232 Of th SOLIDS 
a rectangle, of which the breadth is 2 BC, and the height 2 BL, 
the attraction of that plane, or of the thin folid, having that 
plane for its bafe, and 2, for its thicknefs, is 47.9. Now, 9, 
which is thus proportional to the attraction of the plane, is al- 
fo proportional to the fpherical furface, or the angular {pace, 
fubtended by the plane at the centre A. 
For fuppofe PSQ_ (Fig. 12.) and OQ_ to be two quadrants of 
great circles of a fphere, cutting one another at right angles in 
Q; let QO9=E, and QR=z. Through S, and O the pole of 
PSQ; draw the great circle OST, and through P and R, the 
great circle PTR, interfecting OS in T. The fpherical quadri- 
lateral SQRT, is that which the rectangle CL (Fig. 11.) would 
fubtend, if the {phere had its centre at A, if the point Q was 
in the line AB, and the circle PQ; in the vertical plane ABL. 
Now, in the fpherical triangle PST, right angled at S, cof T 
= cof PS x fin SPT = fin QS X fin QR = fin EX fin z. ~ But 
this is alfo the value of fin ¢, and therefore ¢ is the complement 
of the angle T, or g=90—T. 
Burt the area of the triangle PQR, in which both Q and R 
are right angles, is equal to the rectangle under the arch QR, 
which meafures the angle QPR, and the radius of the fphere. 
Alfo the area SPT =arc.(S+T+P—180°)73 that is, be- 
caufe S is a right angle, = arc.(T + P — 90) Xr = 
arc. (T+QR—go) Xr; and taking this away from the triangle 
PQR, there remains the area QSTR = arc.(QR —T—QR 
+90°)Xr=(g0—T)r=9xr. Thearch 9, therefore, mul- 
tiplied into the radius, is equal to the fpherical quadrilateral 
QSTR, fubtended by the rectangle BD. 
Tus propofition is evidently applicable to all rectangles 
whatfoever. For when the point B, where the perpendicular 
from A meets the plane of the rectangle, falls anywhere, as in 
Fig. 15. then it may be fhewn of each of the four rectangles 
BD, 
