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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 42, page id 1041163592:0076
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IIIIMIMIMIIIII
+2
PHTILOSOPHLSE NATDRALIS
De MOrO Cl Pagittx dupli arcus e P, in cujus medio cAt P, et duplum crian-
Sulis F sire SP X QT, tempori quo arcus ilte duplus describitur
proxorcionale cAt, ideoque pro temporis exponente scribi potest.
Corol. 2. Eodem argumento ris centripeta cA reciproce uc solidum
ST4X Q 4, A modo Sr perpendiculum sit a cenero virium in Or-
K
XQUanEUT.
eESFXd
Corol. 3. Si Orbis vel circulus est, vel angulum contactus cum cir-
culo quam minimum contince, eandem habens curraturam cundem-
que radium curratura ad punctum contactus P; et II F V chorda
sic circuli hujus a corpore per cenerum ririum acta: erir vis cenrri-
Deca reciproce ut solidum SYgZ PV. Nam PV CA 9
R
Corol. 4. Tisdem positis, est ris centripeta ut velocitas bis directe,
et chorda illa inverse. Nam relocitas es reciproce ut perpendicu,
lum STper Corol. E PrOD. T.
Corol. 5. Hlinc (i detur Agura quaeris curvilinca A P 9. dc in ca
detur etiam punctum Sad quod ris centripeta perpecuo dirigitur,
inveniri porest lex vis centripecae, qua corpus quodris F a cursut
rectilineo perpetuo retractum in Aguex illius perimerro detinebitur
eamque revolrendo describet. Nimirum computandum cA vel (0-
lidum S 4Z ~ FQ vel solidum SZgX P V huic vI rCCIPFOCCPrO.
C
e
portionale. Ejus rei dabimus exempla in Problematis sequentibus.
PROPOSITIO VII. PROBLEMA II.
Orretur corpus in circumferentia Circuli, requiritur L ex vis centri
petae tendentis ad punctum quodcunque datum.
Esto Circuli circumterentia
DP A. punctum datum ad
quod visceu ad centru Cuu ten-
dicS, corpus in circumferentia
lacum F, locusproximusinquem
morebitur 9. ex circulitangens
ad locum priorem F RZ. PeF
punctum Sducatur chorda Y
Sc acta circuli diameeroV A
Batur AP, _ ad S P demittatur
perpendiculum _T, quod productum occurrat
genti P R
1t L
I1
CIIIIII
11I
pI
11I
11
L OMPOROM
2