[ 111 ] 
is exerted to turn the wheel, and none of it loft by ob- 
lique adion. Therefore the force which the weight 
A, exerts to oppofe the weight P, and turn the wheel 
when it hangs from D, is, to the force it exerts when 
it hangs from K, as the line DC to A D, or as O 
K, to O D, (fim. triang. ADC, DOK) that is the 
force exerted by the weight A, hanging from the 
points D, and K, are inverfely as the radii O D, and 
O K. And therefore to fuppofe, that thefe two forces 
will have the fame effect in turning the wheel and 
oppofing the weight P, is the fame as fuppofing that 
two forces will have equal efteds in moving the arms 
of a lever (on which they ad perpendicularly) when 
they are inverfely as the lengths of thofe arms. — 
But this is the very conclufion Sir Ifaac draws from 
his premifes, for he fays : c£ Pondera igitur A & P, 
“ quae font reciproce ut radii in diredum pofiti O K, 
cc O L, idem pollebunt et ftc confiftent in aequili- 
“ brio, quae eft proprietas notiflima librae vedis et 
“ axis in peritrochio”. This property of the lever, 
which is here exprefled in general terms, includes two 
cafes. For the arms of the lever may be either per- 
pendicular or oblique to the diredions of the weights. 
The firft of thefe cafes is the ffmpleft, and fhould 
be firft demonftrated : And I do not fee how there can 
be any room for applying the refolution of forces in 
demonftrating this cafe, in which no part of ei- 
ther weight is loft by oblique adion. But when 
this cafe is proved, we have from thence, by the 
refolution of forces, an eafy way of fhewing, in 
the fecond cafe, when the arms of the lever are 
oblique to the diredions of the weights, that the 
weights will counterballance each other, when they 
are reciprocally as the perpendicular diftances of their 
lines 
