III. Historical, Epistemological & Axiomatic Scriptorium

Primary Philosophical, Renaissance, Axiomatic & Cosmogonic Editions

To understand what geometric objects are and how the mind knows their necessity, Pillar III publishes critical multi-language Book Codices of the thinkers who shaped the philosophy, aesthetics, and axiomatics of space.

aristotle — Loci Geometrici et Noetici

Curated multi-track edition (Bekker Greek, English translation, and mathematical commentary) of the foundational Aristotelian passages on demonstrative science (Posterior Analytics), the continuum and infinity (Physics), geometric actualization by construction (Metaphysics IX.9), mathematical abstraction and phantasia (De Anima III), and celestial spheres (De Caelo).

proclus — Commentary on Book I of Euclid’s Elements

4-Track Book Codex (English, Friedlein Greek 1873, Summary, Notes) of Proclus Lycius’s fifth-century philosophical and mathematical commentary on Euclid Book I, paired with a 164-locus concordance. Preserves the Eudemian history of Greek geometry, the six classical parts of a Euclidean proposition (protasis, ekthesis, diorismos, kataskeue, apodeixis, symperasma), and the doctrine of imaginative projection (probole) onto the screen of phantasia.

aquinas — Opera de Scientia Mathematica et Materia Intelligibili

4-Track Book Codex (Latin, English, Summary, Notes) across 5 Parts and 37 sections collecting St. Thomas Aquinas’s decisive texts on the epistemology of mathematics—centered on Super Boetium De Trinitate (qq. 5–6) on intelligible matter (materia intelligibilis) and terminatio ad imaginationem, alongside selections from In Posteriora Analytica, In De Anima, In Physicorum, and In Metaphysicorum, cross-linked via a 78-locus Hoenen concordance.

pacioli — Fra Luca Pacioli’s De Divina Proportione (1509)

5-Track Book Codex (English, Italiano 1509, Deutsch 1889, Latin/Greek, Notes) of Fra Luca Pacioli’s Renaissance masterpiece De Divina Proportione (Venice, Paganino Paganini, 1509; Constantin Winterberg critical edition, Vienna, 1889). Spans 318 archival folios and 482 recalibrated woodcuts, including Pacioli’s treatise on the thirteen effects of the Divine Proportion, architectural letterforms, Piero della Francesca’s Libellus on the five regular bodies, and all 60 solid and skeletal polyhedra plates drawn by Leonardo da Vinci.

hilbert — David Hilbert’s Grundlagen der Geometrie (1899/1902)

Multi-track edition (German original, E. J. Townsend English translation, and metamathematical commentary) of David Hilbert’s Foundations of Geometry—reorganizing Euclidean geometry into five rigorous axiom groups (Incidence, Order, Congruence, Parallels, Continuity), building the algebra of segments from Desargues’s and Pascal’s theorems, and proving axiom consistency and independence through explicit algebraic coordinate fields.

bertrand-russell — Foundations of Geometry & Principles of Mathematics

Scholarly edition of Bertrand Russell’s two foundational works on geometric space—An Essay on the Foundations of Geometry (1897) and Part VI (Space) of The Principles of Mathematics (1903)—examining the philosophical transition from Kantian intuition through projective and Cayley–Klein non-Euclidean geometries to pure relational logic. (Distinct from Walter & Lao Russell’s cosmogonic edition below.)

hoenen — Petrus Hoenen, S.J.’s De Noetica Geometriae (1954)

First complete digital edition and facing Latin–English translation of Fr. Petrus Hoenen, S.J.’s De Noetica Geometriae Origine Theoriae Cognitionis (Analecta Gregoriana, Rome, 1954). Answering modern axiomatic formalism, Hoenen demonstrates through Aristotle, Euclid, Proclus, Aquinas, Hilbert, and Russell that universal geometric nexus is first grasped through intuitive formal abstraction directly within constructed spatial continua.

russell — Walter & Lao Russell’s Home Study Course (1950–1952)

Complete 12-Unit, 48-Lesson digital codex of Walter and Lao Russell’s Home Study Course in Universal Law, Natural Science and Living Philosophy, featuring 180 vector-reconstructed scientific diagrams and interactive 3D visualizations of the Russells’ cube-sphere optical wave-field cosmogony.