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Using This Edition¶

Interactive Features & Reader’s Guide to John Casey’s Sequel to Euclid

Welcome to the GEOMETOR Digital Scriptorium edition of John Casey's landmark treatise, A Sequel to the First Six Books of the Elements of Euclid (1888 Fifth Edition & 1892 Sixth Edition edited by Patrick A. E. Dowling). This edition bridges classical Euclidean planar deduction with nineteenth-century synthetic circle, projective, and modern triangle geometry through interactive multi-track codices and exact symbolic proofs.

Interactive Reader Features¶

1. Synchronized Reading Tracks¶

Every unit in the Book Codex is published as a synchronized 3-track edition accessible via the companion track switcher bar:

English: Complete primary text of Casey’s propositions, corollaries, and exercises, paired with calibrated interactive .euclid-graphic SVGs.
Summary: Executive summaries condensing the deductive trajectory, key theorems (Euler line, Nine-Points Circle, Casey’s theorem, Feuerbach’s point $X(11)$, Lemoine point $K = X(6)$, Brocard points $\Omega, \Omega'$), and algebraic invariant ledgers.
Notes: Scholarly commentary detailing historical provenance, Dowling 1892 collation notes, and systematic cross-references to Euclid’s Elements, Altshiller-Court’s College Geometry, Kimberling’s Encyclopedia of Triangle Centers (ETC), and Pappus’s Synagoge.

2. Primary-Source Folio Milestones¶

Marginal folio links such as [f. 0007] or [p. 45] record the exact leaf and printed page boundaries of the 1888 Dublin University Press witness (PDF Folio = Printed Page + 26). Clicking any marginal folio link or the header Folio badge opens high-resolution 300-DPI archival scans directly, verifying every proposition against the historical print.

3. Interactive Diagrams & Deductive Links¶

Every diagram across the six units is rendered natively as an interactive SVG generated from exact SymPy coordinates:

Geometric Cross-References: In-line mathematical expressions and geometric markers highlight corresponding geometric elements in the diagram upon hover or click.
Rational & Symbolic Precision: Every figure is constructed in geometor.casey using exact rational or radical numbers (such as the canonical Heronian triangle $(15, 13, 14)$ with integer coordinates and rational circumradius/inradius), completely eliminating floating-point rounding errors.

4. Full-Text Search with In-Page Highlighting¶

The search box in the sidebar provides instantaneous full-text indexing across the treatise, apparatus, and demonstrations. Queries append ?highlight= parameters to URLs, automatically highlighting searched terminology directly inside proofs, lemmas, and historical notes.

5. Categories, Tags, Document Types & Collection Views¶

The sidebar exposes faceted taxonomy browsing:

Categories & Tags: Navigate topics by mathematical domain (circles, inversion, triangles, symmedians, brocard, projective, poles-and-polars).
Document Types: Filter pages by content type (treatise, unit, demos, biography, log).
Collection Views: Collection index pages offer view toggles between Cards, Banners, and List modes.

6. People, Bibliography & Glossary Tooltips¶

Prosopographical Hover Cards: Links marked with :person: (e.g., John Casey, Patrick A. E. Dowling, Karl Wilhelm Feuerbach, Émile Lemoine, Henri Brocard) open instant biographical profiles and direct links to the People register.
Bibliographic Citations: Citations formatted with :cite: link directly to the Bibliography.
Glossary Tooltips: Technical terms linked with :term: provide instant geometric definitions.
Light / Dark Theme: Toggle visual themes using the control in the upper navigation bar.

Command-Line & Python API¶

Command-Line Interface (CLI)¶

The geometor-casey CLI provides immediate shell-level verification and concordance tables:

# Display an executive Rich summary table of all verified theorems
        python3 -m geometor.casey summary

        # Display the master cross-repository concordance table
        python3 -m geometor.casey concordance
        

Python API¶

Run exact symbolic verifications and inspect geometric invariants:

from geometor.casey.brocard import construct_brocard_and_lemoine_circles
        from geometor.casey.coaxial import construct_radical_axis_and_coaxial_pencil
        from geometor.casey.feuerbach import prove_casey_feuerbach_heronian, prove_casey_theorem_symbolic
        from geometor.casey.poles_polars import construct_pole_and_polar, verify_lahire_reciprocity_symbolic

        # Verify Casey's Generalized Ptolemy Theorem symbolically
        casey_res = prove_casey_theorem_symbolic()
        print("Casey's Theorem verified:", casey_res.verified)

        # Verify Feuerbach's Theorem on the canonical Heronian triangle
        fb = prove_casey_feuerbach_heronian()
        print(f"Feuerbach point Fe: {fb.feuerbach_point}")
        print(f"Distance |N - I| == R/2 - r: {fb.ni_distance == fb.r9 - fb.r}")

        # Construct Coaxal Circles and Limiting Points
        coax = construct_radical_axis_and_coaxial_pencil()
        print(f"Radical Center: {coax.radical_center}")
        print(f"Poncelet Limiting Points: {coax.limiting_points}")
        