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lunar Equations, given by Sir Ifaac Newton , are 
only fuch Approximations as may be exhibited by 
the firft Term of a Series derived by the Method 
here delivered, 
\ ' 
'Proportion. 
The Fluent of afcz n * m Xz ?n ''z being given [either 
in algebraic Terms , or from the Quadrature of 
the Conic Sett tons, &c.) it is propofed , by 
means thereof t o approximate the Fluent of 
fup- 
felond firm™* ** T ° conveT & e tM a f‘ er the 
Make cz~c x’‘^dx™ J r e x \«&c. and let Q be th< 
given Fluent of a + tvs")” x^ pn " z, anfweting to an; 
propofed Value of x-. Moreover let v=#p» or yi 
—x\ and let this Value of be fubftituted in th, 
firft Equation, and it will become cz.°=ejrf-L fy - r 
^ &C - whe,eof « he , being extrafled/w, 
lhall (by making R = — r_ fr+; .> pe 
“ 2 c<L 
T — ttl y a ’ 3 t *■ *+4 de pf , 
X i7 + -T- X cT — ' j &e.) 
ha\ 
3 («0=^rf Rz p ”+" -f &5 pn +“ &(. whence we 
a!fo obtain x pn “ x =r z p "'‘ z _J_ £il * Rz po+n-ia 
‘ ‘ P 
Let this Value, with that of cx n -J- dx 2n -^ex 2n 
&c. (above given) be now fubftituted in the pro- 
pofed 
