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 Archimedes' Book of Lemmas

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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 Sand-reckoner", "Quadrature of the parabola", "On Floating Bodies", "Book of Lemmas" and "The Method".

In the book "Book of Lemmas", attributed by Thabit ibn-Qurra 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.

Table of Content
 


Proposition 1


 


Proposition 2


Proposition 3


Proposition 4
Arbelos


Proposition 5
Arbelos, Archimedean Twins
 


Proposition 6

Arbelos


Proposition 7
 


Proposition 8
Angle Trisection
 


Proposition 9.
 


Proposition 10
 


Proposition 11

 


Proposition 12
 


Proposition 13
 


Proposition 14
Salinon
 


Proposition 15.
 


 

 

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Last updated: March 12, 2008