to be as rtoc) and the Surfdce generated by the Se- 
micircumferehce B K A is equal to a Re dangle whofe 
bafe is the fumm of that Semicircamference and Dia- 
meter B A, and height the Circmiiference of a Circle 
. whofe Diameter is B C. As for the Surface generated 
by the arc G F, 'tis well known, that it is equal to a 
Reaangle whofe ! bafe is the Circiiroference of a Cir^ 
cle vvhofe Raffius h B Q and height D E 3 Therefore 
the Surface generated by the Converfion of the Port i^ 
on M H F G is known. 
If upon B A f Fig. 2. ) you take any two Points 
I, and draw I N, L V perpendicular to it, cutting 
the Quadrant in O and T, and the Circumference in 
N and V, the Solid genemted by the converfion of the 
Portion O N U Tabout the Axis B A,is equal to a Prifm 
whofe Bafe is I O T L, and height the Circumference 
of a Circle whofe Diameter is B A. 
Having bifefted B A m R,.)and drawn C R meeting 
the Quadrant in G,, the Surface > generated by ^uhe 
Converfion of the Arc OT about B A 3s . equal to 
cgFTl^cr^ot. 
Bifeft DEin Y (Fig. i,) through the Center R 
draw S Q parallel to B C, meeting the Circumference 
B K A in B K parallel to A C in V^and the Lines D 
EM in N and O ^ the Solid generated by the Con- 
verfion of the Portion FG M H about the Axis A C,. is 
c^MO'^H^'^PCx NOMH ^ CY^^ DNOE-, iiXj' 
^TD?^y and the Solid generated by the Segment 
^ X , VK \^FCy. BUKS. Therefore the Solid 
generated by t he Semicircle B K A about A^ is 
:x PC X VQ-\lv PC X BCQV^-3- KOWW^' * PC 
F^BVKS, which by due redudion will be found equal 
to the Solid generated by the Converfion of the fame 
Semicircle about the Axis BC, 
