PROPERTIES of the CIRCLE. «65 
that is, equal to five times.a multiple, by the number of the fides 
of the figure of the cube on the fide of the infcribed decagon, 
together with fifteen times a multiple, by the fame number, of the 
folid, which has the fquare on the fide.of the infcribed decagon 
as its bafe, and 7 for its altitude, together with five times a 
multiple, by the fame number of the folid, which has = for its 
bafe, and the fide-of the decagon for its altitude. 
Let the circumference of a circle-be divided into any number 
n of equal parts, and from any point in the circumference let 
chords be drawn to the points of divifion, and let 3m be any 
number lefs than 2, the fum of the 2 powers of the lines 
which have refpectively to 27 the diameter, the ratios which 
the cubes of the chords have refpectively to 87°, the cube of 
the diameter, is equal to ” X HS: Sr etic Morea Ts 
: 1+2-3-4i . » 3m 2 
Let the chords be denoted by A, B, C, D, &c, to ” terms ; 
and let 872: A3 =27r:a,873:Bs=27r.b, 87: = arise, 
" H A3 fa " A™ 
$73:D? = 27:4, &c. Thenag=—,, and a" =, o"= 
af 47 Pe 
; Bo . A™ 
cae &c.; and a” -+ 4”-+ &c. to ” terms, is = sare 
ae vise ae 
B™ : 3 
+o t+ &e. to aterms.. If p=3m, we have a” + 
ee g 
A’? BY? ; 
be + &. = etm Pre + py ne &c, But the fum of 
p—1 
the 2p powers of the chords A, B &c. isa X en y re, 
Vou. VI.—P. I. I Therefore 
