Chapter 3 - Three Samples of Archimedean Mathematics

Summary

Archimedes' Life

In weightiness of matter and elegance of style, no classical mathematical treatise surpasses the works of Archimedes. This was recognized already in antiquity; thus Plutarch says of Archimedes' works:

It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanations. Some ascribe this to his genius; while others think that incredible effort and toil produced these, to all appearances, easy and unlaboured results.

Plutarch, who lived in the second half of the first century a.d., writes this in his Lives of the Noble Grecians and Romans, more specifically in his life of Marcellus. Marcellus was the general in charge of the Roman army that besieged, and ultimately took, the Greek colony of Syracuse on Sicily during the second Punic War (218–201 b.c.). Archimedes' ingenious war-machines played an important role in the defense of Syracuse, and for this reason Plutarch writes about him at some length.

Archimedes introduces each of his books with a dedicatory preface, where he often gives some background for the problem he is about to treat. These prefaces contain precious information for the historian of mathematics, and they even throw some light on Archimedes' life. There are, furthermore, scattered references to him in the classical literature, and so he becomes the Greek mathematician about whom we have the most biographical information, even though it is precious little.