Dr. Waring on 
velocity H ; and let the perpendicular from S to the tall- 
gent PY' be A; from the general fluent of fx D, where 
D denotes the diflance from S, and f is a function of 
D, properly corrected find its velocity V at diflance D» 
and confequently the perpendicular SY from the center S 
to the tangent PY at diflance D=SP, which will be 
A— 1 — S Y ; but A and II are given quantities, and V a known 
function of D; therefore SY and x/SP^D^ — SY 2 = PY will 
be known functions of D ; and from the fimilar triangles 
SPY and PQT may be deduced PY : SY :: PT=l 3 : QT, 
and confequently SP x QT — D x -yy- (which is a known 
• 
function of D multiplied into D) will be as the increment of 
the area defcribed round the center of force, of which the 
fluent properly corredted is proportional to the area defcribed 
round the center of force*, and confequently to the time. In 
like manner, (proportional to the increment of the 
l > x PY SP u 1 
angle defcribed by the body round S) is a function of D rttul- 
tiplied into D, of which the fluent properly corrected, or angle* 
will be as a function of D. 
1.2. Fig. 7. Given the above-mentioned force, &c. ; to find 
an equation exprefling the relation between the abfcifs SM = * 
and ordinate MP 2 = y of the curve defcribed, and their fluxions. 
From the fimilar triangles P 'po and LPM can be deduced 
po~y : oVzzx :: PM - y : LM=^-; but LM±SM^ -±A-a 
y y 
y ~* y - = LS ; a n d confequently P pz=\/x z +y z ; po —y :: LS 2= 
> Y A— . • SY = -y- zHL ; but SY is a function to be deduced 
as 
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