
Classical Theorems  Page 1




Pythagorean Theorem.


Euclid's Elements Book II, Proposition 12: Law of Cosines.


Euclid's Elements Book II, Proposition 13: Law of Cosines.


Median
length, Apollonius' Theorem 

The significance of the Pythagorean theorem by Jacob
Bronowski.
Pythagorean Theorem, 47th Proposition of Euclid's Book I. 

Carnot's Theorem. Geometry Problem 889
Carnot's Theorem in an acute triangle, Circumcenter, Circumradius, Inradius. GeoGebra, HTML5 Animation for Tablets. 

Ceva's Theorem.
Concurrency. Interactive proof with animation. Key concept:
Menelaus Theorem. 

Menelaus' Theorem. Interactive proof with
animation and key concepts..


van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation. 

van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation for Tablets, iPad,
Nexus, Galaxy. 

Heron's Formula.
Key facts and
a purely geometric
stepbystep proof.


Euclid's Elements
Book I, 23 Definitions. Onepage visual illustration.
Euclid's Elements Book.
Index 

Euclid's Elements Book VI, Proposition 3: Angle Bisector Theorem 

Euclid's
Elements, Book XIII, Proposition 10 One page visual illustration. 

Ptolemy's Theorem.


Dynamic Geometry: Brahmagupta Theorem,
. GeoGebra, HTML5 Animation for Tablets 

Brianchon's Theorem in a Circumscribed Hexagon. 

Brianchon Corollary, Circumscribed Hexagon, Concurrency lines. 

Carnot's
Theorem in an Acute Triangle. 

Carnot's
Theorem in an Obtuse Triangle. 

Clifford's Circle Chain
Theorems. This is a step by step presentation of the first theorem.
Clifford discovered, in the ordinary Euclidean plane, a "sequence or
chain of theorems" of increasing complexity, each building on the last
in a natural progression.


Cyclic
Quadrilateral: Ratio of the Diagonals


NinePoint Center, NinePoint Circle, Euler Line.
Interactive illustration.


Soddy
Circles and Descartes Theorem.
Three tangent circles, Inscribed and Circumscribed Circles, Radii. 

Euler's Problem, Problem 155. Distance between the Incenter to the Circumcenter. 

The Simson Line, Theorems
and Problems  Index. 

Casey's Theorem. Generalized Ptolemy's Theorem.


Brahmagupta's Formula
Area of a cyclic quadrilateral.


Brahmagupta's Theorem
Cyclic quadrilateral.


Platonic
Solids, Interactive animation.
HTML5 Animation for iPad and Nexus
Flash Animation. 

Theaetetus' Theorem, Platonic Solids, Interactive animation 
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