520 Mr. milner on the 
elements of mechanics and the dodtrine of moving 
forces ; and therefore I muft believe that it is by miftake 
that one author of note entirely omits fo neceflary a ftep 
which affedts the conclufion by juft one half. When a 
body moves with any velocity in the direction am (fig. 
7.) which would carry it through the fpace ad in a fmall 
particle of time, and any force which may be reckoned 
conftant for that time urges the body through the fpace 
do perpendicular to am, the body at the end of that time 
will arrive at the point c ; but joining ac we are not to 
fuppofe, that, if that force ceafed to act, the body would 
proceed in the diredtion acl : for take c m equal and pa- 
rallel to ad, and cdin. cd produced equal to 2 CD, and 
the diredtion of c at that point will be c /, the diagonal of 
the parallelogram c dim. 
Thus when a body revolves in any curve by a centri- 
petal force (fig. 8.) we may, with Sir isaac newton, 
fuppofe the curve to be compofed of an indefinite num- 
ber of right lines, and the body to move either in the 
chords or the tangents of the curve ; but then we are to 
take care that we make not fuppofitions inconfiftent with 
each other. Let the curve be a circle, and ad a tangent 
at the point a the diredtion of the body’s motion when 
it arrives at that point, and let dc, parallel to the diame- 
ter al be the effedt of the centripetal force : then, if we 
a fuppofe 
