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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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3C
PHLLOSOPHLL NATDRALIS
Dp. popo bi arcus illi in infinitum diminuuntur. Nam hae lagiceae sunt se
Forronon misses diagonalium de quibus esimus in Corollario tertio.
Corol. 5. Ideoque rires caedem lunt ad vim gravitatis, ut hx (a-
sitex ad lasictas horizonti perpendiculares arcuum Parabolicorum
quos projectilia eodem cempore describunt.
Corol. 6. Eadem omnia obtinent per Legum Corol. LV, ubi plana
in quibuS COFPOTA moventur, una cum ceneris ririum quae in ipss
Cica sune, non quiescune, sed morentur unitormiter in directum.
PROPOSITIO II. THEOREMA II.
Corpus omne, quod movetur in linea aliqua curva in plano de
Scripta, es racio ducto ad punctum vel immobile, v et moturectili.
neo uniformiter proerediens; describit areas circa punctum illud
temporibus proportionales, urcetur a vi centripeta tendente ad idem
DunCTUM.
Cas. 1. NNam corpus omne quod moretur in linea curva, decor-
quetur de cursu rectilineo per vim aliquam in ipsum agentem (per
LCg. T.) Ec ris illa qua corpus de cursu rectilinco deEOrGUCEUF, e
eogitur criangula quam minima S AB, SBC, SCD, Sc. circa
punctum immobile s temporibus aequalibus aequalia describere, a-
sic in loco B sccundum lineam parailelam ipA CC (PEF PFOP. XL,
Lib. LFlem. ex LCg. IT.) hoc est, secundum lineam BS; et in loco
C secundum lincam ipsi d D parallelam, hoc cA, secundum lincam
SC, ec. Agic ergo semper secundum lincas cendentes ad punctum
illud immobile S. 9. F. D.
Cas. 2. F.F, per Lesum Corollarium quintum, perinde eA sivo
quieseat superticies in qua corpus describit figuram currilineam
Tire moreatur eadem una cum corpore, tigura descripta, et puncto
cuo S’uniformiter in directum.
Corol. T. In Spatiis vel Mediis non resistentibus, s arCX nOn TUnE
temporibus proportionales, vires non tendunt ad concursum radio-
rum; Scd inde declinant in consequentia seu versus plagam in quam
Hcmocus, si modo arearum descriptio acceleratur: sin recardatur, de-
elinane in antecedentia.
Corol. 2. In Mediis eriam resistentibus, A arcarum delcriprio accele
racur, virium direetiones declinant a concurluradiorum rertus placam
in quam AE MOEUS.
Scholiums
IIIIII