Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MUNDI
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SYSTEMATE</
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PROPOSITIO XXXI. PROBLEMA XII.
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Invenire motum horarium Nodorum Lunæ in Orbe Elliptico.
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>Deſignet
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Qpmaq
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Ellipſin, axe majore
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Qq,
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minore
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ab
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de
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ſcriptam,
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QAq
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Circulum circumſcriptum,
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T
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Terram in utriuſque
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centro communi,
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S
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Solem,
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p
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Lunam in Ellipſi motam, &
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pm
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ar
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cum quem data temporis particula quam minima deſcribit,
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N
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&
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n
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Nodos linea
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Nn
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junctos,
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pK
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&
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mk
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perpendicula in axem
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Qq
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demiſſa & hinc inde producta, donec occurrant Circulo in
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P
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&
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M,
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& lineæ Nodorum in
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D
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&
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d.
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Et ſi Luna, radio ad Terram du
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cto, aream deſcribat tempori proportionalem, erit motus Nodi in
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Ellipſi ut area
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pDdm.
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PF
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tangat Circulum in
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P,
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& producta occurrat
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TN
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in
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F,
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&
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pf
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tangat Ellipſin in
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p
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& producta occurrat eidem
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TN
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