F.4 Carnot’s Theorem — Folios

Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.4 (Carnot’s Theorem) (SeeligNotebooks).

Folio 0020 (Page 1 of 1): Carnot’s Theorem & The Japanese Theorem

[Folio 0020]

Folio 0020 (original scan 0020.jpg) from resources/seelig/04_carnots-theorem.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0020 (0020.jpg, Sheet 1 of 1):

States Lazare Carnot’s signed-distance relation \(\sum d_m = R + r\) with an obtuse-triangle circumcircle diagram (\(-OH_A + OH_B + OH_C = R + r\)) and two triangulated cyclic polygon diagrams illustrating the invariance of the sum of inradii.

\[\sum_{m \in \{A, B, C\}} d_m = d_a + d_b + d_c = R(\cos\alpha + \cos\beta + \cos\gamma) = R + r\]

Editorial & Symbolic Notes

Archival scan 0020.jpg from Fred W. Seelig’s notebook dossier on F.4 Carnot’s Theorem (Page 1 of 1). Companion OpenDocument worksheet(s): General Reference, Circumcircle-Circumcenter, Incircle-Incenter. Classical Euclidean foundations: III.20, IV.4, IV.5. Kimberling Encyclopedia of Triangle Centers loci: X(1) — Incenter, X(3) — Circumcenter.