
Archimedes' Book of Lemmas
Table of Content
Exercise your brain. Archimedes wrote
the "Book of Lemmas" more than 2200 years ago. Solve these 15
high school level problems and lift up your geometry skills. 



Proposition 1.
Tangent circles and parallel diameters 

Proposition 2
Semicircle, diameter, tangents, secant line. 

Proposition 3
Semicircle, perpendicular to diameter, chords. 

Proposition 4
Semicircles, perpendicular to diameter, Arbelos.


Proposition 5
Arbelos, Archimedean Twins,
Semicircles, Circles


Proposition 6
Arbelos, Semicircles, Circle.


Proposition 7
Square and inscribed and circumscribed Circles


Proposition 8
Angle Trisection. Neusis construction. 

Proposition 9.
Perpendicular chords, sum of arcs. 

Proposition 10
Tangents to a circle, secant line and chords, Parallel. 

Proposition 11
Perpendicular chords and radius, square. 

Proposition 12
Semicircle, Diameter, Chords, Tangents, Perpendicular. 

Proposition 13
Circle, Diameter, Chord, Perpendicular, Congruence. 

Proposition 14
Salinon: Semicircles, Perpendicular, Circles, Areas. 

Proposition 15
Circle, Diameter, Inscribed Regular Pentagon, Arc, Midpoint,
Perpendicular, Radius. 

Arbelos, Theorems and Problems
Three tangent semicircles with collinear
centers.
Index 