Master Chapter, Boethius & GEOMETOR Canon Concordance

Hoche (1866) · D’Ooge (1926) · Boethius De Institutione Arithmetica (1867) · GEOMETOR Canon

Complete structural concordance mapping all 20 canonical chapter groups across Books I–II of Nicomachus of Gerasa's Introductio Arithmetica to Richard Hoche's Teubner Greek pagination (hoche:1866), Martin Luther D'Ooge's English pagination (dooge:1926), Boethius's Latin De Institutione Arithmetica (boethius:friedlein:1867), and companion GEOMETOR Digital Scriptorium codices.

Chapters	Theme & Codex Unit	Hoche (1866)	D’Ooge (1926)	Boethius Parallel	GEOMETOR Parallels
I.1–2	Philosophy as Love of Wisdom; Eternal Immaterial Reality vs. Bodily Flux	pp. 1–5	pp. 181–183	De Inst. Arith. I.1 (p. 7–9 Friedlein)	plato (Timaeus 27d–28a); proclus (In Eucl. 35–37); aquinas (In Boeth. de Trin. q. 5)
I.3	Magnitude (Pēlikon) vs. Multitude (Poson) & the Four Mathematical Sciences (Mathemata)	pp. 5–9	pp. 183–187	De Inst. Arith. I.1 (quadruvium coined at p. 7.25 & 9.28 Friedlein)	plato (Republic VII 525a–534e; Epinomis 991d–992a); aristotle (Cat. 4b20); proclus (In Eucl. 35.17–36.25)
I.4–5	Ontological Priority of Arithmetic via Asymmetric Co-Removal (Synanairein)	pp. 9–12	pp. 187–189	De Inst. Arith. I.1 (p. 10–12 Friedlein)	aristotle (Post. An. I.27 87a31; Top. 123a14); aquinas (In Boeth. de Trin. q. 5 a. 3)
I.6–7	Number in the Divine Mind as Cosmic Exemplar; Definitions of Number, Even, and Odd	pp. 12–14	pp. 189–192	De Inst. Arith. I.2–3 (p. 12–14 Friedlein)	plato (Timaeus 29a, 37d); euclid (Elements VII Defs. 1–7); kepler (Harmonices Mundi IV)
I.13	Prime & Incomposite Numbers and the Odd Sieve (Koskinon) of Eratosthenes	pp. 29–36	pp. 204–207	De Inst. Arith. I.17 (p. 36–39 Friedlein)	euclid (Elements VII Defs. 11–14; VII.2; IX.20); elements (Book VII)
I.16	Superabundant, Deficient, and Perfect Numbers (6, 28, 496, 8128)	pp. 39–44	pp. 209–212	De Inst. Arith. I.19–20 (p. 41–45 Friedlein)	euclid (Elements VII Def. 22; IX.36); elements (IX.36)
I.17–18	Absolute vs. Relative Quantity; Equality and the Five Species of Inequality; Multiple Ratios	pp. 44–49	pp. 212–216	De Inst. Arith. I.21–23 (p. 45–50 Friedlein)	euclid (Elements V Defs. 3–6; VII Def. 20); pacioli (De Divina Proportione)
I.19	Superparticular (Epimoric) Ratios (3:2 Hemiolios, 4:3 Epitritos, 9:8 Epogdoos)	pp. 49–55	pp. 216–219	De Inst. Arith. I.24–27 (p. 50–57 Friedlein)	plato (Timaeus 35b–36b); euclid (Sectio Canonis); walter-russell (Harmonic Octave)
I.20–22	Superpartient (Epimeric), Multiple Superparticular, and Multiple Superpartient Ratios	pp. 55–64	pp. 219–225	De Inst. Arith. I.28–31 (p. 57–66 Friedlein)	fibonacci (Liber Abaci fraction taxonomy)
I.23	The Three Prostagma Commands Unfolding Every Inequality from Equality (1, 1, 1)	pp. 64–72	pp. 225–229	De Inst. Arith. I.32 (p. 66–72 Friedlein)	pappus (Synagoge projective & Stern–Brocot/Calkin–Wilf tree kinship)
II.1–2	Primordial Element & Inverse Three-Subtraction Reduction to Equality (1, 1, 1)	pp. 73–76	pp. 230–232	De Inst. Arith. II.1 (p. 77–80 Friedlein)	plato (Timaeus 48b; Philebus 16c–26d); euclid (Elements VII.1–2 anthyphairesis)
II.6–7	Alpha-Graphia Pebble Notation; Point, Line, Triangle, and Dimensional Generation of Number	pp. 82–86	pp. 237–240	De Inst. Arith. II.4–6 (p. 86–92 Friedlein)	euclid (Elements I Defs. 1–19; VII Defs. 16–19); aristotle (Metaphysics N.5 1092b10)
II.8–12	Triangular, Square, Pentagonal, Hexagonal & Heptagonal Numbers by Arithmetic Gnomons; Polygonal Decomposition	pp. 86–99	pp. 240–248	De Inst. Arith. II.7–19 (p. 92–105 Friedlein)	euclid (Elements II Def. 2); wildberger (Discrete quadrance & gnomons)
II.13–17	Solid Pyramidal, Truncated, Cubic, Scalene, Spherical/Recurrent & Heteromecic Numbers	pp. 99–112	pp. 248–257	De Inst. Arith. II.20–30 (p. 105–122 Friedlein)	euclid (Elements VIII.11–12; IX.1–6); plato (Theaetetus 147e–148b)
II.18–19	Plato’s Same (Tauton) and Other (Thateron); Alternating Weave of Squares n^2 and Oblongs n(n+1)	pp. 112–117	pp. 257–261	De Inst. Arith. II.31–33 (p. 122–130 Friedlein)	plato (Timaeus 35a; Philebus 23c–26d); aristotle (Physics III.4 203a10)
II.20	Cubes from Consecutive Odd Blocks & Nicomachus’s Sum-of-Cubes Theorem	pp. 117–119	pp. 261–263	De Inst. Arith. II.39 (p. 136 Friedlein)	elements (II.4 gnomonic dissection); wildberger (Polynomial summation laws)
II.21–24	Proportion (Analogia) Strictly vs. Broadly; Arithmetic & Geometric Proportions and Properties	pp. 119–131	pp. 264–273	De Inst. Arith. II.40–46 (p. 137–152 Friedlein)	plato (Timaeus 31c–32a); euclid (Elements V Def. 8; VI.13); pappus (Synagoge III)
II.25–26	The Harmonic Mean (3, 4, 6 & 6, 8, 12), Cube Dimension Naming, and Musical Consonances	pp. 131–136	pp. 273–279	De Inst. Arith. II.47–49 (p. 152–161 Friedlein)	plato (Timaeus 35b–36b); pappus (Harmonic range cross-ratio -1); pacioli (Cube & consonances)
II.27–28	Insertions Between Two Even or Odd Extremes & the Complete System of Ten Pythagorean Means	pp. 136–144	pp. 279–284	De Inst. Arith. II.50–52 (p. 161–169 Friedlein)	pappus (Synagoge III semicircle construction of A, G, H); fibonacci (Means)
II.29	The Most Perfect Three-Dimensional & Four-Term Proportion (6 : 8 :: 9 : 12)	pp. 144–147	pp. 284–286	De Inst. Arith. II.54 (maxima et perfecta symphonia, p. 170–173 Friedlein)	plato (Timaeus 35b–36b; Epinomis 991a–b); kepler (Harmonices Mundi III & V)