Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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pagenum
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DE MOTU
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CORPORUM</
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Corol.
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3. Aucta autem vel diminuta longitudine aquæ, auge
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tur vel diminuitur tempus reciprocationis in longitudinis ratione
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ſubduplicata. </
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PROPOSITIO XLV. THEOREMA XXXVI.
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Undarum velocitas eſt in ſubduplicata ratione latitudinum.
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>Conſequitur ex conſtructione Propoſitionis ſequentis. </
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PROPOSITIO XLVI. PROBLEMA X.
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Invenire velocitatem Undarum.
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>Conſtituatur Pendulum cujus longitudo, inter punctum ſuſpen
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ſionis & centrum oſcillationis, æquetur latitudini Undarum: & quo
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tempore pendulum illud oſcillationes ſingulas peragit, eodem Un
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dæ progrediendo latitudinem ſuam propemodum conficient. </
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<
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>Undarum latitudinem voco menſuram tranſverſam, quæ vel val
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libus imis, vel ſummis culminibus interjacet. </
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ABCDEF
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ſuperficiem aquæ ſtagnantis, undis ſucceſſivis aſcendentem ac deſ
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cendentem; ſintque
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A, C, E,
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&c. </
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<
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B, D, F,
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&c. </
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valles intermedii. </
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>Et quoniam motus undarum fit per aquæ ſuc
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ceſſivum aſcenſum & deſcenſum, ſic ut ejus partes
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A, C, E,
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&c. </
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quæ nunc altiſſimæ ſunt, mox fiant infimæ; & vis motrix, qua
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partes altiſſimæ deſcendunt & infimæ aſcendunt, eſt pondus aquæ
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elevatæ; alternus ille aſcenſus & deſcenſus analogus erit motui re
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ciproco aquæ in canali, eaſdemque temporis leges obſervabit: &
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propterea (per Prop. </
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<
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>XLIV) ſi diſtantiæ inter undarum loca altiſ
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ſima
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A, C, E
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& infima
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B, D, F
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æquentur duplæ penduli longitu
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dini; partes altiſſimæ
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A, C, E,
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tempore oſcillationis unius evadent
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infimæ, & tempore oſcillationis alterius denuo aſcendent. </
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inter tranſitum Undarum ſingularum tempus erit oſcillationum
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duarum; hoc eſt, Unda deſcribet latitudinem ſuam, quo tempore
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pendulum illud bis oſcillatur; ſed eodem tempore pendulum, cu
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jus longitudo quadrupla eſt, adeoque æquat undarum latitudinem,
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oſcillabitur ſemel.
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Q.E.I.
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Corol.
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1. Igitur Undæ, quæ pedes
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Pariſienſes
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(3 1/18) latæ ſunt,
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tempore minuti unius ſecundi progrediendo latitudinem ſuam con
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ficient; adeoque tempore minuti unius primi percurrent pedes
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183 1/3, & horæ ſpatio pedes 11000 quamproxime. </
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