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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIPLA MATHEMATICA
partium illarum aliqua. Cenero C, interrallis C D, C a actCHBAH- L. THF. H
cur circuli DF, dt, linex curvae SF+ R occurrentes in Y d t. FF enimon
ex data tum lege vis centripeta, tum
alticudine CS de qua corpus cecidit;
dabitur velocicas corporis in alia qua-
vis alcitudine CT, Per PEOD. XXXIX.
lempus aurem, quo corpus describit
lincolam TF, est ut lineolx hujus lon-
sicudo (id cM ut secans anguli +TC
directe, et velociras inverse. Tempori
huic proportionalis sic ordinatim appli-
Cata D N ad rectam C S per punctum
D perpendicularis, ec ob datam D d
erit rectangulum D d XD N, hoc CA
area D Nn d, cidem tempori proxor-
tionalc. RrgO A SNn sE curra illa li-
nea quam punctum N Perpetuo cangit,
erit arca S ND Sproportionalis tem
Pori quo corpus descendendo descrip-
Sc lineam SF; proindeque ex inventa illa area dabitur Tempus.
2. F. I.
DROPOSITIO LV. THEOREMA ZIX.
Si corpus movetur in superficie quacunque curva, cujus axis per
centrum Virium transit, e a corpore in axem demittatur per-
pendicularis, eique parallela e aequalis ab axis puncto quovis
dato ducatur: dico quod parallela illa aream tempori proportio-
nalem describet.
Sic BSHL L Suxerkcies curra, F CorpuS in ea revolvens, STY R
Prajectoria quam corpus in eadem describit, Sinitium Trajecto-
rix, OM NK axis supericiei curra, T N recta a corpore in axem
perpendicularis, O P huic Parallela ec aequalis a puncto O quod in
axe datur educta, AP restisium Trajcetorix a puncto P in lincae
volubilis O P plano 1O P descriptum, A veltisii inicium puncto s
respondens, TC recta a corpore ad centrum ducta; TG pars ejus
vi centripeta qua cOrpuS urgetur in centrum C proxortionalis:
M recta ad superticiem curvam perpendicularis, P L Pars ejus vi
Crectionis, qua corpusurs ec super liciem ricissimque ursecur versus I