X^ X 

 MATHEMATICA. 



MF.TIIODVS AEQ.VAT10XCS DIFFERFATIALFS Al>TIO- 



It\M (JllADVWM 1\'1KGRAN!)1 VLlKItlVb rROMOlA 



AVCTOKli L tl'LtRO. 



H;KC Difleitatio fine dubio infignc continct culciili.jn- 

 icgr.ilis aiignKnaiin ; cum in c:i tnui.iLur nicthodus 

 innumcribilcb •acquationcs ;iltioiiim gniduum ita cxpcdite 

 intograndi , vt pcr vn.un opcrationcm (hitim acqu.itio in- 

 tcgralis obtincutur , ncijuc opus fit , tot intcgr.uioncs luc- 

 cciruic inflitucrc , quoti elt gradus acquatio diffcrcntialis 

 piopofita , ^cuiu^modi opcrationcs aliac mcthodi adhuc 

 cognitac rcquirant. Tradidcrat autcm Ai]{tor iti VII. fo- 

 himlne Miscell : Bcroini.iijiuiii iam fpccimcn huius nic- 

 thodi , vbi docucrat vna opcrationc intcgrak huius .tcqua- 

 tionis inucnire : 



O — Aj-H ax-r- dx^-r- j^j -t- ax* -r- -oTr -t- etc. 

 Tbi elcmennim d x fumtum elt conltans , litterac autem 

 A , B , C , D etc. coclBcicntcs dcnotant quo^cunquc 

 confiantcs : nuiic autcm hanc mcthodum extcudit ad hanc 

 formam multo iatius patcntcm : 



\bi littcn X denotat quantitatcm qunmcunquc cx varia- 

 bili X ct conrtantibus vtcunquc conflatam. Omnino hic 

 ntnatu cft dignnm , quod opcratio ftmpcr fucccdat , ad 

 qucmcunque ctiam gradum diff-rcntialiiim acquatio atcen- 

 dat , nc gradu quidcm infinitcfimo cxclufb , cu ns exiniia 

 e\cmp'a Au(flor in fcqucnribus cxhibct. In hac autcm 

 Djfltiutiouc primum cafum admodum fimpliccm hic ac- 



qu.iiione 



