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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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ERINCIPTA MATHEMATICA.
Stantibus quae in superiore Propositione constructa TUnE, exCAE LIBEU
corpus de loco s in Trajectoriam inveniendam STFR; dc, Cx da- PRimvS.
ta ejus velocitate in alcieudine SC, dabitur ejus relocitas in alia
quaris alcitudine TC. Fa cum velocitate, dato tempore quanr
minimo, deseribat corpus Frajectorix sua particulam PF, sIEque
P veltisium ejus in plano AOP descriprum. Pungatur Op, de
Circellicentro P interrallo T+ in Superticie curra descripei(IE P D L
restigium Fllipticum in eodem plano O A P p descripcum. FF ob
datum magnitudine ex politione Circellum, dabitur Ellipsis illa
PE. Cumque area P Op sic rempori proxortionalis, atque ad.
eo ex dato tempore detur, dabitur Op potitione, ec inde dabitur
communis ejus ex Ellipleos incersectio p, una cum angulo O F p,
in quo Trajectorix rectigium AP p secat lineam OP. Inde au-
cem invenietur Trajectoria restigium illud A F p, eadem methodo
qua curra linea VIK_, in Propolrione XEI, ex limilibus datis
inventa fuit. Tum ex singulis rectigii punctis P crisendo ad pla-
num AO F perpendicula P F superticiei currae occurrencia in F,
dabuntur singula Trajectorixe puncta F.
d. F. I.
47
due u a
De Motu Corporum Viribus centripetis se mutuo petentium.
Fractenus exposui Mocus corporum attractorum ad centrum Im-
mobile, quale camen vix extat in rerum nacura. Atcractiones enim
Feri solene ad corpora; ex corporum crahentium ex accractorum
actiones semper mutux sunt e aequales, per Legem certiam: ad
Co ut neque actrahens possie quiclcere neque accractum, si duo sint
corpora, sed ambo (per Leoum Corollarium quartum) quali aE-
cractione mutua, circum graritaris centrum commune revolvantur:
eE AI pIUra TINE COrPOra (quae vel ab unico accratiantur vel omnia
se mucuo actrahant) haec ica inter se moreri debeane, ut graritatis
centrum commune vel quiescac vel uniformiter moreatur in direc-
cum. Oua de causa jam perso Motum exponere corporum le mu-
cuo trahentium, considerando Vires centripetastanquam Aerractio-
nes, quamvis Fortasse, si physice loquamur, verius dicantur Im
pulsus. In Machematicis enim jam versammur, et propterca missis
dispuracionibus Physicis, tamiliari utimur sermone, quo possimus
a Lectoribus Machemacicis Facilius intelligi.
a R