GEOMETOR • casey¶
Digital Scriptorium Book Codex & Exact Symbolic Demonstrations of John Casey’s A Sequel to the First Six Books of the Elements of Euclid (1888 / 1892)
Digital critical edition, calibrated interactive .euclid-graphic geometric diagrams, exact geometor.model symbolic demonstrations, and prosopographical, bibliographic, glossary, and cross-repository concordance apparatus for John Casey, LL.D., F.R.S. (1820–1891), Fellow of the Royal University of Ireland, published natively as a 3-Track Book Codex (English | Summary | Notes) with photon-platform/publish.
Featured Treatise¶
A Sequel to the First Six Books of the Elements of Euclid (1888 / 1892)¶
Fifth Edition, Revised and Enlarged (Dublin: Hodges, Figgis, & Co.; London: Longmans, Green, & Co., 1888; 276 archival folios) collated with the Sixth Edition, Revised and Enlarged, edited by Patrick A. E. Dowling, B.A. (Dublin / London, 1892 — cited as [casey:sequel:1892] in Nathan Altshiller-Court’s College Geometry).
The foundational English-language bridge from classical Euclidean constructions (geometor/euclid, geometor/elements) to 19th-century synthetic circle, projective, and triangle geometry:
Unit 1 — Books I, II & IV Extensions: Orthocentre, Mean Centres, Maxima & Minima, Euler Line, Apollonius & Stewart’s Theorems, Heron’s Area Formula, and the Nine-Points Circle (English · Summary · Notes).
Unit 2 — Book III & VI Sec. V Extensions: Inverse Points, Power of a Point, Orthogonal Circles, Radical Axis, Radical Centre, Coaxal Circles & Poncelet’s Limiting Points (English · Summary · Notes).
Unit 3 — Book IV & VI Extensions, Part A: Ceva & Menelaus, Centres of Similitude (Monge), Harmonic Section, Complete Quadrilaterals, Anharmonic Ratio, Desargues & Pascal (English · Summary · Notes).
Unit 4 — Book VI Extensions, Part B & Book III Props. 25, 27: Circular Inversion, Pappus’s Arbelos Chain, Casey’s Generalized Ptolemy Theorem, Feuerbach’s Theorem at $X(11)$, Hart’s Circle, Poles & Polars, La Hire’s Reciprocity, and Brianchon’s Theorem (English · Summary · Notes).
Unit 5 — Supplementary Chapter, Secs. I & III: Isogonal & Isotomic Conjugates, Antiparallels, Symmedians, Lemoine’s Point $K = X(6)$, Lagrange’s Minimum Property, and Lemoine’s First & Cosine Circles (English · Summary · Notes).
Unit 6 — Supplementary Chapter, Secs. II–VII & Misc.: Figures Directly Similar, Brocard Points $\Omega, \Omega'$ & Brocard Angle $\omega$, Brocard’s Circle & First Triangle, Tucker & Taylor Circles, M’Clelland’s Second Proof of Feuerbach, Harmonic Polygons, Steiner $X(99)$, Tarry $X(98)$, Neuberg & Longchamps $X(20)$ Circles (English · Summary · Notes).
Constructive Demonstrations & Scholarly Apparatus¶
Exact Symbolic Demonstrations: 4 Runnable SymPy / geometor.model Construction Suites (Casey & Feuerbach, Coaxal Pencils & Limiting Points, Poles/Polars & La Hire Reciprocity, and Symmedian–Lemoine–Brocard Geometry).
Critical Apparatus: Euclid–Casey–Altshiller-Court–ETC–Pappus Concordance & SymPy Circle Audit · Systematic Bibliography · Index of Persons · Technical Glossary.
Architecture & Reference: Mission & Scope · John Casey & Editorial Methodology · Python API Reference · Curation Log.