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METHODS AND THEORIES FOR GEOMETRICAL CONSTRUCTIONS¶

Applied to 410 Problems — Julius Petersen (1866 / 1879)

Editio Princeps (Dansk, 1866): Methoder og Theorier til Løsning af geometriske Konstruktionsopgaver, anvendte paa c. 400 Opgaver, Karl Schønbergs Forlag, Kjøbenhavn, 1866 (2nd rev. ed., Andr. Fred. Høst & Søns Forlag, 1879).
Authorized English Edition (1879): Translated by Sophus Haagensen, Cand. Polyt. C. E., Andr. Fred. Høst & Son, Copenhagen / Sampson Low, Marston, Searle & Rivington, London, 1879 (100% Public Domain).
Digital Critical Codex: Synchronized 3-track edition (English 1879 · Summary · Notes) curated within the GEOMETOR canon.

“Method is my principal object. It has been my endeavour to systematize these methods and display them in clear, elementary form so that the beginner may learn how to attack a proposed problem methodically rather than by blind trial.”

—Julius Petersen, Methods and Theories, Preface (1879), pp. 1–2

Conspectus Totius Operis (7 Thematic Units)¶

Unit I: Preface & The Anatomy of a Geometric Construction (Forord og Indledning — Analyse, Konstruktion, Bevis og Diskussion — pp. 1–6 (with Problem 42, p. 15); Foundations & Problem 42): English (1879) · Summary · Notes
Unit II: Chapter I, Part A — Loci of Points & The Method of Two Loci (Kapitel I.A — Geometriske Steder for Punkter (a–k) — pp. 7–22, 37–40; Problems 1–116 & 202–219): English (1879) · Summary · Notes
Unit III: Chapter I, Part B — Loci of Lines & Tangential Envelopes (Kapitel I.B — Geometriske Steder for Linier (l–p) — pp. 40–45; Problems 220–245): English (1879) · Summary · Notes
Unit IV: Chapter II, Parts A & B — Parallel Translation & Replacing (Kapitel II — Figurens Omdannelse: Parallelforskydning og Omlægning — pp. 46–60; Problems 246–335): English (1879) · Summary · Notes
Unit V: Axial Reflection & Chapter III — The Theory of Revolution (Drejning om en Axe og Kapitel III — Drejningstheorien (O, v, f) — pp. 60–68; Problems 336–362): English (1879) · Summary · Notes
Unit VI: Multiplication of Curves & The Method of Similitude (Kurvers Multiplikation og Ligedannethedsmethoden — pp. 22–33; Problems 117–191): English (1879) · Summary · Notes
Unit VII: Inverse Figures, Circle Systems & Constructibility Criteria (Inversion, Cirkelsystemer og Konstruktion ved Lineal og Passer — pp. 33–37 & Appendix pp. 89–102; Problems 192–201 & 403–410): English (1879) · Summary · Notes

Apparatus Criticus & Cross-Repository Indices¶

Petersen Master Cross-Repository Concordance — Mapping Petersen’s heuristic loci, transformations, circle systems, and constructibility criteria across geometor/altshiller-court, geometor/euclid, geometor/elements, geometor/hilbert, geometor/pappus, geometor/lemoine, and geometor/etc.
Systematic Bibliography — Primary Danish/English/French/German editions, classical treatises, and modern heuristic descendants.
Prosopographical Index of Persons — Ancient and modern geometers cited across the 410 problems and commentary.
Technical Glossary of Constructive Geometry — Bilingual Danish/English/Greek analytical and transformational vocabulary.