Britannica –
“The most famous mathematician and inventor of ancient Greece. Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. He is known for his formulation of a hydrostatic principle (known as Archimedes’ principle) and a device for raising water, still used in developing countries, known as the Archimedes screw.
Far more details survive about the life of Archimedes than about any other ancient scientist, but they are largely anecdotal…
There are nine extant treatises by Archimedes in Greek:
On Conoids and Spheroids deals with determining the volume.
On the Equilibrium of Planes (or Centres of Gravity of Planes; in two books) is mainly concerned with establishing the centers of gravity of various rectilinear plane figures et al.
The Sand–Reckoner is a small treatise that is a jeu d’esprit written for the layman—it is addressed to Gelon, son of Hieron—that nevertheless contains some profoundly original mathematics. Its object is to remedy the inadequacies of the Greek numerical notation system by showing how to express a huge number—the number of grains of sand that it would take to fill the whole of the universe.
Method Concerning Mechanical Theorems describes a process of discovery in mathematics. It is the sole surviving work from antiquity, and one of the few from any period, that deals with this topic. In it Archimedes recounts how he used a “mechanical” method to arrive at some of his key discoveries.
On Floating Bodies (in two books) survives only partly in Greek, the rest in Medieval Latin translation from the Greek. It is the first known work on hydrostatics, of which Archimedes is recognized as the founder.
Archimedes is known, from references of later authors, to have written a number of other works that have not survived. Of particular interest are treatises on catoptrics, in which he discussed, among other things, the phenomenon of refraction….
Archimedes’ mathematical proofs and presentation exhibit great boldness and originality of thought on the one hand and extreme rigor on the other…
In antiquity, Archimedes was also known as an outstanding astronomer.”
Encyclopaedia Britannica Online, http://www.britannica.com/EBchecked/topic/32808/Archimedes (accessedJuly 1, 2009)