P - 3 
or^-a-x 
( 1*59 > 
X X . 
2 a 
whofe flowing quantity is -- 
p 
_ 1 
2 
X3 
D 3X “ 
-XX + -» i: 
2 a ' 
-3 V V* * 
V* V- V 
u* A A 
3C X X « 
fan 
x4 P 
Which Solid being divided by — a a ( the Area 
8 a-' ‘ D 
of a Circle whofe Radius is a ) gives -~- A """" — ■ - ~ + 
2 a 2 a a a a a 
for the height of a Cylinder on the fa id circular Bale, 
and equal to the Solid made by converfion of the Area 
F a b H F about the Line H b as an Axis. When x = a 
( that is when the whole Figure is turn'd about its A- 
X X 
fymptote ) , the height — ^ 
X’ 
2 a a 
+ 
x* 
8 a a 
become i a. 
VI. The Curve furface of the Solid generated by the 
Converfion of the Figure Fab H F about H SI is equal to * 
the. Curve furface of a Cylinder whole Radius is <*., and 
height equal to- — x + - ~ - VII. * * X — , And the whole 
0 1 2 4 a 12 a a 
Curve Surface of the Solid infinitely continued, is equal to 
one third part of the Curve Surface of a Cylinder whofe Radius 
and Height are equal to F H or a . Which may be demon- • 
ftrated after the manner of the precedent Propofition” 
VII. The Radius of the Curvature of any Particle of 
t t 
the Quadratrix is and this found Geometrically. 
a ■ x* 
In Fig. 3. FA E is the S&adratrixi H D the Afymptot^ 
A D the Tangent, B D the Subtangent tb a given point A. 
Make B V = A D. Upon V rife the perpendicular V W. 
from A draw A W perpendicular to the Tangent A D till 
it 
