Chapter X: Recent Geometry of the Triangle

Trilinear Polars, Symmedians & Lemoine Geometry, Apollonian Circles & Isodynamic Points, Isogonal Conjugates, Brocard Geometry, Tucker & Taylor Circles, Orthopole

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• Archival Span: Folios 0263–0313 · Printed Pages 244–[294] · Articles §§ 547–699

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• Companion Track: Switch to the Commentary tab above for mathematical synthesis, triangle-center mappings, and GEOMETOR connections.

Section & Article Conspectus

Section	Title	Folios	Pages	Articles
A	Poles and Polars with Respect to a Triangle (Trilinear Polar)	0263–0266	244–247	§§ 547–557
B.a	Lemoine Geometry — a. Symmedians	0266–0271	247–252	§§ 558–571
B.b	Lemoine Geometry — b. The Lemoine Point	0271–0276	252–257	§§ 572–587
B.c	Lemoine Geometry — c. The Lemoine Circles	0276–0279	257–260	§§ 588–596
C	The Apollonian Circles (incl. Isodynamic Points & Lemoine Axis)	0279–0286	260–267	§§ 597–624
D	Isogonal Lines (Isogonal Conjugates & Pedal Triangles)	0286–0293	267–274	§§ 625–648
E.a	Brocard Geometry — a. Brocard Points	0293–0298	274–279	§§ 649–665
E.b	Brocard Geometry — b. Brocard Circle (Brocard Triangles, Steiner & Tarry Points)	0298–0303	279–284	§§ 666–683
F	Tucker Circles (incl. Taylor Circle § 689)	0303–0306	284–287	§§ 684–689
G	The Orthopole	0306–0310	287–291	§§ 690–699
Supplementary	Supplementary Exercises & Blank Verso	0310–0313	291–[294]	—

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