J^ ) o ( ili^ 141 



§. 19. Equidem his nil novi detegitur, cum tamen utile Tab. VI. 

 fit, inventionum referare fontes, licebitadiiuc adnectere inven- 

 tionem feriei LEIBNIZIANtE ex formulis, quas prò finibus 

 arcuum multiplorum eruit fummus NEWTONUS. Sit finus 

 arcus lìmpli =a, cofìnus = b, radius =r, finus anguli vel ar- 



cus m tupli =x, erit x= —zrr ( ^^ — ^^ ^^— ^ 



>^ \ 2. 3 



^3 ^-^ ^f,!!!^ !!:i^. '^i- ^ill^^^-^ &c.) 

 234^ 

 Hinc erit finus tn tupli x pars 4 



I y- m-i 3 »»~3 \ 



Z^ (b a 0»-'l). 0?/-2) /> « if< &C. j 



\ 2 3 



Quodfi iam ponatur ;;; infinite parva , five == o erit - 



X r> X 



=- arcus nnui b refpondens, adeoque - v r 



( — ? ** ^ = * &c. ) 



h t 



Sit tangens huius arcus == ty erit - ==-' unde v = 



a r 



3 >- 5 > 7 >-^ 



Eadem haec feries ex formula tangentium x m 



(r->t — '"^^ ''±:^ r-= ^3 ^ w::!- '«;-a. ;_«^ W..4. ^^..4^, 



^ 2 2 3 



— &c. 



S 3 diredle 



