Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Globus vel Cylindrus incidit, vi reflexionis quam maxima reſiliant.
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Et cum reſiſtentia Globi (per Propoſitionem noviſſimam) ſit duplo
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minor quam reſiſtentia Cylindri, & Globus ſit ad Cylindrum ut
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duo ad tria, & Cylindrus incidendo perpendiculariter in particulas
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ipſaſque quam maxime reflectendo, duplam ſui ipſius velocitatem
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ipſis communicet: Cylindrus quo tempore dimidiam longitudinem
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axis ſui deſcribit communicabit motum particulis qui ſit ad totum
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Cylindri motum ut denſitas Medii ad denſitatem Cylindri; & Glo
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bus quo tempore totam longitudinem diametri ſuæ deſcribit, com
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municabit motum eundem particulis; & quo tempore duas tertias
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partes diametri ſuæ deſcribit communicabit motum particulis qui
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ſit ad totum Globi motum ut denſitas Medii ad denſitatem Globi.
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Et propterea Globus reſiſtentiam patitur quæ ſit ad vim qua totus
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ejus motus vel auferri poſſit vel generari quo tempore duas tertias
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partes diametri ſuæ deſcribit, ut denſitas Medii ad denſitatem
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Globi.
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LIBER
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SECUNDUS.</
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Cas.
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2. Ponamus quod particulæ Medii in Globum vel Cylin
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drum incidentes non reflectantur; & Cylindrus incidendo perpen
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diculariter in particulas ſimplicem ſuam velocitatem ipſis commu
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nicabit, ideoque reſiſtentiam patitur duplo minorem quam in pri
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ore caſu, & reſiſtentia Globi erit etiam duplo minor quam prius.
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Cas.
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3. Ponamus quod particulæ Medii vi reflexionis neque ma
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xima neque nulla, ſed mediocri aliqua reſiliant a Globo; & reſi
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ſtentia Globi erit in eadem ratione mediocri inter reſiſtentiam in
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primo caſu & reſiſtentiam in ſecundo.
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Q.E.I.
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Corol.
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1. Hinc ſi Globus & particulæ ſint infinite dura, & vi om
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ni elaſtica & propterea etiam vi omni reflexionis deſtituta: re
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ſiſtentia Globi erit ad vim qua totus ejus motus vel auferri poſſit
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vel generari, quo tempore Globus quatuor tertias partes diametri
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ſuæ deſcribit, ut denſitas Medii ad denſitatem Globi.
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Corol.
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2. Reſiſtentia Globi, cæteris paribus, eſt in duplicata ra
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tione velocitatis.
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Corol.
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3. Reſiſtentia Globi, cæteris paribus, eſt in duplicata ra
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tione diametri.
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Corol.
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4. Reſiſtentia Globi, cæteris paribus, eſt ut denſitas Medii.
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Corol.
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5. Reſiſtentia Globi eſt in ratione quæ componitur ex du
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plicata ratione velocitatis & duplicata ratione diametri & ratione
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denſitatis Medii. </
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