(io5) 



p ^. Q / - I — A tang. (a: H- j/ ]/ — i) , 

 erit figno in^aginarii mutato ■■-' 



p «. Q / _ 1 — A tang. (x —y / — i). 

 His jam formulis additis prodit 



2 P — A tang. (x -^y y — i) -4- A tang. (.v — ^ |/ — , i) 



= A f'^"g- .-,.'/_-,^ 5 ideoque 

 P n: I A tang aJE — — ^ A tang L£ . 



Deinde fubtradio iliarum formularum praebet 

 2 Q |/ — I — A tang. {x -^y ]/ — i) 



— A tang. (.V — / / — i) nz A tang. '^^^r . 



Quia vero efl; 



A tang. // / — I =: r ^^V--< — ■/ — j f du _. v^-i / i±u 



*=■ ' -^ i~uu " ■' 1 — v.u a i — u^ 



hinc, cum noftro cafu fit u nr ^-2 , erit 



i-hxx— yy' 

 ^' 2 xx-i-(y-i)'^ *-^6" 



^ "* X3C+l^ — I)» 



prorfus vti invenimus. Hoc autem imprimis pro aliis cafibus 

 eft notandum, vbi , quoties integralc /Z 3 s per logarithmos 

 vel arcus circulares exprimere licct , quoniam, pofito z zzi x 

 "^-y V — i? lios in partes duas refolvere licet, alteram realcm, 

 alteram fimpliciter imaginariam, inde valores quantitatum PetQ 

 afTignari poterunt , quantumus ipfae formulae integrales pro 

 his iitteris refultantes fuerint perplexae et abftrufae. 



III. Euolutio 

 formula^^ difFerentialis : j-^, cujus integrale conftat efle 



ll(i-hz) — ll-/(i-z + zz)H--LA tang. ;_^'^ . 

 §. 13. Ponamus igitur hic z — X-hy y — 1 , eritque 



