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THE

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AKCHIMEDES.

JLontom: C. J. CLAY AND SONS, CAMBRIDGE UNIVERSITY PRESS WAREHOUSE, AVE MARIA LANE.
263,

ARGYLE STREET.

flefo gorfc:

F. A. BROCK HAUS THE MACMILLANCOMPANY.

PREFACE.
S book
is

intended to form a companion volume to

my

edition of the treatise of Apollonius on Conic Sections
lately published.

If

it

was worth while

to

attempt to make the

work of "the great geometer" accessible to the mathematician of to-day who might not be able, in consequence of its length
and of
its

form, either to read
or,

it

in theoriginal
it,

Greek or

in a

Latin translation,

having read

to master

it

and grasp the
less of

whole scheme of the

treatise, I feel that I

owe even

an

apology for offering to the public a reproduction, on the same lines, of the extant works of perhaps the greatest mathematical
genius that the world has ever seen. Michel Chasles has drawn an instructivedistinction between
the predominant features of the geometry of Archimedes and of the geometry which we find so highly developed in Apollonius.

Their works

may be

regarded, says Chasles, as the origin
to share
is

and basis of two great inquiries which seem them the domain of geometry. Apollonius
the Geometry of

between

concerned with

Forms and

Situations, while inArchimedes

we

find the

Geometry of Measurements dealing with the quad-

rature of curvilinear plane figures and with the quadrature

and cubature of curved

surfaces, investigations

birth to the calculus of the infinite
to perfection successively

which "gave conceived and brought

and Newton."

But whether Archimedes

by Kepler, Cavalieri, Fermat, Leibniz, is viewed as thewith the limited means at his disposal, nevertheless succeeded in performing what are really integrations for the

man who,

purpose of finding the area of a parabolic segment and a

VI

PREFACE.

spiral,

the surface and volume of a sphere and a segnrent of a sphere, and the volume of any segments of the solids of revolution of the second degree, whether he is seen finding
ofparabolic segment, calculating arithmetical approximations to the value of TT, inventing a system for expressing in words any number up to that which

the centre

gravity of

a

we should

write

down with

1

followed

by 80,000

billion

ciphers, or inventing the

whole science of hydrostatics and at

the same time carrying it so far as to give a most complete investigationof the positions of rest and stability of a right

segment of a paraboloid of revolution floating in a fluid, the intelligent reader cannot fail to be struck by the remarkable
range of subjects and the mastery of treatment. And if these are such as to create genuine enthusiasm in the student of
Archimedes, the
attractive.

style

and method are no

less

irresistibly

One

featurewhich will probably most impress the

mathematician accustomed to the rapidity and directness secured

by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems.
effects, is

Yet

this very characteristic, with its incidental

calculated to excite the
tactics

more admiration because the
some greatstrategist

method suggests the
foresees

of

who

everything not immediately conducive to the execution of his plan, masters every position
everything, eliminates
in its order,

and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator,
ultimate object) strikes the
final

its

blow.

Thus we read
which

in
is

Archimedes...