Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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PO
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ad V. </
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>Quare cum tempora, quibus æqualia corpora per
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æqualia ſpatia impelluntur, ſint reciproce in ſubduplicata ratione
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virium, erit tempus vibrationis unius urgente vi illa Elaſtica, ad
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tempus vibrationis urgente vi ponderis, in ſubduplicata ratione
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VV ad
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PO
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XA, atque adeo ad tempus oſcillationis Penduli cu
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jus longitudo eſt A, in ſubduplicata ratione VV ad
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PO
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XA, &
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ſubduplicata ratione
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PO
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ad A conjunctim; id eſt, in ratione in
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tegra V ad A. </
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<
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>Sed tempore vibrationis unius ex itu & reditu com
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poſitæ, pulſus progrediendo conficit latitudinem ſuam
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BC.
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Ergo
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tempus quo pulſus percurrit ſpatium
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BC,
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eſt ad tempus oſcillati
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onis unius ex itu & reditu compoſitæ, ut V ad A, id eſt, ut
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BC
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ad circumferentiam circuli cujus radius eſt A. </
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<
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>Tempus autem,
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quo pulſus percurret ſpatium
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BC,
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eſt ad tempus quo percurret
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longitudinem huic circumferentiæ æqualem, in eadem ratione;
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ideoque tempore talis oſcillationis pulſus percurret longitudinem
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huic circumferentiæ æqualem.
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Q.E.D.
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DE MOTU
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CORPORUM</
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Corol.
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1. Velocitas pulſuum ea eſt quam acquirunt Gravia, æqua
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liter accelerato motu cadendo, & caſu ſuo deſcribendo dimidium
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altitudinis A. </
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<
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>Nam tempore caſus hujus, cum velocitate cadendo
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acquiſita, pulſus percurret ſpatium quod erit æquale toti altitu
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dini A, adeoque tempore oſcillationis unius ex itu & reditu com
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poſitæ, percurret ſpatium æquale circumferentiæ circuli radio A
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deſcripti: eſt enim tempus caſus ad tempus oſcillationis ut radius
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circuli ad ejuſdem circumferentiam. </
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Corol.
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2. Unde cum altitudo illa A ſit ut Fluidi vis Elaſtica di
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recte & denſitas ejuſdem inverſe; velocitas pulſuum erit in ratione
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compoſita ex ſubduplicata ratione denſitatis inverſe & ſubdupli
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cata ratione vis Elaſticæ directe. </
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PROPOSITIO L. PROBLEMA XII.
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Invenire pulſuum diſtantias.
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<
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>Corporis, cujus tremore pulſus excitantur, inveniatur numerus
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Vibrationum dato tempore. </
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tium quod pulſus eodem tempore percurrere poſſit, & pars in
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venta erit pulſus unius latitudo.
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Q.E.I.
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Scholium.
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<
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>Spectant Propoſitiones noviſſimæ ad motum Lucis & Sonorum. </
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Lux enim cum propagetur ſecundum lineas rectas, in actione ſola </
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