Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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LIBER
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PRIMUS.</
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SECTIO IX.
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De Motu Corporum in Orbibus mobilibus, deque motu Apſidum.
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PROPOSITIO XLIII. PROBLEMA XXX.
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Efficiendum est ut corpus in Trajectoria quacunque circa centrum
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Virium revolvente perinde moveri poſſit, atque corpus aliud in
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eadem Trajectoria quieſcente.
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<
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>In Orbe
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VPK
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po
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ſitione dato revolvatur
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corpus
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P
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pergendo a
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V
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verſus
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K.
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A centro
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C
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agatur ſemper
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Cp,
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quæ ſit ipſi
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CP
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æqualis,
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angulumque
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VCp
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an
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gulo
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VCP
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proportio
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nalem conſtituat; & a
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rea quam linea
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Cp
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de
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ſcribit erit ad aream
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VCP
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quam linea
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CP
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ſimul deſcribit, ut velo
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citas lineæ deſcribentis
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Cp
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ad velocitatem li
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neæ deſcribentis
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CP
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;
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hoc eſt, ut angulus
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VCp
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ad angulum
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VCP,
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adeoQ.E.I. data ra
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tione, & propterea tempori proportionalis. </
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proportionalis ſit quam linea
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Cp
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in plano immobili deſcribit, ma
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nifeſtum eſt quod corpus, cogente juſtæ quantitatis Vi centripeta,
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revolvi poſſit una cum puncto
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p
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in Curva illa linea quam punctum
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idem
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p
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ratione jam expoſita deſcribit in plano immobili. </
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lus
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VCu
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angulo
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PCp,
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& linea
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Cu
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lineæ
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CV,
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atque Figura
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uCp
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Fi
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guræ
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VCP
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æqualis, & corpus in
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p
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ſemper exiſtens movebitur in </
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