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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 451, page id 1041163592:0485
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PRINOIPTA MATHEMATICA.
L. E M M A XI.
Si Cometa motu omni privatus de alcitudine 8)) seu Su = ?Luu
demitteretur, ut caderet in Solem, ex ea semper vi uniformiter
continuata urceretur in Solem, qua ursetur sub initio; idem se-
misse temporis quo in Orbe suo describat arcum RC, descensit
suo describeret spatium loncitudini Iu aequale.
Nam Cometa quo compore describat arcum Parabolicum AC,
eodem tempore ca cum velocitate quam habet in alcicudine sF
(Per Lemma novistimum) describet chordam AC, adeoque (per
COrol. 7. Prop. ZVI. Lib. l.) eodem cempore in Circulo cujus lemi-
diameter esset SF, vi graritatis sux revolvendo, describeret arcum
cujus longieudo eltet ad arcus Parabolici chordam AC, in subdu-
plicata racione unius ad duo. Lc propterea co cum pondere quod
habet in Solem in alcitudine SP, cadendo de alcitudine illa in
Solems describeret semisse temporis illius (per Corol. 9. PrOD. IV.
Lib. I.) Spatium aequale quadraro lemistis chordae illius applicato
ad quadruplum alcicudinis sP, id est, spatium=
B. Unde cum
pondus Comerxe in Solem in alcieudine SN, sit ad ipsius pondus
in Solem in altitudine SF, uE SF ad Su: Cometa pondere
quod habet in alticudine sN eodem tempore, in Solem caden-
dos delcribet spatium L
+5 p
MH xqualC. Q. F.. D.
id eA, spacium longitudini Ju vel
PROPOSITIO XLI PROBLEMA ZXI
Cometae in Parabola moti Trajectoriam ex datis tribus
Observationibus determinare.
Problema hocce longe difficillimum multimode aggrestus, com-
polui Problemata quaedlam in Libro primo guae ad ejus Colucio-
nem spectant. Pottea solurionem seguentem paulo simpliciorem
excogicavi.
Seligantur eres obserrationes equalibus temporum interrallis ab
invicem quamproxime distantes. Sit autem temporis interrallum
illud ubi Comeca cardius movecur paulo majus alcero, ita videlicet
Mmm 2
L TBFI
X ER TEVO.