Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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<
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>Nam ſi uniformis ſit reſiſtentia
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DK,
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Figura
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aBKkT
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rectangu
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lum erit ſub
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Ba
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&
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DK
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; & inde rectangulum ſub 1/2
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Ba
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&
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Aa
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erit æquale rectangulo ſub
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Ba
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&
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DK,
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&
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DK
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æqualis erit 1/2
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Aa.
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Quare cum
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DK
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ſit exponens reſiſtentiæ, & longitudo penduli ex
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ponens gravitatis, erit reſiſtentia ad gravitatem ut 1/2
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Aa
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ad longi
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tudinem Penduli; omnino ut in Prop. </
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<
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>XXVIII demonſtratum eſt. </
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<
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>Si reſiſtentia ſit ut velocitas, Figura
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Ellipſis erit quam
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proxime. </
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>Nam ſi corpus, in Medio non reſiſtente, oſcillatione
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integra deſcriberet longitudinem
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BA,
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velocitas in loco quovis
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D
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foret ut Circuli diametro
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AB
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deſcripti ordinatim applicata
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DE.
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Proinde cum
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Ba
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in Medio reſiſtente, &
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BA
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in Medio non reſi
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ſtente, æqualibus circiter temporibus deſcribantur; adeoque velo
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citates in ſingulis ipſius
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<
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Ba
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punctis, ſint quam
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proxime ad velocitates
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in punctis correſpon
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dentibus longitudinis
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BA,
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ut eſt
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Ba
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ad
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BA
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;
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erit velocitas
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DK
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in
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Medio reſiſtente ut Cir
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culi vel Ellipſeos ſuper
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diametro
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Ba
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deſcripti
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ordinatim applicata; adeoque Figura
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BKVTa
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Ellipſis, quam pro
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xime. </
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<
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>Cum reſiſtentia velocitati proportionalis ſupponatur, ſit
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OV
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exponens reſiſtentiæ in puncto Medio
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O
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; & Ellipſis
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aBRVS,
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centro
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O,
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ſemiaxibus
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OB, OV
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deſcripta, Figuram
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aBKVT,
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eique æquale rectangulum
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AaXBO,
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æquabit quamproxime. </
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<
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>Eſt
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igitur
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AaXBO
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ad
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OVXBO
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ut area Ellipſeos hujus ad
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OVXBO
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:
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id eſt,
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Aa
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ad
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OV
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ut area ſemicirculi ad quadratum radii, ſive ut
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11 ad 7 circiter: Et propterea (1/11)
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Aa
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ad longitudinem penduli ut
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corporis oſcillantis reſiſtentia in
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O
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ad ejuſdem gravitatem. </
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<
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DK
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ſit in duplicata ratione velocitatis, Fi
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gura
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BKVTa
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Parabola erit verticem habens
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V
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& axem
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OV,
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id
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eoque æqualis erit rectangulo ſub 2/3
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Ba
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&
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OV
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quam proxime. </
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<
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>Eſt
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igitur rectangulum ſub 1/2
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Ba
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&
<
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Aa
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æquale rectangulo ſub 2/3
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Ba
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&
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OV,
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adeoque
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OV
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æqualis 1/4
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Aa:
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& propterea corporis oſcillan
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tis reſiſtentia in
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O
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ad ipſius gravitatem ut 1/4
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Aa
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ad longitudi
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nem Penduli. </
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<
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>Atque has concluſiones in rebus practicis abunde ſatis accuratas
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eſſe cenſeo. </
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<
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>Nam cum Ellipſis vel Parabola
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BRVSa
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congruat </
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