Almagest I & Planisphaerium

ΚΛΑΥΔΙΟΥ ΠΤΟΛΕΜΑΙΟΥ

ΜΑΘΗΜΑΤΙΚΗΣ ΣΥΝΤΑΞΕΩΣ ΒΙΒΛΙΟΝ ΠΡΩΤΟΝ (ΚΕΦ. Αʹ–ΙΔʹ)

ET PLANISPHAERIUM

Mathematical Systematic Treatise (Book I, Chs. 1–14) & Planar Representation of the Sphere

Greek Text (Almagest): J. L. Heiberg (Leipzig: B. G. Teubner, 1898)

Latin Text (Planisphaerium): Hermann of Carinthia (1143), ed. J. L. Heiberg (Leipzig: B. G. Teubner, 1907)

English Translation, Diagrams & Symbolic Apparatus: GEOMETOR Scriptorium

Conspectus Operis

Composed at Alexandria around 150 CE by Claudius Ptolemy and dedicated to Syrus, the opening fourteen chapters of the Syntaxis Mathematica (Almagest) and its companion treatise Planisphaerium constitute the supreme surviving synthesis of classical Greek computational geometry, spherical trigonometry, and conformal cartographic projection. Each unit of this Multi-Track Book Codex provides synchronized reading tracks (English, Greek (1898) or Latin, Summary, and Notes) wired to interactive .euclid-graphic figures:

  • Unit I (Almagest I.1–I.9 & I.10a · Heiberg I, pp. 4–35): Cosmic Preliminaries & Golden Pentagon–Decagon Construction — Theoretical philosophy, spherical heavens and central Earth, the sexagesimal circle ($360^\circ$, $D = 120^p$, $R = 60^p$), and Ptolemy’s single-circle compass construction of the regular decagon ($s_{10} = R/\phi = 37;4,55^p$) and regular pentagon ($s_5 = \sqrt{R^2 + s_{10}^2} = 70;32,3^p$). (EN · EL · Summary · Notes)

  • Unit II (Almagest I.10b · Heiberg I, pp. 36–46): Ptolemy’s Theorem on Cyclic Quadrilaterals & Chord Calculus — Complete proof of Ptolemy’s Theorem ($AC \cdot BD = AB \cdot CD + BC \cdot DA$), the Chord of Difference ($\operatorname{crd} 12^\circ$), the Half-Arc Chord Lemma ($6^\circ \to 3^\circ \to 1\frac{1}{2}^\circ \to \frac{3}{4}^\circ$), the Chord of Sum, impossibility of trisecting $1\frac{1}{2}^\circ$ by means of lines, and Ptolemy’s Inequality Lemma ($\operatorname{crd} 1^\circ \approx 1;2,50 \implies \pi \approx 3;8,30 = \frac{377}{120}$). (EN · EL · Summary · Notes)

  • Unit III (Almagest I.11–I.14 · Heiberg I, pp. 47–78): Table of Chords, Ecliptic Obliquity & Menelaus Sphaerica — Architecture and self-checking of the Table of Chords, meridian measurement of $2\varepsilon = \frac{11}{83}$ of a circle ($47^\circ 42'40''$), the Planar Menelaus Sector Lemma (kata synthesin & kata diairesin), the 3D Spherical Menelaus Theorem, and the Solar Declination Law ($\operatorname{crd} 2\delta = \operatorname{crd} 2\varepsilon \cdot \operatorname{crd} 2\lambda / 120$). (EN · EL · Summary · Notes)

  • Unit IV (Planisphaerium §§1–4 · Heiberg II, pp. 227–234): Planisphaerium: Stereographic Projection & Astrolabe Geometry — South-Pole stereographic projection onto the equatorial plane, the Equator ($abgd$), Tropics ($tl, km$), and eccentric Ecliptic circle ($mbtd$) bisecting the equator via $\angle mdt = 90^\circ$, Apollonius's Conics I.5 subcontrary cone section, and circular inversion ($ez : ed = ed : ek$, $92;8,15 \times 39;4,19 \approx 60^2$). (EN · LA · Summary · Notes)

Editorial & Translation Note

All primary polytonic Greek (Almagest) and medieval scientific Latin (Planisphaerium) texts in this codex are transcribed directly via multimodal page-scan inspection from J. L. Heiberg's public-domain Teubner critical editions (Heiberg 1898; Heiberg 1907), cross-checked against the public-domain editions of N. B. Halma (1813) and K. Manitius (1912). Every English translation (-en), summary (-summary), and commentary (-notes) in this repository is 100% originally authored for GEOMETOR directly from Heiberg’s Greek and Latin; no copyrighted modern English translations were consulted or reproduced.

Critical Apparatus & Concordances