Chapter III: Properties of the Triangle

Circumcircle, Medians, Tritangent Circles, Altitudes, Euler Line, Nine-Point Circle, Feuerbach’s Theorem, Orthocentric Quadrilateral

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• Archival Span: Folios 0072–0142 · Printed Pages 53–123 · Articles §§ 54–239

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Section & Article Conspectus

Section	Title	Folios	Pages	Articles
A	Preliminaries (Harmonic Division of a Segment & Apollonian Circle)	0072–0075	53–56	§§ 54–67
B	The Circumcircle (incl. Problem of Pappus § 84)	0076–0083	57–64	§§ 68–86
C	Medians (Centroid, Complementary & Anticomplementary Triangles)	0084–0090	65–71	§§ 87–110
D.a	Tritangent Circles — a. Bisectors	0091–0092	72–73	§§ 111–116
D.b	Tritangent Circles — b. Tritangent Centers	0092–0097	73–78	§§ 117–130
D.c	Tritangent Circles — c. Tritangent Radii (Carnot’s & Euler’s Theorems)	0097–0106	78–87	§§ 131–155
D.d	Tritangent Circles — d. Points of Contact	0106–0113	87–94	§§ 156–174
E.a	Altitudes — a. The Orthocenter	0113–0116	94–97	§§ 175–182
E.b	Altitudes — b. The Orthic Triangle	0116–0119	97–100	§§ 183–200
E.c	Altitudes — c. The Euler Line	0120–0121	101–102	§§ 201–205
F	The Nine-Point Circle (incl. Feuerbach’s Theorem § 215)	0122–0127	103–108	§§ 206–219
G	The Orthocentric Quadrilateral	0128–0134	109–115	§§ 220–239
Review	Review & Miscellaneous Exercises	0134–0142	115–123	—

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