A history of Greek mathematics - Wilbourhall.org

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THE COLLECTION. BOOK VIII 429
mathematics and the practical work, he who has not the former
must perforce use the resources which practical experience in
his particular art or craft gives him. Other varieties of
mechanical work included by the ancients under the general
term mechanics were (1) the use of the mechanical powers,
or devices for moving or lifting great weights by means of
a small force, (2) the construction of engines of war for
throwing projectiles a long distance, (3) the pumping of water
from great depths, (4)
'
the devices of wonder-workers
(Oavfiao-iovpyoi), some depending on pneumatics (like Heron
in the Pneumatica), some using strings, &c, to produce movements
like those of living things (like Heron in 'Automata and
Balancings '), some employing floating t
bodies (like Archimedes
in Floating Bodies ' '), others using water to measure time
(like Heron in his ' Water-clocks'), and lastly ' sphere-making
',
or the construction of mechanical imitations of the movements
of the heavenly bodies with the uniform circular motion of
water as the motive power. Archimedes, says Pappus, was
held to be the one person who had understood the cause and
the reason of all these various devices, and had applied his
extraordinarily versatile genius and inventiveness to all the
purposes of daily life, and yet, although this brought him
unexampled fame the world over, so that his name was on
every one's lips, he disdained (according to Carpus) to write
any mechanical work save a tract on sphere-making, but
diligently wrote all that he could in a small compass of the
most advanced parts of geometry and of subjects connected
with arithmetic. Carpus himself, says Pappus, as well as
others applied geometry to practical arts, and with reason
'
for geometry is in no wise injured, nay it is by nature
capable of giving substance to many arts by being associated
with them, and, so far from being injured, it may be said,
while itself advancing those arts, to be honoured and adorned
by them in return.'
The object of the Book.
Pappus then describes the object of the Book, namely
to set out the propositions which the ancients established by
geometrical methods, besides certain useful theorems discovered
by himself, but in a shorter and clearer form and