Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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ſingulis ſeparatim uniformis, at in diverſis diverſa; & per jam de
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monſtrata, ſinus incidentiæ in planum primum
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Aa
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erit ad ſinum
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emergentiæ ex plano ſecundo
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Bb,
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in data ratione; & hic ſinus,
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qui eſt ſinus incidentiæ in planum ſecundum
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Bb,
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erit ad ſinum
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emergentiæ ex plano tertio
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Cc,
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in data ratione; & hic ſinus ad
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ſinum emergentiæ ex plano quarto
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Dd,
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in data ratione; & ſic in
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infinitum: & ex æquo, ſinus incidentiæ in planum primum ad ſi
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num emergentiæ ex plano ultimo in data ratione. </
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<
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>Minuantur jam
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planorum intervalla & augeatur numerus in infinitum, eo ut attra
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ctionis vel impulſus actio, ſecundum legem quamcunque aſſignatam,
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continua reddatur; & ratio ſinus incidentiæ in planum primum ad
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ſinum emergentiæ ex plano ultimo, ſemper data exiſtens, etiam
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num dabitur.
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E. D.
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LIBER
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PRIMUS.</
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PROPOSITIO XCV. THEOREMA XLIX.
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Iiſdem poſitis; dico quod velocitas corporis ante incidentiam eſt
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ad ejus velocitatem poſt emergentiam, ut ſinus emergentiæ ad
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ſinum incidentiæ.
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<
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>Capiantur
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AH, Id
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æquales, & erigantur perpendicula
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AG, dK
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occurrentia lineis incidentiæ & emergentiæ
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GH, IK,
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in
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G
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&
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K.
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In
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GH
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capiatur
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TH
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æqualis
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IK,
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& ad planum
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Aa
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demittatur
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normaliter
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Tv.
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Et (per Legum Corol. </
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>2) diſtinguatur motus cor
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poris in duos, unum planis
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Aa, Bb, Cc,
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&c. </
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>perpendicularem, al
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terum iiſdem parallelum. </
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<
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>Vis attractionis vel impulſus, agendo ſe
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cundum lineas perpendiculares, nil mutat motum ſecundum paralle
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las, & propterea corpus hoc motu conficiet æqualibus temporibus
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æqualia illa ſecundum parallelas intervalla, quæ ſunt inter lineam
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AG
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& punctum
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H,
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interque punctum
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I
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& lineam
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dK
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; hoc eſt,
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æqualibus temporibus deſcribet lineas
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GH, IK.
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Proinde velo
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citas ante incidentiam eſt ad velocitatem poſt emergentiam, ut
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GH
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ad
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IK
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vel
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TH,
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id eſt, ut
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AH
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vel
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Id
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ad
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vH,
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hoc eſt
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(reſpectu radii
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TH
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vel
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IK
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) ut ſinus emergentiæ ad ſinum inci
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dentiæ.
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E. D.
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