Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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PDXAZ
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proportionalis, & conjunctis rationibus,
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PKXPH
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eſt ut contentum
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KkXPDXAZ,
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&
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PKXPHXAZ
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ut
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KkXPDXAZ qu.
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id eſt, ut area
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PDdM
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&
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AZqu.
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con
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junctim.
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E. D.
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LIBER
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TIRTIUS.</
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Corol
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2. In data quavis Nodorum poſitione, motus horarius
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mediocris eſt ſemiſſis motus horarii in Syzygiis Lunæ, ideoque eſt
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ad 16″. </
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<
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>35′. </
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<
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>16
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iv
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. </
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>36
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v
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. </
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<
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>ut quadratum ſinus diſtantiæ Nodorum a
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Syzygiis ad quadratum Radii, five ut
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AZqu.
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AD
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AT.qu.
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Nam
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ſi Luna uniformi cum motu perambulet ſemicirculum
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QAq,
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ſum
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ma omnium arearum
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PDdM,
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quo tempore Luna pergit a
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Q
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ad
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M,
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erit area
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QMdE
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quæ ad circuli tangentem
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QE
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termina
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tur; & quo tempore Luna attingit punctum
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n,
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ſumma illa erit
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area tota
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EQAn
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quam linea
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PD
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deſcribit, dein Luna pergente
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ab
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n
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ad
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q,
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linea
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PD
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cadet extra circulum, & aream
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nqe
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ad
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circuli tangentem
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qe
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terminatam deſcribet; quæ, quoniam Nodi
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prius regrediebantur, jam vero progrediuntur, ſubduci debet de
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area priore, & cum æqualis ſit areæ
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QEN,
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relinquet ſemicircu
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lum
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NQAn.
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Igitur ſumma omnium arearum
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PDdM,
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quo
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tempore Luna ſemicirculum deſcribit, eſt area ſemicirculi; &
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ſumma omnium quo tempore Luna circulum deſcribit eſt area cir
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culi totius. </
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>At area
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PDdM,
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ubi Luna verſatur in Syzygiis, eſt
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rectangulum ſub arcu
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PM
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& radic
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MT
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; & ſumma omnium huic
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æqualium arearum, quo tempore Luna circulum deſcribit, eſt
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rectangulum ſub circumferentia tota & radio circuli; & hoc
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rectangulum, cum ſit æquale duobus circulis, duplo majus eſt
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quam rectangulum prius. </
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<
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>Proinde Nodi, ea cum velocitate uNI
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formiter continuata quam habent in Syzygiis Lunaribus, ſpatium
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duplo majus deſcriberent quam revera deſcribunt; & propterea
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motus mediocris quocum, ſi uniformiter continuaretur, ſpatium
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a ſe inæquabili cum motu revera confectum deſcribere poſſent, eſt
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ſemiſſis motus quem habent in Syzygiis Lunæ. </
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<
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>Unde cum mo
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tus horarius maximus, ſi Nodi in Quadraturis verſantur, ſit
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33″. </
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<
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>10′. </
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<
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>33
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iv
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. </
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>12
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v
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, motus mediocris horarius in hoc caſu erit
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16″. </
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<
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>35′. </
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<
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>16
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iv
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. </
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>36
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v
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. </
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<
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>Et cum motus horarius Nodorum ſemper ſit
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ut
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AZqu.
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& area
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PDdM
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conjunctim, & propterea motus ho
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rarius Nodorum in Syzygiis Lunæ ut
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AZqu.
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& area
<
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PDdM
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conjunctim, id eſt (ob datam aream
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PDdM
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in Syzygiis de
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ſcriptam) ut
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AZqu.
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erit etiam motus mediocris ut
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AZqu.
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atque
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adeo hic motus, ubi Nodi extra Quadraturas verſantur, erit ad
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16″. </
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>
<
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>35′. </
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>
<
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>16
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iv
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. </
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>
<
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>36
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v
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type
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. </
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>
<
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>ut
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AZqu.
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ad
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ATqu. </
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<
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>Q.E.D.
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