C 765 ] 
ol-\- s/ olol — if: which values being fubftituted 
above, we thence get 
— A x log. 1 — qx -j- log. 1 — r x 
+ V A A — ix log. 1 . — qx — log. 1 — rx ; 
whereof the former part (which, excluflve of the 
fadtor A, I fhall hereafter denote by M) is manifeftly 
equal to — A x log. 1 — qx x 1 rx (by the na- 
ture of logarithms) = — A x log. 1 — q -j- r.x + 
qrx z = — Ax log. 1 — 2 a,x -j- xx (by fubflituting 
the values of q and r) : which is now intirely free 
from imaginary quantities. But, in order to exter- 
minate them out of the latter part alfo, put y zxz 
log. 1 — qx — log. 1 — rx; then will y — 
+ 
r X 
rxx 
I — r x 
2 A CLCL I X X 
2 \A — 1 l — -cuXX 
I — q~\~ rXx xx I — 2 * X x x 
where 1/1 * * 
ex- 
I__ 2 XX XX ^ ' I — Z/lx + xx 
preflfeth the fluxion of a circular arch ( 2 V) whofe radius 
is 1 , and fine = ^ ^ > confequently y will be 
— — 2 A — 1 x N: which, multiplied by A A A — i, 
or its equal y/^T x y/i — AA, gives 2 y/i —AA xN> 
the correfponding fubmultiples of thofe above, anfwering to the co- 
fine X (— 1). In the fame manner, if X be taken — i — - 
co-f. 1 8o° — co-f. 3 X 1 8o° — co-f. 5 X 1 8o°, & c. then will z n — - — c, 
or z” + 1 = o ; and the values of x will, in this cafe, be the co fines 
, 180 0 180° 180° 
ef , 3 X , 5 X , C 2 V, 
n n n 
and v 
n 
