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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 114, page id 1041163592:0148
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MIMIIMIMBIIIINII
124
PHTLOSODMTTL NATDRALIS
Corol. 3. Tempus quoque innocelcet crigendo ordinatam em re-
ciproce proportionalem laceri quadrato ex P 9 R D + vel-D L5 C,
e capiendo cempus quo corpus descripsit lincam De ad tempus
quo corpus alcerum viunitormi cecidit a F et cadendo pervenit ad
D, nearea currilinca D C. me ad rectangulum 2F D X DF. Nam
que cempus quo corpus ri unitormi descendens descripsit lineam
PD est ad cempus quo corpus idem deseripsic lineam P P. in sub-
duplicata ratione P D ad F P, id est (lincola D F. jamjam nascen-
tC) in ratione F D ad PD + E D P (Cu 2 P D ad 2P D + D F
ec dirisim, ad tempus quo corpus idem descripsic lineolam D F.
UE 2 P D ad D C, adeoque ut rectangulum 2F D X D L ad arcam
DL MF; eAtque tempus quo corpus utrumque descripie linco-
Jam D E ad tempus quo corpus alcerum inaequabili motu descrip.
sic lineam De UE arCa D L. MIF ad aream D L. M e, e CX aequo
cempus primum ad cempus ultimum uE rectansulum 2 F D X D L
d arCaM D L. Me.
S E C TIO
VIII
De Inventione Orbium in quibus corpora Viribus quibuscunque cen-
tripetis aritata revolvuntur.
PROPOSITIO XL. THEOREMA XIII.
Si corpus, cogente Vi quacunque centripeta, moveatur utcunque, es
corpus aliud recta ascendat vel descendat, (int que eorum Velocita
res in aliquo aequalium altitudinum casu aequales, Velocitates eorum
in omnibus aequalibus altitudinibus erunt aequales.
Descendat corpus aliquod ab  Per D, F, ad centrum C, et
MOreatur CorpuS aliud a V in linea CUrVa VIKK, CentrO C in-
cerrallis quibutris describantur circuli concentrici DL, P R rectae
AC in D _E F, CUrVRGHC V YK in Y et RL Occurrentes. Junga-
EUr PC OCCUErENS ipSI R F. in NV; ec in PK demittatur perpendi-
culum NT; sieque circumterenciarum circulorum interrallum D F.
vel LN quam minimum, et habeane corpora in D et l velocita-
tC5
LIIIISPILIIHIMIHIMMIHMIINAMHHHITIAMIIIIIIIIMIIMIIMIIIIEIIIEIIIMHNIA
De HTOTD
lORFORV