Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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& maxima fit ubi Apſides ſunt in Syzygiis. </
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<
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>Si Apſides conſtituan
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tur in Quadraturis, ratio prope Apſides minor eſt & prope Syzy
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gias major quam duplicata diſtantiarum, & ex ratione illa majori
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oritur Augis motus velociſſimus, uti jam dictum eſt. </
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<
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>At ſi con
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ſideretur ratio incrementi vel decrementi totius in progreſſu inter
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Apſides, hæc minor eſt quam duplicata diſtantiarum. </
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<
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>Vis in Ap
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ſide ima eſt ad vim in Apſide ſumma in minore quam duplicata
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ratione diſtantiæ Apſidis ſummæ ab umbilico Ellipſeos ad di
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ſtantiam Apſidis imæ ab eodem umbilico: & e contra, ubi
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Apſides conſtituuntur in Syzygiis, vis in Apſide ima eſt ad vim
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in Apſide ſumma in majore quam duplicata ratione diſtantiarum. </
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Nam vires
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LM
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in Quadraturis additæ viribus corporis
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T
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compo
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nunt vires in ratione minore, & vires
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KL
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in Syzygiis ſubductæ
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viribus corporis
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T
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relinquunt vires in ratione majore. </
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<
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>Eſt igi
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tur ratio decrementi & incrementi totius, in tranſitu inter Apſides,
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minima in Quadraturis, maxima in Syzygiis: & propterea in tran
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ſitu Apſidum a Quadraturis ad Syzygias perpetuo augetur, auget
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que Excentricitatem Ellipſeos; inque tranſitu a Syzygiis ad
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Quadraturas perpetuo diminuitur, & Excentricitatem diminuit. </
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LIBER
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PRIMUS.</
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Corol.
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10. Ut rationem ineamus errorum in Latitudinem, finga
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mus planum Orbis
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EST
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immobile manere; & ex errorum expo
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ſita cauſa manifeſtum eſt quod, ex viribus
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NM, ML,
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quæ ſunt
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cauſa illa tota, vis
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ML
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agendo ſemper ſecundum planum Orbis
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PAB,
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nunquam perturbat motus in Latitudinem; quodque vis
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NM,
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ubi Nodi ſunt in Syzygiis, agendo etiam ſecundum idem Orbis
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planum, non perturbat hos motus; ubi vero ſunt in Quadraturis
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eos maxime perturbat, corpuſque
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P
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de plano Orbis ſui perpetuo
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trahendo, minuit inclinationem plani in tranſitu corporis a Qua
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draturis ad Syzygias, augetque viciſſim eandem in tranſitu a Syzy
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giis ad Quadraturas. </
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<
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>Unde fit ut corpore in Syzygiis exiſtente in
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clinatio evadat omnium minima, redeatque ad priorem magnitudi
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nem circiter, ubi corpus ad Nodum proximum accedit. </
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<
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>At ſi Nodi
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conſtituantur in Octantibus poſt Quadraturas, id eſt, inter
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C
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&
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A,
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D
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&
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B,
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intelligetur ex modo expoſitis quod, in tranſitu corporis
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P
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a Nodo alterutro ad gradum inde nonageſimum, inclinatio pla
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ni perpetuo minuitur; deinde in tranſitu per proximos 45 gradus,
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uſque ad Quadraturam proximam, inclinatio augetur, & poſtea de
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nuo in tranſitu per alios 45 gradus, uſque ad Nodum proximum,
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diminuitur. </
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<
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>Magis itaQ.E.D.minuitur inclinatio quam augetur, &
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propterea minor eſt ſemper in Nodo ſubſequente quam in præce-</
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