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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIDTA MATHEMATICA.
E
tus iidem peragantur ac prius, aucebitur in subduplicata ratione LTVEE
densicatis, ac diminuetur in subduplicata ratione vis Elattice. EF SccVRnOS.
Propterea relocitas pulsuum erit in ratione composita ex raTIONC
lubduplicota densitatis Medii inverse ex ratione subduplicata ris
Elasticae dircctc. d. F. D.
Hlaec Propolitio ulterius parebit ex constructione sequentis.
PROPOSITIOZLIZ. PROBLEMA XI.
Datis Medii densitate e vi Flastica, invenire velocitatem pul-
suum.
Fingamus Medium ab incumbente pondere, pro more Aeris
noctri comprimi; sicque A alcitudo Medii homogeneis cujus pon-
Jus adaequet pondus incum bens, e cujus densIEaS eade sIE CUM
densieare Medii compressi, in quo pulsus propagantur. Consti-
cui durem incelligatur Pendulum, cujus longitudo inter punctum
suspensionis ex cenerum oscillationis sIC A: E quo tempore Pen-
dulum illua oscillarionem inteoram ex itu ex reditu compositam
perasit, eodem pulsus cundo consiciet spatium circumterentix
circuli radio A descripei aequale.
Nam Aantibus quae in PEOPOSITIOnC XEVEI ConSructa TUNE,
Si linca quaeris PhysiCa F F, singulis ribrationibus describendo
spatium F S, urgeatur in extremis itus ex reditus cujusque locis
F et S, 2 vi Elastica quae ipsius ponderi equetur; peraset haec
vibraciones singulas quo tempore eadem in Crcloide, cujus peri-
meter tora lonsitudini FS aequalis cAt, oscillari postet: id adco
quia rires aequales aequalia corpuscula per aequalia spatia simul im-
Pellent. Quare cum oscillationum tempora sine in subduplicata
ratione longitudinis Pendulorum, ee lonsicudo Penduli aequetur
dimidio arcui Crcloidis torius; Foret tempus vibrationis unius ad
cempus oscillationis Penduli cujus lonsitudo eAt A, in subdupIi-
cata ratione longitudinis = PS Peu PO ad longicudinem A. Sed
vis Flastica qua lincola Phylica F. C, in locis suis extremis P, S
existens, urgetuT, Crac (in demonstratione Propositionis XLVIT)
ad ejus vim eoram Flacticam uE IIL -K N ad V, hoc eAt
cum punctum X jam incidat in P) ut HYK ad V: ec vis illa
eota, hoc es pondus incumbens, quo lineola L comprimitur,
est ad pondus lineola ut ponderis incumbentis alcitudo A ad linc-
Ole longicudinem P. Cr; adeoque ex aequo, vis qua lincola P. C in
lOcis TUIS F _ S urgetur, est ad lineolae illius pondus uE LLR X A
ad YXF C, Eire ut POX A ad V V, nam Hk eraC ad L. 6 u1