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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 29, page id 1041163592:0063
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PRINOIPLA MATTIEMATIC A
L F MIM A IX.
Si recta AFP. ∞ curva ABC positione datae se mutuo secent in
anculo dato a, e ad rectam illam in alio dato anculo ordina-
tim applicentur BD, CF, curvae occurrentes in B, C; dein
puncta B, C simul accedant ad punctum A: dico quod areae tri
ansulorum ABD, ACF erunt ultimo ad invicem in duplicata
ratione laterum.
Ecenim dum puncta B, C accC
dune ad punctum A, incelligatur
semper AD produciad puncta lon-
sinqua d ee e, uc lnE Ad. Ae ip.
(1S AD, AF proxortionales, et e
rigantur ordinatae ab, ec ordina.
tis D B, L.C Parallelae quae Occur
ranC ipsIS AB, AC productis it
b ec c. Duci incelligatur, tum curva
Abc ipA ABC similis, tum recta
A8, Guxe tangat curram utramque
in A, e secet ordinatim applica
taS D B, F C, ab, ec in P, (, f, C.
a
Tum manente longitudine Ae cocane puncta B, C cum puncto 3
et angulo c Ae cranelcente, coincident areae curvilincae Ab d. Acc
cum rectilineis 1Fd, A5e: adeoque (per Lemma v) crunt in dupli.
cata ratione laterum 1d, Ac: Sed his arcis proportionales semper
TUnE AECa AB D, AC F, ec his laceribus latera A D, AF. RrOO_C
arCx AB D, AC F. Cunc ultimo in duplicata ratione laterum AD,
AF. d. F. D.
L F MI M A X.
Spatia quae corpus urcente quacunque Vi finita describit, sive Vis
illa determinata es immutabilis sit, sive eadem continuo auce-
atur vel continuo diminuatur; sunt ipso motus initio in duplica
ta ratione Temporum.
EXDONAnEUErempOTA per lincas AD, AF, de velocitates genitx
Der Ordinatas D B, P.C; ex spatia his velociratibus deleripea, crune
UE area ABD, AC F. his ordinatis descripce, hoc eA, ip (O mOTuS
nicio (per Lemma 1X) in duplicata ratione temporum AD, AL.
. F. D
Corobu
PATMDSI