Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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geret illud hæc plana viribus
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pN, HN
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perpendiculariter, nimirun
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planum
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pQ
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vi
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pN,
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& planum
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pG
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vi
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HN.
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Ideoque ſi tollatur pla
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num
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pQ,
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ut pondus tendat filum; quoniam filum ſuſtinendo pon
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dus jam vicem præſtat plani ſublati, tendetur illud eadem vi
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pN,
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qua planum antea urgebatur. </
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>Unde tenſio fili hujus obliqui erit
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ad tenſionem ſili alterius perpendicularis
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PN,
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ut
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pN
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ad
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pH.
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Id. </
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eoque ſi pondus
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p
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ſit ad pondus
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A
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in ratione quæ componitur ex
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ratione reciproca minimarum diſtantiarum ſuorum ſuorum
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pN,
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AM
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a centro rotæ, & ratione directa
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pH
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ad
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pN
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; pondera idem
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valebunt ad rotam movendam, atque adeo ſe mutuo ſuſtinebunt,
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ut quilibet experiri poteſt. </
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<
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>Pondus autem
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p,
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planis illis duobus obliquis incumbens, rationem
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habet cunei inter corporis fiſſi facies internas: & inde vires cunei
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& mallei innoteſcunt: utpote cum vis qua pondus
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p
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urget planum
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pQ
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ſit ad vim, qua idem vel gravitate ſua vel ictu mallei impellitur
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ſecundum lineam
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pH
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in plano, &c. </
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pN
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and
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pH
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; atque ad vim, qua
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urget planum alterum
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pG,
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ut
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pN
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ad
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NH.
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Sed & vis Cochleæ per
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ſimilem virium diviſionem colligitur; quippe quæ cuneus eſt a ve
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cte impulſus. </
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>Uſus igitur Corollarii hujus latiſſime patet, & late
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patendo veritatem ſuam evincit; cum pendeat ex jam dictis Mecha
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nica tota ab Auctoribus diverſimode demonſtrata. </
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>Ex hiſce enim
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facile derivantur vires Machinarum, quæ ex Rotis, Tympanis,
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Trochleis, Vectibus, nervis tenſis & ponderibus directe vel obli
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que aſcendentibus, cæteriſque potentiis Mechanicis componi ſo
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lent, ut & vires Tendinum ad animalium oſſa movenda. </
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COROLLARIUM III.
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Quantitas motus quæ colligitur capiendo ſummam motuum factorum
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ad eandem partem, & differentiam factorum ad contrarias, non
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mutatur ab actione corporum inter ſe.
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<
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>Etenim actio eique contraria reactio æquales ſunt per Legem 111,
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adeoque per Legem 11 æquales in motibus efficiunt mutationes ver
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ſus contrarias partes. </
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<
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>Ergo ſi motus fiunt ad eandem partem; quic
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quid additur motui corporis fugientis, ſubducetur motui corporis
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inſequentis ſic, ut ſumma maneat eadem quæ prius. </
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<
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>Sin corpora ob
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viam eant; æqualis erit ſubductio de motu utriuſque, adeoQ.E.D.ffe
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rentia motuum factorum in contrarias partes manebit eadem. </
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<
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>Ut ſi corpus ſphæricum
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A
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ſit triplo majus corpore ſphærico
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B,
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ha
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beatQ.E.D.as velocitatis partes; &
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B
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ſequatur in eadem recta cum ve-</
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