Mission

Recovering the Logical, Continuum, and Noetic Foundations of Classical Geometry

geometor/aristotle (Loci Geometrici et Noetici) establishes the philosophical and epistemological keystone of the GEOMETOR historical canon. Before Euclid compiled the Elements around 300 BC, Aristotle of Stagira (384–322 BC) formulated the first rigorous theory of what makes a geometric proposition demonstratively necessary, why continuous magnitude cannot be dissolved into indivisible points, and how the human intellect grasps universal spatial necessities inside concrete diagrams.

Why GEOMETOR Needs Aristotle

Across the existing historical editions in GEOMETOR, Aristotle is the single unspoken—and continually invoked—authority:

  1. Pre-Euclidean Logic & First Principles in geometor/euclid: In The Thirteen Books of Euclid's Elements, Sir Thomas Heath cites 145 distinct Aristotelian Bekker passages to explain the division of first principles into common axioms, postulates, and hypotheses (An. Post. I.2, I.10), the elimination of circular parallel proofs (An. Pr. II.16), the Eudoxian revolution in general proportion (An. Post. I.5), and pre-Euclidean reciprocal subtraction (antanairesis, Top. VIII.3).

  2. Intuitive Abstraction in the Phantasm in geometor/hoenen: In De Noetica Geometriae, Fr. Peter Hoenen, S.J. builds his entire epistemology of geometric judgment upon 64 Aristotelian Bekker keys—demonstrating from An. Post. I.12 (77b30), De Anima III.7–8 (431b2, 432a8), and Metaphysics Z.10 (1036a9) and Θ.9 (1051a21–33) that geometric axioms and theorems are discovered by intellectual vision (noēsis) into intelligible matter displayed within the spatial phantasm.

  3. Mathematical Exactitude & Subalternation in geometor/pacioli: In De Divina Proportione, Fra Luca Pacioli invokes 17 Aristotelian passages across the Posterior Analytics, Physics, De Caelo, and Metaphysics to defend mathematical certitude (nel primo grado di certezza), the subalternation of perspective and harmony to geometry and arithmetic (An. Post. I.7, I.9, I.13), and the three-dimensional completeness of corporeal magnitude (De Caelo I.1).

Editorial Principles

  • 100% Verbatim Primary Texts: Every Greek chapter is drawn intact from Immanuel Bekker's Prussian Academy edition (1831/1837) and W. D. Ross's Oxford critical edition of the Metaphysics (1924), paired with classic public-domain Clarendon Press Oxford Translations and verified by SHA-256 checksums.

  • Complete Chapters, Not Isolated Snippets: Because Aristotle’s mathematical illustrations serve organic dialectical and demonstrative arguments, Loci Geometrici et Noetici presents fifty-four complete chapters across eight treatises rather than decontextualized fragments.

  • Pure Philological Fidelity: In keeping with Aristotle’s own distinction between philosophical science of principles and constructive geometric diagramming, this historical codex contains zero anachronistic Python construction scripts—preserving pure textual, philological, and philosophical integrity while cross-linking every Bekker locus across the GEOMETOR ecosystem.