Archimedes

n. He was no compiler or writer of text-books, and in this respect he differs from Euclid and Apollonius, whose work largely consisted in systematising and generalising the methods used and t

ticular discoveries made by his predecessors had suggested to him the possibility of extending them in new directions; thus he says that, in connexion with the efforts of earlier geometers to square the circle, it occurred to him that no one had tried to square a parabolic segment; he accordingly attempted the problem and finally solved it. Similarly he describes his discoveries about the v

k text of Archimedes give his

re and Cylinde

ement of

oids and

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Equilibriums

Sandr

ture of a

unately with only partial success) to wash out the old writing, and then the parchment was used again to write a Euchologion upon. However, on most of the leaves the earlier writing remains more or less legible. The important fact about the MS. is that it contains, besides substantial portions of the treatises previously known, (1) a considerable portion of the work, in two books, On Floating Bodies, which was formerly supposed to

ion; but from the various prefaces and from internal evidence generally we are ab

ne Equili

ture of a

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he M

here and Cyl

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oids and

ating Bod

ement of

Sandre

bably collected by some later Greek writer for the purpose of illustrating some ancient work. It is, however, quite likely that some of the propositions, which are remarkably elegant, were of Archimedean origin, notably those concer

ources is that the formula for the area of any trian

? a) (s ? b

ecause Heron gives the geometrical pro

he problem was communicated by Archimedes to the mathematicians at Alexandria in a letter to Eratosthenes; and a scholium to Plato's Charmides speaks of the proble

himedes the followin

a description of thirteen other polyhedra discovered by Archimedes which are semi-regular, being contained by polygons eq

nded a system of expressing large numbers which could not be written in the ordinary Greek notation. In setting out the same system in

his work Archimedes proved that "greater circles overpowe

parate treatises, Possibly Book I. On Plane Equilibriums may have been part of a larger work (called perhaps Elements of Mechanics), a

from which Theon of Alexandria

construction of a sphere to represent the moti

circle, (3) On circles touching one another, (4) On parallel lines, (5) On triangles, (6) On the prop