i6p 
Method of correfpondent Values, &c. 
an tCi A? ccn 2 h end C 4- &C. 
’• ( 3 pa -f- ( 3 p z b -f* [3 p c -f* &c* 
yaCl^r y<r~b + ycr^C 4 ~ &C® 
&c. &c. &c. ~ 
and then made the fnm of each of the terms refpedtively equal 
to its correfpondent term of the quantity r^+fi + fV-f &c,, 
and confequently an + / 3 p + ycr -j- &c. = r, an' '-P/ 3 p 2 -t-y<r 2 4 -&Co 
— r% an + ( 3 p + ycr 3 + &c. ~ t 3 , &c. 1 a flu me d as many equa^ 
tions of this kind as there were given values 7 r, p, cr, &c. of % $ 
and confequently as many equations resulted as unknown 
quantities a, ( 2 * y , &c. ; whence, by the common re foliation of 
Ample equations, or more eafily from differences, can be found 
the unknown quantities ( 3 , y , &c., and thence the equation 
fought a x Sn 4-/3 x Sp 4- y x So- 4- &c. ~'Sr nearly, 
3. In the Meditationes are aflumed for n } g, <r, &c, the 
quantities p , 2 p, 3 p, 4 p, . . . » - 2p r n — ip , and np for t ; 
which, if fubftituted for their values in the preceding equa- 
tions, will give a + 2/G + 37 + 4<? + &c. = n, a + 4/2 + p>+ 16S4-] 
&c. — /f , # 4 - 8 / 34 - 27^ 4- &c. ~n 3 , a 4- 1 6/3 4 - 8 1 y 4 - &c. ~ /f ; 
and if the fums of the feries 4- bx % + cx 3 4* &c. which re- 
fpedtively correfpond to the values p 9 2 p, 3^, . . . n — ip of x be 
Si, S2, S3, S4, . . . Sn — 1, and the fum of the feries ax 4- bx z -p ! 
cx 3 4-&c. which correfponds to » value of #beS/z; then will 
S n — nbn - 1 —n . - — bn — 2 + n . . bn — 3 . . . « Si 
2 2 2 u 
nearly, which equation is given in the above-mentioned Book* 
3. The logarithm from the number, the arc from the fine, 
&c. are found by feriefes of the formula ax +-bx t + cx 3 4- &c. ; 
and confequently this equation is applicable to them* 
6 4, In 
