Full text: Gravesande, Willem Jacob: Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam

PHYSICES 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-
nari poteſt, nam valet ſummam virium in caſu in quo hæc minima eſt . Sit nunc m + n = r.

211.1.

536.
531.

Datur ratio inter m & n & componendo 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 & n valores ſumma hæc erit
{ Aaa + Ccc x Bbb + Ddd q x aarr + Bbb + Ddd x Aaa + Ccc q x bbrr/{ /Aaa + Ccc x bb + Bbb + Ddd x aa q }
Dividendo numeratorem & denominatorem per Aaa + Ccc x bb +

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