F.34 Nine-Point Circle — Folios

Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.34 (Nine-Point Circle) (SeeligNotebooks).

Folio 0224 (Page 1 of 1): Nine-Point Circle & Orthocenter Distance Identities

[Folio 0224]

Folio 0224 (original scan 0224.jpg) from resources/seelig/34_nine-point-circle.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0224 (0224.jpg, Sheet 1 of 1):

Defines \(\Gamma_N\) through the three altitude feet with center \(N = X(5)\) on the Euler line and radius \(r_N = R/2\), records \(|OH| = \sqrt{2r^2+4R^2-S_\omega}\) and \(|OH|^2 = AH^2+BH^2+CH^2-3R^2\), and sketches the \((2,3,4)\) obtuse configuration.

\[r_N = \frac{1}{2} R, \qquad N = \frac{O + H}{2} = X(5), \qquad |ON| = \frac{1}{2}|OH|\]

Editorial & Symbolic Notes

Archival scan 0224.jpg from Fred W. Seelig’s notebook dossier on F.34 Nine-Point Circle (Page 1 of 1). Companion OpenDocument worksheet(s): 9-Point Circle, Euler Line, Orthocenter. Classical Euclidean foundations: IV.5. Kimberling Encyclopedia of Triangle Centers loci: X(2) — Centroid, X(3) — Circumcenter, X(4) — Orthocenter, X(5) — Nine-Point Center.