F.20 Extangent — Folios

Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.20 (Extangent) (SeeligNotebooks).

Folio 0127 (Page 1 of 1): Extangents Triangle & Derivative of Euler’s Distance d_{IO}

[Folio 0127]

Folio 0127 (original scan 0127.jpg) from resources/seelig/20_extangent.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0127 (0127.jpg, Sheet 1 of 1):

Compass construction of the extangents triangle around an inscribed triangle and differentiation of \(d_{IO} = \sqrt{R^2 - 2rR}\) with respect to \(R\).

\[d_{IO}^2 = R^2 - 2 r R, \qquad \frac{d}{d R}(d_{IO}) = \frac{R - r}{\sqrt{R^2 - 2 r R}}, \qquad r_a = \frac{K}{s - a}, \quad r_b = \frac{K}{s - b}, \quad r_c = \frac{K}{s - c}\]

Editorial & Symbolic Notes

Archival scan 0127.jpg from Fred W. Seelig’s notebook dossier on F.20 Extangent (Page 1 of 1). Companion OpenDocument worksheet(s): Excenters, Incircle-Incenter, Centers of Similitude. Classical Euclidean foundations: IV.4. Kimberling Encyclopedia of Triangle Centers loci: X(1) — Incenter, X(3) — Circumcenter, X(40) — Bevan Point, X(55) — Internal Center of Similitude of Incircle and Circumcircle, X(56) — External Center of Similitude of Incircle and Circumcircle.