Palimpsest in 1906: Archimedes’ epistle to Eratosthenes crediting Democritus and Eudoxus, slice-balancing discovery of the parabola and sphere, and cubature of the cylindrical ungula (Props. 12–14) and bicylinder (Prop. 15). (English · Summary · Notes)

• Unit 7 — Thirteen Semi-Regular Solids, *Stomachion* & *The Sand-Reckoner* (Ψαμμίτης · Στομάχιον · Τρισκαίδεκα στερεά · Heiberg II, 242–291 · Heath 1897, pp. xxxvi, 221–232 · Pappus V.19): Semi-Regular Solids, Stomachion & The Sand-Reckoner — Complete structural concordance of the 13 Archimedean Polyhedra with geometor/pacioli and \(\mathbb{Q}(\phi)\), the 14-piece Stomachion dissection, and The Sand-Reckoner to King Gelon preserving Aristarchus's heliocentric cosmos and the myriad-octad exponential calculus up to . (English · Summary · Notes)

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Apparatus Criticus & Cross-Corpus Indices

• Heiberg–Heath–GEOMETOR Concordance — Master cross-reference of all 34 canonical proposition & treatise loci across euclid, elements, etc, pappus, pacioli, divine, wildberger, proclus, and hilbert.

• Bibliography & Critical Editions — Archival editions, ancient scholia, and GEOMETOR companion codices (covering 100% of geometor/euclid Archimedes citation keys).

• Prosopography (Index Personarum) — Chronological register of 27 geometers, astronomers, Syracusan patrons, translators, and philologists.

• Greek–Latin–English Technical Glossary — Lexicon of 23 Doric, Koine, Arabic-Latin, and modern geometric terms.