Cosmos & Harmony Codex

IOANNIS KEPLERI

MYSTERIVM COSMOGRAPHICVM (1596 / 1621)

STRENA SEV DE NIVE SEXANGVLA (1611)

ET HARMONICES MVNDI LIBRI I, II & V (1619)

Polyhedral Cosmography, Sixfold Crystallography & Close-Packing, Constructible Polygons, Architectonic Congruence, and the Harmonic Laws of Planetary Motion

Latin Text: Editio Princeps (1596, 1611, 1619, 1621) & Ch. Frisch, Opera Omnia (1858–1868)

English Translation, Interactive SVG Plates & Symbolic Apparatus: GEOMETOR Scriptorium

Conspectus Operis

Spanning twenty-five years from his youthful flash of insight at Graz on July 19, 1595 to the Linz Harmonices Mundi (1619) and Frankfurt annotated Mysterium (1621), Johannes Kepler forged the decisive bridge between classical Greek synthetic geometry (Euclid, Archimedes, Apollonius, Ptolemy, Pappus, Proclus) and modern mathematical physics, crystallography, and algebra. Each unit of this Four-Track Bilingual Book Codex provides synchronized reading tabs (English, Latin, Summary, and Notes) wired to interactive .euclid-graphic SVG figures:

• Unit I (Mysterium Cosmographicum · 1596 / 1621; Frisch I, pp. 106–152): Mysterium Cosmographicum: Five Regular Solids & the Six Planetary Orbs — The July 19, 1595 Graz Great-Conjunction triangle ($r_{\text{in}} : R_{\text{out}} = 1 : 2$), Nicholas of Cusa's theology of curved and straight, the Two Great Treasures of Geometry (Pythagoras & the Divine Section), polar-duality insphere/circumsphere equality ($\text{Cube} = \text{Octahedron}$ with $Q = \frac{1}{3}$; $\text{Dodecahedron} = \text{Icosahedron}$ with $Q = \frac{5 + 2\sqrt{5}}{15}$), and Terra as Circulus mensor omnium. (EN · LA · Summary · Notes)

• Unit II (Strena seu de Nive Sexangula · 1611; Frisch VII, pp. 715–730): Strena: Six-Cornered Snowflakes, Rhombic Polyhedra, Sphere Packing & Fibonacci — Crossing the Prague bridge, trihedral bee honeycomb bases, discovery of the space-filling Rhombic Dodecahedron ($\sqrt{2}:1$, dihedral $120^\circ$) and golden Rhombic Triacontahedron ($\phi:1$), pomegranate compression and the Kepler Sphere-Packing Conjecture ($\frac{\pi}{3\sqrt{2}} \approx 74.048\%$), and self-propagating Fibonacci pentamery ($1, 1, 2, 3, 5, 8, 13, 21 \to \phi$). (EN · LA · Summary · Notes)

• Unit III (Harmonices Mundi Liber I · 1619; Frisch V, pp. 75–125): Harmonices Mundi Book I: Geometric Scibilitas, Divine Section & the Heptagon — Defense of Euclid's Book X against Petrus Ramus and Willebrord Snellius, the eight degrees of geometric knowability (effabilis longitudine, effabilis potentia, mese, binominis & apotome, mizon & elasson), self-propagation of the Sectio Divina, and Proposition XLV proving the Euclidean non-constructibility of the regular heptagon ($x^3 + x^2 - 2x - 1 = 0$) against Jost Bürgi's cossic chord equation. (EN · LA · Summary · Notes)

• Unit IV (Harmonices Mundi Liber II · 1619; Frisch V, pp. 126–144): Harmonices Mundi Book II: Architectonic Congruence, Tilings & Star Polyhedra — Planar and spatial congruence ($\sum \theta_i = 360^\circ$), complete enumeration of the 11 uniform Archimedean planar tilings, Kepler’s pentagonal/decagonal star tessellation (Figure Aa, precursor to Roger Penrose's aperiodic tilings), reconstruction of all 13 Archimedean convex solids, and discovery of the Small & Great Stellated Dodecahedra ($\{5/2, 5\}$ and $\{5/2, 3\}$). (EN · LA · Summary · Notes)

• Unit V (Epistola 1597 & Harmonices Mundi Liber V · 1619; Frisch I p. 377, V pp. 269–329): Harmonices Mundi Book V: The Kepler Triangle, Celestial Consonances & Third Law — The October 1597 letter to Michael Mästlin formulating the Kepler Right Triangle $(1, \sqrt{\phi}, \phi)$ over $\mathbb{Q}(\sqrt{\phi})$, harmonic marriage of the five regular solids with Tycho Brahe's orbital eccentricities, aphelion/perihelion musical consonances ($4:5, 5:6, 2:3, 15:16, 24:25, 5:12$), and Kepler’s Harmonic Third Law (proportio sesquialtera, $(T_1/T_2)^2 = (a_1/a_2)^3$). (EN · LA · Summary · Notes)

Editorial & Translation Note

All primary Neo-Latin texts in this codex are edited from the 1596, 1611, 1619, and 1621 editiones principes and Christian Frisch's critical Joannis Kepleri Astronomi Opera Omnia (1858, 1864, 1868). Every English translation (-en), geometric executive summary (-summary), and scholarly commentary (-notes) is 100% originally authored for GEOMETOR directly from Kepler’s Latin; no modern copyrighted translations were consulted or reproduced.

Critical Apparatus & Concordances

• Cross-Corpus Geometric Concordance — Bidirectional mapping linking Kepler’s theorems to model, euclid, elements, divine, pacioli, pappus, proclus, hilbert, hoenen, wildberger, phyllotaxis, and ptolemy.

• Bibliography & Primary Editions — Early modern imprints, Frisch Opera Omnia, classical mathematical authorities, and modern proofs.

• Index Nominum (Persons) — Prosopographical register of 32 geometers, astronomers, philosophers, and editors.

• Latin & Mathematical Glossary — Lexicon of 20 technical Latin, Greek, and symbolic-geometry terms.