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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINOIPLA MATHEMATTCA.
53
Ex datis corporum motibus sub initio, datur uniformis mOTUS LTBEn
centri communis graritatis, ut ec motus spatii quod una cum hoc PeIMOS
centro moretur uniformiter in directum, nec non corporum mo-
tus iniciales respectu hujus spatii. MOtus autem subsequentes
per Lecum Corollarium quincum, ec Theorema novistimum)
Derinde hune in hoc spacio, ac si spatium ipsum una cum commu-
ni illo sraritatis centro quiesceret, et corpora non traherene le
mutuo, sed a corpore certio lico in centro illo EraherenEUT. COr-
poris isitur alterutrius in hoc spatio mobilis de loco daco, secun-
dum datam rectam, dara cum relocitare excuntis, et vi centripeta
ad centrum illud cendente correptis determinandus CAt MOtUS PCF
Problema nonum ex vicesimum sextum: ex habebitur simul mo-
cus corporis alterius c regione. Cum hoc motu componendus
est unitormis ille Systematis spatii ec corporum in eo orrantium
mocus progressirus supra inventus, se habebitur mocus absolutuS
corporum in spacio immobili. Q. F. L.
PROPOSITIO LXIV. PROBLEMA XL.
Viribus quibus Corpora se mutuo trabunt crescentibus in simplici ra-
tione distantiarum a centris: requiruntur Motus plurium Cor-
porum inter se.
Ponantur primo corpOrZ duo T ec L commune habentia gravi-
catiscentrum D. Describent haec (per Corollarium primum Theo-
rematis XXL) FIipses centra habentes in D, quarum magnitudo ex
Problemare v. innotescit.
Trahac jam corpuscertium
S priora duo T et L. viri
bus acceleratricibus ST, SY
ee ab ipss vicissim erahaeUE.
VisSF (per Legum COr. 2.
resolvitur in vires SD, DT.
ex visSL in vires SD, DL.
Viresautem D Z, D L, quae
sunt ue ipsarum summa T L3
atque adeo ut vires accelera-
crices quibus corpora T ex L. se mutuo trahune, addicxe his viri-
bus corporum T et L prior priori ex polterior polteriori, com
Donunt vires distantiis DZ ac D P. Proportionales, ut prius, led
viribus