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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 97, page id 1041163592:0131
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PRINCIPTA MATHIEMATICA
SECTIO V
De Tnventione Motuum in Orbibus datis.
PROPOSTTIO XXX PROBLEMA XXII.
corporis in data Trajectoria Parabolica moti invenire locum ad
tempus assirnatum.
Sie Sumbilicus ec A vertex principa-
lis Parabolae, sicque 4 ASXMI aequale
arex Parabolica abscindendae A F 5,
quae radio SF, vel post excessum cor-
Poris de vertice deleripta fuit, vel an-
ce appulsum ejus ad verricem descri-
benda eAt. Innocescit quanticas areae il-
lius abscindendae ex tempore ipsi pro-
portionali. Biseca AS in C, crigeque
verpendiculum C H aequale 3 M, e
Circulus cenero I, interrallo H S
descriptus secabit Parabolam in loco
quaesico P. Nam, demissa ad axem
Derpendiculari PO 8x ducta P HI, eAt
ACg + GTI9(= H F g = AO = AG: quad. + FO -C H
2d.)=
AO9. + FOg = 26AO - 2GTIX FO + AGg + GFIg. Ondo
2CFXPO(= AO9 + FO9 -26A0) = AOg + = P Og.
PrO AOq seribe AOX
PO0
L 5: des applicatis cerminis omnibus acl
3FOductisque in 2AS,HCEZGTIX AS(= 5AOXFO + E ASZFO
AO + 3
Ex DO-+ AO -35C
X PO = aTCX A FO = SFO)
Fareae A F S. Sed G FLCTaLZM, d inde FC TT X AS CA 4 ASXN.
Frgo area abscissa AP Saequalis est abscindenda 4 ASXH. Q. L. D.
Corol. I. Elinc CTFY CA 2d S, ut tempus quo corpus deserip.
sic arcum AP ad tempus quo corpus descripsie arcum inter verti-
cem A e perpendiculum ad axem ab umbilico S crectum.
Corol. 2. FF C irculo AS P Per COrpUS motum P PerpetuO tran(
unce, relocicas puncti H est ad velocitatem quam corpus habu. F
PX 1MVS.