178 EXERCITATIONES 



ita eft comparata , vt omnes adhuc labores ad eius 

 fummam inueftigandam firuftra fufcepti fiat. Cum 

 igitur fit cof. 2-=ii TT z:: o et fin. 5Lri^ w = i> noftra 

 aequatio banc induet formam : 



'+P+^+.^ + ^^<^^_-i 7r'(i+(o/7r) ^ i-2* + 3*-4-'4-etc.j 



M^t+p +^ + ,^ + eic^ — TT w' 2-f-(3-2X)w^-w(2V2-3V3+4V4- -etc.)} 

 Verum quia 



I - 2' H- 3' - 4* 4- etc. =: O, 

 pofito carro, habebimus 

 i+li+f, + 7J+etc.zzi7rX2V2- 3^/3+4/ 4-5V5+etc.) 



ficque ad fcopum pertingeremus , fi huius feriti lo- 

 garithmicae 



2^ / 2 - 3' / 3 -f- 4' / 4 - 5' / 5 -H etc. 

 fummam affignare liceret. Simili autem modo pro 

 reliquis poteftatibus reperitur 

 x + ^+ii-|-^^,+etc.=z,:=^(272-3V3+4/4-5V5+etc.> 



,4-l_+l^ + i, + etc.i=^t!Ii(2V2-3V3+4'/4-5'/5+etc.) 



»+P+^p + J5 + etc.=i:,-^(2V2-3'/3+4V4-5V5+etc.) 



8. Propofita ergo nobis fit haec feries infinita; 

 2V2-3'/3 + 4'/4-5'^5+6'/(J-7'/7+ctc. = Z 



■vt fiat I -f- ^ -i- 7i -f- ^ -i- etc. =z ^ TT 71 2 , 



et quo minus de eius fumma defperemus , notetur 



efle 



/2-/3+/4-/5+/<?-etc. = ^/r. 



Illa 



