Archimedes Texts

312
seth to be raised by a lesser, are the Pulley, the Inclined Plane, the
Wedg, the Capsten, or Wheel, the Screw, the Leaver, and some
others, for if we will not apply or compare them one to another,
we cannot well number more, and if we will apply them we need
not instance in so many.

Let A B C be a Chord put about the Pulley D, to which let
the Weight E be fastned; and first, supposing that two
men sustain or pull up equally each of them one of the

ends of the said Chord:
it is manifest, that if the
Weight weigheth 200
pounds, each of those
men shal employ but the
half thereof, that is to say,
the Force that is requisite
for sustaining or raising
of 100 pounds, for each
of them shal bear but the
half of it.

Afterwards, let us sup
pose that A, one of the
ends of this Chord, being
made fast to some Nail,
the other C be again su
stained by a Man; and it
is manifest, that this Man in C, needs not (no more than before)
for the sustaining the Weight E, more Force than is requisite for
the sustaining of 100 pounds: because the Nail at A doth the
same Office as the Man which we supposed there before. In fine,
let us suppose that this Man in C do pull the Chord to make the
Weight E to rise, and it is manifest, that if he there employeth
the Force which is requisite for the raising of 100 pounds to the
height of two feet, he shall raise this Weight E of 200 pounds to
the height of one foot: for the Chord A B C being doubled, as it
is, it must be pull'd two feet by the end C, to make the Weight E
rise as much, as if two men did draw it, the one by the end A,
and the other by the end C, each of them the length of one foot
only.

There is alwaies one thing that hinders the exactness of the Cal
culation, that is the ponderosity of the Chord or Pulley, and the
difficulty that we meet with in making the Chord to slip, and in
bearing it: but this is very small in comparison of that which