== (158) = 



ciiiiis intcgrale eft 



V vd^ — /1 (3 t' — 3 ^) r^ C =r A B /. 



§. 17. Diuidamus niinc h;uiim ncquationum intcgrata- 



rum priorcm pcr qundratum polkrioris , vt clcmcntum tcm- 



poris () t elidamus, ficque nancifccmur hanc acquationcm: 

 n\iv — rf ♦ >» -4- 1) V a e* r 



in qua fi (V.ituairuis vt fupra d&—pdv^ prodibit hacc acquatio: 



n ( I — p)' -i- V 1' f p — r 



[i- V p — T! 1 I — p)]' A A * 



Sicque ndco inter binas qnantitatcs v ct p rclationem alge- 

 braicam fumus adcpti, quac crgo crit intcgralis acquationis il» 

 liu:) diffcrcntiali"', quac incxtricabilis ernt vila, fcilicet: 



V v p^ d V ::^ n V d p -i- ti p d 'V (i — />) ( - — />)• 



Quod fi enim illa acquatio ditfcrcntictur, haec iplii prodibit , 

 vti calculum inlUtucns mox rcpcrict. 



§. 1%. Quo has formulas fimpliciorcs rcddnmus, fta- 

 tuamus porro, vr lupra fccimus, vi^ziztiu^ atquc huius ac- 

 quationis diifcrcntialis : 



p' tl () II z^ 2U d p -\- p c) u (i — />) (- — p) 



intcerale crit : Li^z±l±Ji±l. — "-'"- . Hinc occafionem anipia* 



fcqucntia thcorcmata fubiiingcndi , quac, quotics ficri licct , 

 inuho gcncialius intcgrationcm talium acquationum dcclarant. 



Tlicorcma I. 



§. 19. Propofita hac ac(]iiationc diffcrcntiali : « ^ // -f- 

 P3w-+-tfBQr=:o, in qua littcrac P ct Q fint eiusmodi fun- 



( n^ \* -\- n Q fi 

 «flioncs ipfius p, vt valor huius forniulac: l_j^^ , fiat 



quan- 



