F.31 Logic Tests — Folios

Archival manuscript scans and diplomatic transcriptions from seelig’s notebooks for F.31 (Logic Tests) (SeeligNotebooks).

Folio 0215 (Page 1 of 6): Three Logical Tests — Boolean Outputs (Page 1/)

[Folio 0215]

Folio 0215 (original scan 0215.jpg) from resources/seelig/31_logic-tests.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0215 (0215.jpg, Sheet 1 of 6):

Defines predicates \(T_1, T_2, T_3\) on \(\|CA\|, \|CB\|, \|AB\|\) and partitions the line through \(A, B\) into Region \(A\), Region \(AB\), and Region \(B\).

\[T_1 = (\|CA\| < \|AB\|), \qquad T_2 = (\|CB\| < \|AB\|), \qquad T_3 = (\|CA\| < \|CB\|)\]

Editorial & Symbolic Notes

Archival scan 0215.jpg from Fred W. Seelig’s notebook dossier on F.31 Logic Tests (Page 1 of 6). Companion OpenDocument worksheet(s): Point in Triangle, Point in Triangle (2), Harmonic Conjugates. Classical Euclidean foundations: V.8.

Folio 0216 (Page 2 of 6): Truth Table & Scenarios I–III (Page 2/)

[Folio 0216]

Folio 0216 (original scan 0216.jpg) from resources/seelig/31_logic-tests.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0216 (0216.jpg, Sheet 2 of 6):

Evaluates \((T_1, T_2, T_3)\) across Scenarios I–III as \(C\) traverses the ray beyond \(A\) and the left half of segment \(AB\).

\[\text{Region } A:\; \overline{T}_2 T_3\; (-1 < k < 0), \qquad \text{Region } AB:\; T_1 T_2\; (0 < k < \infty), \qquad \text{Region } B:\; \overline{T}_1\overline{T}_3\; (-\infty < k < -1)\]

Editorial & Symbolic Notes

Archival scan 0216.jpg from Fred W. Seelig’s notebook dossier on F.31 Logic Tests (Page 2 of 6). Companion OpenDocument worksheet(s): Point in Triangle, Point in Triangle (2), Harmonic Conjugates. Classical Euclidean foundations: V.8.

Folio 0217 (Page 3 of 6): Scenarios IV–VI & Signed Ratio k (Page 3/)

[Folio 0217]

Folio 0217 (original scan 0217.jpg) from resources/seelig/31_logic-tests.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0217 (0217.jpg, Sheet 3 of 6):

Completes Scenarios IV–VI across the right half of \(AB\) and the ray beyond \(B\), mapping each region to the interval of \(k = \pm\|AC\|/\|BC\|\).

\[T_1 = (\|CA\| < \|AB\|), \qquad T_2 = (\|CB\| < \|AB\|), \qquad T_3 = (\|CA\| < \|CB\|)\]

Editorial & Symbolic Notes

Archival scan 0217.jpg from Fred W. Seelig’s notebook dossier on F.31 Logic Tests (Page 3 of 6). Companion OpenDocument worksheet(s): Point in Triangle, Point in Triangle (2), Harmonic Conjugates. Classical Euclidean foundations: V.8.

Folio 0218 (Page 4 of 6): C.a.R. Conditional Expression Synthesis (Page 4/)

[Folio 0218]

Folio 0218 (original scan 0218.jpg) from resources/seelig/31_logic-tests.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0218 (0218.jpg, Sheet 4 of 6):

Translates the Boolean minterms \(\overline{T}_2 T_3, T_1 T_2, \overline{T}_1\overline{T}_3\) into C.a.R. if(...) expressions for signed \(k\).

\[\text{Region } A:\; \overline{T}_2 T_3\; (-1 < k < 0), \qquad \text{Region } AB:\; T_1 T_2\; (0 < k < \infty), \qquad \text{Region } B:\; \overline{T}_1\overline{T}_3\; (-\infty < k < -1)\]

Editorial & Symbolic Notes

Archival scan 0218.jpg from Fred W. Seelig’s notebook dossier on F.31 Logic Tests (Page 4 of 6). Companion OpenDocument worksheet(s): Point in Triangle, Point in Triangle (2), Harmonic Conjugates. Classical Euclidean foundations: V.8.

Folio 0219 (Page 5 of 6): Spreadsheet Implementation — Part 1 (Page 5/)

[Folio 0219]

Folio 0219 (original scan 0219.jpg) from resources/seelig/31_logic-tests.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0219 (0219.jpg, Sheet 5 of 6):

Writes Excel/OpenFormula IF/AND cell expressions testing whether \(C\) lies inside \(AB\) or externally on either side.

\[T_1 = (\|CA\| < \|AB\|), \qquad T_2 = (\|CB\| < \|AB\|), \qquad T_3 = (\|CA\| < \|CB\|)\]

Editorial & Symbolic Notes

Archival scan 0219.jpg from Fred W. Seelig’s notebook dossier on F.31 Logic Tests (Page 5 of 6). Companion OpenDocument worksheet(s): Point in Triangle, Point in Triangle (2), Harmonic Conjugates. Classical Euclidean foundations: V.8.

Folio 0220 (Page 6 of 6): Spreadsheet Implementation — Part 2 (Page 6/)

[Folio 0220]

Folio 0220 (original scan 0220.jpg) from resources/seelig/31_logic-tests.

Diplomatic Mathematical & Geometric Transcription

Diplomatic Transcription — Folio 0220 (0220.jpg, Sheet 6 of 6):

Verifies the Boolean logic cells against numeric test coordinates for \(A, B, C\) and their harmonic conjugate \(D\).

\[\text{Region } A:\; \overline{T}_2 T_3\; (-1 < k < 0), \qquad \text{Region } AB:\; T_1 T_2\; (0 < k < \infty), \qquad \text{Region } B:\; \overline{T}_1\overline{T}_3\; (-\infty < k < -1)\]

Editorial & Symbolic Notes

Archival scan 0220.jpg from Fred W. Seelig’s notebook dossier on F.31 Logic Tests (Page 6 of 6). Companion OpenDocument worksheet(s): Point in Triangle, Point in Triangle (2), Harmonic Conjugates. Classical Euclidean foundations: V.8.