F.17 Ellipse — Folios

Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.17 (Ellipse) (SeeligNotebooks).

Folio 0118 (Page 1 of 4): Five-Circle Construction Ellipse — Steps 1–4

[Folio 0118]

Folio 0118 (original scan 0118.jpg) from resources/seelig/17_ellipse.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0118 (0118.jpg, Sheet 1 of 4):

Sets up bounding box \((a, b)\), diagonals \(L_1, L_2\), normals \(L_3, L_4\) meeting at \(C_1, C_2, C_3\), and end-cap circles of radius \(r\).

\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \qquad r_1 + r_2 = 2 a, \qquad V = a = \sqrt{d \cdot F}, \qquad L = \frac{2 b^2}{a}\]

Editorial & Symbolic Notes

Archival scan 0118.jpg from Fred W. Seelig’s notebook dossier on F.17 Ellipse (Page 1 of 4). Companion OpenDocument worksheet(s): General Reference. Classical Euclidean foundations: I.47, VI.13.

Folio 0119 (Page 2 of 4): Five-Circle Construction Ellipse — Steps 5–7

[Folio 0119]

Folio 0119 (original scan 0119.jpg) from resources/seelig/17_ellipse.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0119 (0119.jpg, Sheet 2 of 4):

Locates \(Q\) with \(|BQ| = 2r\), draws circle \((C_1, |C_1 Q|)\) to find \(C_4, C_5\), and draws transition radials through \(C_2, C_3\).

\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \qquad r_1 + r_2 = 2 a, \qquad V = a = \sqrt{d \cdot F}, \qquad L = \frac{2 b^2}{a}\]

Editorial & Symbolic Notes

Archival scan 0119.jpg from Fred W. Seelig’s notebook dossier on F.17 Ellipse (Page 2 of 4). Companion OpenDocument worksheet(s): General Reference. Classical Euclidean foundations: I.47, VI.13.

Folio 0120 (Page 3 of 4): Full-Page Compass Execution of the Five-Circle Oval

[Folio 0120]

Folio 0120 (original scan 0120.jpg) from resources/seelig/17_ellipse.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0120 (0120.jpg, Sheet 3 of 4):

Precision compass-and-straightedge construction showing centers \(C_1..C_5\) and smooth tangent circular arcs.

\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \qquad r_1 + r_2 = 2 a, \qquad V = a = \sqrt{d \cdot F}, \qquad L = \frac{2 b^2}{a}\]

Editorial & Symbolic Notes

Archival scan 0120.jpg from Fred W. Seelig’s notebook dossier on F.17 Ellipse (Page 3 of 4). Companion OpenDocument worksheet(s): General Reference. Classical Euclidean foundations: I.47, VI.13.

Folio 0121 (Page 4 of 4): Focus, Directrix, Eccentricity & Latus Rectum Identities

[Folio 0121]

Folio 0121 (original scan 0121.jpg) from resources/seelig/17_ellipse.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0121 (0121.jpg, Sheet 4 of 4):

Derives \(F = ae, d = a/e, e^2 = F/d, V = a = \sqrt{dF}\), and latus rectum \(L = 2b^2/a\).

\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \qquad r_1 + r_2 = 2 a, \qquad V = a = \sqrt{d \cdot F}, \qquad L = \frac{2 b^2}{a}\]

Editorial & Symbolic Notes

Archival scan 0121.jpg from Fred W. Seelig’s notebook dossier on F.17 Ellipse (Page 4 of 4). Companion OpenDocument worksheet(s): General Reference. Classical Euclidean foundations: I.47, VI.13.