Archimedes' Book of Lemmas  Index




Archimedes' Book of Lemmas






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. 
Archimedes (287  212 B.C.) was born
at Syracuse of Sicily as a son of the astronomer Pheidias. He learnt from the disciples of the mathematician Euclid
when he was young. Archimedes is considered one of the three
greatest mathematicians of all time (together with Newton and
Gauss).
According to "The Works of Archimedes"
by T. L. Heath, Cambridge 1897, Archimedes' works included "On the Sphere and Cylinder",
"On the Measurement of a Circle", "On Conoids and Spheroids",
"On Spirals", "On the Equilibriums of Planes", "The
Sandreckoner", "Quadrature of the parabola", "On Floating Bodies", "Book of
Lemmas" and "The Method".
In the book "Book of Lemmas",
attributed by Thabit ibnQurra to Archimedes, there were 15
propositions on circles, with the first proposition referred in the subsequent
fifth and sixth propositions. The statements in
"Book of Lemmas" do not seem to concur to a central theme.
Lemma is a subsidiary proposition that
is assumed to be true in order to prove another proposition. There is no technical distinction
between a lemma, a proposition, and a theorem.
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.

