ioB Dr. Waring on 
kind (a 4- bx n -j- cx ln -f-&c.) w + I x x («-(- @ x * +yx ln + &c. in infi- 
nitum). Sir Isaac Newton, by feriefes of the fame kind, 
found the fluents of fluxions of this formula {a + bx n + cx %n + 
&c.) ; x (e 4 -fx ri +gx 2n + &c.') m x &c.x°— l x; the fame principle 
is extended fomewhat more general in the Me dit at tones. 
8. Mr. John Bernoulli found the fluent of any fluxion 
/ 
nz ~ nz 
— - + — 
2 
3* 
&c. from the principles which Mr. 
Craig publifhed for finding the fluents of fluxions involving 
fluents. 
In the Meditationes fomething is added of the convergency 
of thefe feries ; and alfo, 
9. I11 them a new method is given pf finding approxi- 
mations. Let fame terms in the given quantity be much 
lefs or greater than the reft ; then reduce the- quantity into 
terms proceeding according to the dimenfions of the fmalL 
quantities, or according to the reciprocals of the great quan- 
tities, and it is done. If the fluent of the quantity refult- 
ing is required, find it from the common methods, if portable ; 
but if not, reduce the terms not to be found into an infinite fe- 
ries, and then find approximate values to each of the terms, &c. 
Ex. t* Let R the radius, and A the arc of a circle whofe 
line is S and cofine C, and A=t=e an arc of a circle which 
does not much differ from the arc A, that is, let e be a 
very fmall quantity; then will the fine of the arc A^e be 
- z 
o / I c 
I e* 
3~^4 X R 4 
3 • 4 • 5 • 6 
xL + &c .)-C( 
R 
X L 
U3 * 
3*4*5 RS 
L — &c.) ; and the cofine of the fame arc 
will be C ^ 1 - 
4 R 4 
- &c. in infinitum 
