F.39 Pole and Polar with Respect to a Triangle — Folios

Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.39 (Pole and Polar with Respect to a Triangle) (SeeligNotebooks).

Folio 0238 (Page 1 of 1): Pole & Polar W.r.t. a Triangle (May 6, 2015)

[Folio 0238]
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Folio 0238 (original scan 0238.jpg) from resources/seelig/39_pole-polar.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0238 (0238.jpg, Sheet 1 of 1):

Constructs the cevian triangle \(A'B'C'\) of pole \(P\) and the collinear perspectrix/trilinear polar \(L\) through \(X, Y, Z\), posing open metric questions for \(d(P,L), OP, IP, OL, IL\).

\[P = (u : v : w) \iff L:\; \frac{x}{u} + \frac{y}{v} + \frac{z}{w} = 0\]

Editorial & Symbolic Notes

Archival scan 0238.jpg from Fred W. Seelig’s notebook dossier on F.39 Pole and Polar with Respect to a Triangle (Page 1 of 1). Companion OpenDocument worksheet(s): Pole & Polar, Harmonic Conjugates. Classical Euclidean foundations: VI.2, VI.3. Kimberling Encyclopedia of Triangle Centers loci: X(1) — Incenter, X(2) — Centroid, X(3) — Circumcenter.