£34- CONSTRVCTIO AEQJ^ATIONIS 



enim eft, vtcimqiie haec aequatio refultans fiierit per- 

 plexa, eiu!) tamen conftrudionem in promtu fiituram. 

 Nunc igitur niliil aliud efl fliciendum, nifi \t quanti- 

 tates A,B,C, etc. et a,(3,Y, ctc. cfficiantur eius- 

 modi , Yt fummae feriei iftius inuentio ad refolutionem 

 huius aequationis a x^dx — dy -\-j- dx deducatur. Hoc 

 Ycro loco id efl: efficiendum vt feries i-j-A^Q^H-A 

 I3^2Q2 _^ABQ3Q_3_|_ ctc. pofTit in fummam re- 

 digi , quia ahas valor ipfius R non effet cognitus, et 

 promde integra conflrudio inutilis. Quamobrem non 

 licebit loco A,B,C etc. valorcs quosuis pro arbitrio 

 acciperc , fcd tales ^ quae hanc feriem fiimmabikm red- 

 dant. 



§. 6. Quo igitur appareat, cuiusmodi efTe debeat 

 feries i -f-Aa^-i-ABag^=-f- ABCaSy^^ _^ctc. vt 

 cius fummatio perducatur ad refolutioncm aequationis 

 ax^^dx—dj-^-y^dx:, hanc ipfam aequationem in fe- 

 liem refoluo.. Qiiod vt commodius eflici pofTit, pono 

 yzz-i^y fumtcque dx conflante crit ax^^dxzzj^ feu 

 ax^idx^~ddt. Nunc more confiieto fubftituo loco t 

 hanc feriem i -|- 5i' a"^-' -f- 25 .r- "-+-+ -f- ^ .v^ «-h<J -i- 

 etc. erit, ddt—( n-^i](n-h ^ '^x^dx^ -^i 2.;:-\-^) 



( 2 « -H 4 ) 33 ^^^"'*" ' '^^ ^ -f- ( 3 " H- ^ ) ( 3 «H-<J C ■'*^ ^ "■*" * 

 dx^ -f-.etc. Huic igitur ferici aequalis effe debct ax^ 



tdx- , feu ifta ieries ax^^dx^ -{-^{ax-^-^-dx- -{- ^ 



^.^.3n-t-+rt?.v- -f-etc. ^ propterca aequales fiicio terminos 



homogeneos determinandis littcris 5(^ ^/ ^ etc. pro 



arbitrio afTumtis, fietque ^tzr ^^ , ^n^^^ ^^^—^J^^i^-^) 



