24 INVESTIGATION of fome 
chord CP, &c. is equal to the fum of the perpendiculars drawn 
from the point P to right lines touching the circle in the points 
A, 'ByiG, &c. 
AQ. BQ’ CQ’ , &e, - 
AND af = se = fum of perpendiculars 
drawn from Q to the fame lines. 
AGAIN, fince by a well known property of the circle, 
AP* + AQ’ =BP + BO ee + co’'= &e = 2r7+20p, 
r denoting radius, the fum of the fquares of lines drawn from 
the points A, B, C, &c. to any two points f, 7, in the diameter 
equally diftant from the centre, is =2”72?-+ 2X OP = amul- 
tiple of 7*, by twice the number of the points A, B, C, &c. to-. 
gether with the fame multiple of the {quare of Op or O g. 
In like manner, AV +AW+BV'+BW’-+-CV +CW7+, &c. 
—o2nrt-+2n2XOV = amultiple of 7* by twice the number of 
the points A, B, C, &c., together with the fame multiple of OV* 
or OW: 
Anp fince the fquares of the chords AP, BP, CP, &c. are to- 
gether equal to the fum of the fquares of the perpendiculars. 
drawn from P to the right lines touching the circle in the points 
A, B, C, &c. together with the fum of the fquares of the per- 
pendicular diftances of P from. the diameters pafling through 
thefe points, the fum of the fquares of Ap, Bp, CP, &c. is in 
like manner equal to the fum of the fquares of perpendiculars 
from p to thefe lines, together with the fum of the fquares of 
the perpendicular diftances from p to the faid diameters. 
In like manner, Ag t By atk OT fine: &c. = fum of fquares 
of perpendiculars from. to the lines touching the circle in A, 
B, C, &c. together with the fum of the fquares of the perpendi- 
cular diftances of 7 from the diameters pafling through A, B, 
C, &c. 
WHEREFORE 
