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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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236
PHLLOSOPHISE NATORALIS
Corol. 3. Ructa autem rel diminuca longitudine aquas auge.
cur vel diminuitur cempus reciprocarionis in longitudinis ratione
Cubduplicata.
PROPOSITIO XLV. THEOREMA XXXV.
Ondarum velocitas est in subduplicata ratione latitudinum.
Consequitur ex constructione Propoltionis lequencis.
PROPOSITIO ZIVI. PROBLEMA Z.
Invenire velocitatem Ondarum.
Consticuatur Pendulum cujus longitudo, inter punctum suspen-
Fonis ex centrum oscillationis, equetur laticudini Vndarum: Se quo
tempore pendulum illud oscillationes singulas peragit, codem Vn
dxe prosrediendo lacicudinem suam propemodum conticient.
TIndarum laticudinem vocomensuram transvertam, quae vel val-
libus imis, vel summis culminibus interiacet. Desionet ABC DF F
superticiem aquae Ragnaneis, undis successiris ascendentem ac def
cendencem; lintgue A. C, F. ec. undarum culmina, et B, D, F, EC.
valles incermedii. Et quoniam mocus undarum Ac per aqua uc-
cessirum ascensum eE descensum, sC uE ejuS PaETCS A, C, F, _C.
quae nunC alcisIM_ TUINE, MOX BanE intimXe; e vis motrix, qua
varces altissimae descendunt e insimae ascendune, est pondus aquae
eleratae; alternus ille alcensus ec descensus analogus erit morui re-
ciproco aquae in canalis caldemque temporis leges oblerrabit: et
DFODEETCA (PeF PFOD. ZLIV) si distantia inter undarum loca altis
sima A, C, F. e intima B, D, P aequentur duplae penduli longieu-
dini; parces alcistimae A, C, F, tempore olcillationis unius eradene
intimae, e tempore oscillationis alterius denuo aCcendent. Jgitur
inteE cransicum Ondarum singularum tempus erit oscillationum
duarum; hoc est, Inda describet lacicudinem tuam, quo tempore
Dendulum illud bis oscillatur; sed eodem tempore pendulum, cu-
jus lonsitudo quadrupla eAt, adeoque aequat undarum lacirudinem,
oscillabitur Cemel. Q. F. L.
Corol. 2. Tgitur Vndx, quae pedes Parisienses 31 latae sunts
rempore minuti unius secundi progrediendo latitudinem suam con-
ficiene; adeoque tempore minuti unius primi percurrent pedes
1833, et horx spatio pedes 21000 quamproxime.
Corol. L.
DE MOTV
COREORVI