Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1Force in F, that it may raiſe the Weight, muſt move upwards, which
to exanimate Movers, as being for the moſt part Grave Bodies, is al­

together impoſſible, or at leaſt more laborious,
than the making of the ſame Force down­
wards: Therefore to help this inconvenience,
a Remedy hath been found by adjoyning an­
other Nut or Pulley above, as in the adjacent
Figure is ſeen, where the Rope C E F hath
upheld by the Hook L, ſo that the Rope paſſing
to H, and thither transferring the Force E, it
ſhall be able to move the Weight X by pulling
downwards, but not that it may be leſſer than
it was in E: For the Motions of the Force
F H, hanging at the equal Diſtances F D and
D G of the upper Pulley, do alwaies continue
equal; nor doth that upper Pulley (as hath
been ſhewn above) come to produce any di­
minution in the Labour.
Moreover it having been neceſſary by
the addition of the upper Pulley to introduce the Appendix B, by
which it is ſuſtained, it will prove of ſome benefit to us to raiſe
the other A, to which one end of the Rope was faſtned, transferring
it to a Ring annexed to the lower part of the Frame of the upper
Pulley, as we ſee it done in M.
Now finally, this Machine com­
pounded of upper and lower Pullies, is that which the Greeks call

Τποχίλιον.
*Called by ſome
a Nut.
* Or two ends of
the ſame Rope.
In Latine Tro­
chlea.
We have hitherto explained, how by help of Pullies one may
double the Force, it remaineth that with the greateſt brevity poſ­
ſible, we ſhew the way how to encreaſe it according to any Multi­
plicity.
And firſt we will ſpeak of the Multiplicity according to
the even numbers, and then the odde: To ſhew how we may mul­
tiply the Force in a quadruple Proportion, we will propound the
following Speculation as the Soul of all that followeth.
Take two Leavers, A B, C D, with the Fulciments in the ex­

treams A and C; and at the middles
of each of them let the Grave G hang,
ſuſtained by two Forces of equal Mo­
ment placed in B and D.
I ſay, that
the Moment of each of them will
equal the Moment of the fourth part
of the Weight G. For the two For­
ces B and D bearing equally, it is
manifeſt, that the Force D hath not
contraſted with more then one half of the Weight G: But if the
Force D do by benefit of the Leaver D C ſuſtain the half of the