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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 141, page id 1041163592:0175
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PRINOIPTA MATHEMATICA.
L a L.
Oscillationis unius, uE arCUS FYY (tempUS quO COrpUS VY pervenICE LIBEK
ad L) ad semiperipheriam Z_ M (teMPUS quO COrPUS YY Per- Pniuo
veniet ad M.) Ec velociras corporis penduli in loco l CAt ad ve-
locitarem ipsius in loco intimo Re, (hoc cHt, relocitas corporis JL in
loco L. ad velocitarem ejus in loco Ci, sCu INCreMENEUM mOMENEa.
neum linexe I L. ad incrementum momentancum lincx fPCF, arcu-
bus I, HPK aequabili Auxu crescentibus) uc ordinacim applicata
L. T ad radium GK, sIVC uE VSRg. = C Kg. adS R. Onde cum,
in olcillarionibus inaequalibus, delcribantur aequalibus cemporibus
arcus cotis olcillationum arcubus proporcionales; habeneur, Cx dd-
eis temporibus, ex relocitates ec arcus delcripei in olcillacionibus
universis. Ouxe eranc primo invenienda.
Oscillentur jam P’unipendula
corpora in Creloidibus diverts
intra C2l0bO5 diverios, quorum
diverlae sunt criam Vires abTolu-
txes deleriptis: _c, A Vis abColu-
ca Olobicujueris QOS dicaturV
Vis acceleratrix qua Penduluuroe.
cur in circumfereneia hujus Globi, M
ubi incipie directe versus centrum
ejus moveris eric uc distantia C Or-
poris penduli a centro illo ex Vis absoluta Globi conjunctim, hoc
CA, UE COXV. Jeaque lineola HYZ, quae sIE ut haec Vis accelera-
erix COX V, describetur dato tempore; _c, si crigatur normalis YZ
circumterentix OcCurrens in Z, areUS nalCenS YYZ denotabit datum
illud cempus. FR autem arcus hic nascens  Z in Cubduplicata ra-
tione rectanguli G H Y, adCOque UE VGHZCOXV. Unde Tem-
pus olcillacionis incegrae in Creloide RS (cum sit ut semiperi-
Pheria TR M, quae oscillationem illam incegram denotat, directe,
ucque arcus Z qui datum tempus similicer denocar, inverse) ACF
uc C  directe d V G HX CO X V invertes hoc eAt, ob x quales C. I
e SR, UE V SA
C.OXV live (per CorOI. PFOB. L) ut V AR
AC XV
ltagne Oscillationes in Globis et Cycloidibus omnibus, quibus.
cunque cum Viribus absoluris Factae, sune in ratione quae compo.
nitur ex subduplicata ratione lonsitudinis Fili directe, ec subdu-
Plicata ratione distanciae inter punctum suspensionis de centrum
Slobi