Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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mittantur perpendiculares
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BE, DL,
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& vis qua particula Medii,
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ſecundum rectam
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FB
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obliQ.E.I.cidendo, Globum ferit in
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B,
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erit
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ad vim qua particula eadem Cylindrum
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ONGQ
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axe
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ACI
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circa
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Globum deſcriptum perpendiculariter feriret in
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b,
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ut
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LD
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ad
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LB
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vel
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BE
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ad
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BC.
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Rurſus efficacia hujus vis ad movendum
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Globum ſecundum incidentiæ ſuæ plagam
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FB
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vel
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AC,
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eſt ad ejuſ
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dem efficaciam ad movendum Globum ſecundum plagam determi
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nationis ſuæ, id eſt, ſecundum plagam rectæ
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BC
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qua Globum di
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recte urget, ut
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BE
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ad
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BC.
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Et conjunctis rationibus, efficacia
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particulæ, in Globum ſecundum rectam
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FB
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obliQ.E.I.cidentis, ad
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movendum eundem ſecundum plagam incidentiæ ſuæ, eſt ad effi
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caciam particulæ ejuſdem ſecundum eandem rectam in Cylindrum
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perpendiculariter incidentis, ad ipſum movendum in plagam ean
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dem, ut
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BE
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quadratum ad
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BC
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quadratum. </
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>Quare ſi ad Cylin
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dri baſem circularem
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NAO
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erigatur perpendiculum
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bHE,
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& ſit
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bE
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æqualis radio
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AC,
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&
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bH
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æqualis (
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BE quad/CB
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): erit
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bH
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ad
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bE
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ut effectus particulæ in Globum ad effectum particulæ in Cylin
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drum. </
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>Et propterea ſolidum quod à rectis omnibus
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bH
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occu
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patur erit ad ſolidum quod à rectis omnibus
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bE
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occupatur, ut
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effectus particularum omnium in Globum ad effectum particu
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larum omnium in Cylindrum. </
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>Sed ſolidum prius eſt Parabolois
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vertice
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C,
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axe
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CA
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& latere recto
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CA
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deſcriptum, & ſolidum
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poſterius eſt Cylindrus Paraboloidi circumſcriptus: & notum eſt
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quod Parabolois ſit ſemiſſis Cylindri circumſcripti. </
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<
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>Ergo vis
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tota Medii in Globum eſt duplo minor quam ejuſdem vis tota
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in Cylindrum. </
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>Et propterea ſi particulæ Medii quieſcerent, &
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Cylindrus ac Globus æquali cum velocitate moverentur, foret re
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ſiſtentia Globi duplo minor quam reſiſtentia Cylindri.
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Q.E.D.
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Scholium.
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LIBER
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SECUNDUS.</
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<
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>Eadem methodo Figuræ aliæ inter ſe quo
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ad reſiſtentiam comparari poſſunt, eæQ.E.I.
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veniri quæ ad motus ſuos in Mediis reſiſten
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tibus continuandos aptiores ſunt. </
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<
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circulari
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CEBH,
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quæ centro
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O,
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radio
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OC
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deſcribitur, & altitudine
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OD,
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conſtruen
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dum ſit fruſtum Coni
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CBGF,
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quod omni
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um eadem baſi & altitudine conſtructorum & ſecundum plagam </
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