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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 144, page id 1041163592:0178
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244
PTIILOSODHLL NATDRALIS
Nam si vis, qua corpus trahitur de T versus C, exponatur pet
rectam TZ capeam ipsi proporcionalem, resolvetur haec in vires
TY YZ; quarum YZ trahendo corpus secundum longitudinem
Fili PT, morum ejus nil mutac, ris aurem altera TY motum ejus
in curra SF R Q directe accelerat vel directe recardat. Proinde
cum haec siC ut via describenda T R, accelerationes corporis vel re-
cardationes in Oscillationum duarum (majoris ee minoris) parci
bus proportionalibus describendis, crunt semper ut partes illae, et
propterea Facient uc partes illae simul describaneur. COrpora autem
qua parces eoris semper proxorrionales simul describune, simul de-
ScribenE FOTaS. Q. F. D.
Corol. Z. FTinc sI COrpUS Z Filo rectilineo AF a CenErO A pen-
dens describat arcum circularem ST R _, e interea urocatur se
cundum lineas parallelas deorlum a vi aliqua, quae sic ad vim uni
Formem Crraritatis, ut arcus T R ad ejus sinum P N: aequalia c
runt Oscillationum singularum tempora. Ecenim ob parallelas
TZ. AR, similia crune criangula ATN, ZTY; _ PrOPtCrCa
TZ erit ad AZ ut ZY ad TNV; hoc eA, (s Gravicatis vis unifor-
mis exponatur per lonsicudinem datam AY) vis ZZ, qua OCcil.
lationes eradene Tlochronae, erit ad vim GTravitatis AY, UE arCUS
T R ipS TY aequalis ad arcus illius sinum TN.
Corol. 2. Isieur in HIorologiis, si vires a Machina in Pendulum
ad motum conserrandum impressae ita cum vi Graritatis componi
POSTInE, UE viS tota deorlum semper sIE ut linea quae oritur avosi-
cando rectangulum sub arcu Y R et radio AR ad sinum YN.
Oscillationes omnes crune LlOchrOnE.
PROPOSITIO LIV. PROBLEMA XZZVI.
Concessis Ficurarum curvilinearum quadraturis, invenire Tempora
quibus corpora Vi qualibet centripet a in lineis quibuscunque cur-
vis, in plano per centrum Virium transeunte descriptis, descen-
dent ex ascendent.
Delcendat corpus de loco quovis s per lineam quamvis curram
ST+ R, in plano per virium cencrum C cranseunte datam. Junga-
EuP CS e diridatur eadem in partes innumeras aequales, Irque D d
Parcium
DE MOTV
ConORON