F.36 Orthic Triangle — Folios

Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.36 (Orthic Triangle) (SeeligNotebooks).

Folio 0232 (Page 1 of 1): The Orthic Triangle & Fagnano’s Problem

[Folio 0232]

Folio 0232 (original scan 0232.jpg) from resources/seelig/36_orthic-triangle.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0232 (0232.jpg, Sheet 1 of 1):

Records the three fundamental characterizations of the orthic triangle: (1) pedal triangle of \(H\), (2) homothetic to the tangential triangle, and (3) solution to Fagnano’s 1775 minimum-perimeter inscribed triangle problem.

\[a_{\text{orthic}} = a \cos\alpha, \qquad b_{\text{orthic}} = b \cos\beta, \qquad c_{\text{orthic}} = c \cos\gamma\]

Editorial & Symbolic Notes

Archival scan 0232.jpg from Fred W. Seelig’s notebook dossier on F.36 Orthic Triangle (Page 1 of 1). Companion OpenDocument worksheet(s): Orthic Triangle, Orthocenter, Pedal Triangle. Classical Euclidean foundations: I.12, III.32. Kimberling Encyclopedia of Triangle Centers loci: X(3) — Circumcenter, X(4) — Orthocenter, X(5) — Nine-Point Center.