Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

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231144PHYSICES ELEMENTA eſt m - e; & tandem celeritas corporis D eſt {nd - ed/b}. Summa virium nunc
erit Amm + 2Ame + Acc + {Cccmm + 2Cccme + Cccee/aa} + Bnn - 2Bne
+ Bee + {Dddnn - 2Dddne + Dddee/bb}. Sed Aaa + Ccc x bbm
= Bbb + Ddd x aan; ponimus enim de hoc caſu agi; dividendo hanc
æquationem per aabb, habemus Am + {Cccm/aa} = Bn + {Dddn/bb}; idcirco
in ultima ſumma ſeſe mutuo deſtruunt + 2Ame + {2Cccme/aa} & - 2Bne -
{2Dddne/bb} & ſumma ad hanc reducitur Amm + Aee + {Cccmm + Cccee/aa}
+ Bnn + Bee + {Dddnn + {Dddee/bb} quæ primâ memoratâ ſummâ major
eſt. Q. D. E.
Nec diverſa eſt demonſtratio ſi augeatur n, imminutâ velocitate m.
Vis in colliſione quacunque, datâ velocitate reſpectivâ, deſtructa determi-
11536. nari poteſt, nam valet ſummam virium in caſu in quo hæc minima eſt . 22531. nunc m + n = r.
Datur ratio inter m & n & 33533.Aaa + Ccc x bb + Bbb + Ddd x aa, Aaa x Ccc x bb: :
m + n = r, n;
ergo n = {Aaa + Ccc x bbr/Aaa + Ccc x bb + Bbb + Ddd x aa}. Eodem modo detegi-
mus m = {Bbb + Ddd x aar/Aaa x Ccc x bb + Bbb + Ddd x aa}. Summa virium eſt
{Aaa + Ccc x mm/aa} + {Bbb + Ddd x nn/bb} , ſubſtituendo pro m & 44535 valores ſumma hæc erit
{Aaa + Ccc x Bbb + Dddq x aarr + Bbb + Ddd x Aaa + Cccq x bbrr/{/Aaa + Ccc x bb + Bbb + Ddd x aaq}
Dividendo numeratorem & denominatorem per Aaa + Ccc x bb

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