mTERMINATIONE, 83 



dy d dy , d ^ y , d *y , 



ji X =z_y -f- Tdi -t- TTTd^ -4- rnTTdr^ -+- ,.,.j.,dx* -t- ctc. 

 pro tali autem aeqiiatione rcldluenda regula generalis non 

 conftat. At leui negotio haec aequatio in aliam formam 

 transformatur , quam refoluere liceat. Ponatur fciii(;et 

 ^ — f ■" , erit y zz e"^' , ideoque fiet e'"' zn e'" x , fumtisque 

 logarithmis : ij'' — 1' -H / a; , quocirca habebitur : 



, di) ddv &^v , _ d ♦f , div 



quaq aequatio in praecedente continetur , faciendo X — lXy 

 quocirca integrale erit : 



'— fr/ 7 •"*"" '"'"'^" ^ '^^I^^^^- ^^^- - '^■^'+2 Cof. ^'KXjdxlx. COf 47T.Y4- CtC. 



■"•' " +2fin. STrv/fl^.r/.v.fin. STTX+afin. 47rA/r/.v/A-. fin. 47TX-i-etc. 

 Inuento autem valore ipfius v , erit terminus generalis 

 quaefitus y — e"" : denotante e numerum , cuius logarith- 

 mus hyperbolicus eft ~ 1. Q. E. I. 



Scholion. 



$. 60. Primum huius exprefiTionis membnim/ri^Ar/.v 

 cft •=: X l x - x ^ reliqua vero membra fingula per feries 

 infinitas integrari poterunt. Eft enim : 



Jdxlx. cof ;//r^^ fin. mx{lx-^ ^-i - ~: + -^^^^ - etc. ) 



__ -^k ^o^-M^x - ^-1- ij^lr - etc. ) 



fdxJx. fin. mx ~ — ^ coC mx (/.v-f-^i^ - ^i^ H- 1^«^«- — etc.) 



-4-^,fin.m*(^— ;pV*-+-if:t^ "■ etc. ) 



Vndc colligitur , fbre : 



acofm/^x/.v.cof ;/«;_, , j^ j^s._. _u2,r..s.l, . v 

 + afin .mxjdxlx. fin. /«.x^ — »"'"« ^ ™'*' "+■ "'*«* "'*''« +etc. j 



-f- a. cof ;// jv -}- 5( fin. ;//.v 

 ■ L 2 Subfti- 



