F.5 Centers of Similitude — Folios

Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.5 (Centers of Similitude) (SeeligNotebooks).

Folio 0021 (Page 1 of 1): Centers of Similitude (Vol. I, p. 207)

[Folio 0021]

Folio 0021 (original scan 0021.jpg) from resources/seelig/05_centers-of-similitude.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0021 (0021.jpg, Sheet 1 of 1):

Dimensioned construction of circles \((O_1, r_1)\) and \((O_2, r_2)\) with common internal tangents meeting at \(S_{IN}\) and common external tangents meeting at \(S_{EX}\), deriving the four exact distance formulas in terms of \(d, r_1, r_2\).

\[|O_1 S_{IN}| = d \frac{r_1}{r_2 + r_1}, \qquad |S_{IN} O_2| = d \frac{r_2}{r_2 + r_1}\]

Editorial & Symbolic Notes

Archival scan 0021.jpg from Fred W. Seelig’s notebook dossier on F.5 Centers of Similitude (Page 1 of 1). Companion OpenDocument worksheet(s): Centers of Similitude. Classical Euclidean foundations: VI.2, VI.4. Kimberling Encyclopedia of Triangle Centers loci: X(55) — Internal Center of Similitude of Incircle and Circumcircle, X(56) — External Center of Similitude of Incircle and Circumcircle.