Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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ad mediocrem ſuam quantitatem
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TP,
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ut & vis
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TM
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ad medio
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crem ſuam quantitatem 3
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PK.
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Hæ vires, per Legum Corol. </
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componunt vim
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TL
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; & hæc vis, ſi in radium
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TP
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demittatur
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perpendiculum
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LE,
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reſolvitur in vires
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TE, EL,
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quarum
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TE,
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agendo ſemper ſecundum radium
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TP,
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nec accelerat nec retardat
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deſcriptionem areæ
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TPC
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radio illo
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TP
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factam; &
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EL
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agendo
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ſecundum perpendiculum, accelerat vel retardat ipſam, quan
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tum accelerat vel retardat Lunam. </
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<
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>Acceleratio illa Lunæ, in
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tranſitu ipſius a Quadratura
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C
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ad Conjunctionem
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A,
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ſingulis
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temporis momentis facta, eſt ut ipſa vis accelerans
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EL,
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hoc eſt,
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ut (
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3PKXTK/TP
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). Exponatur tempus per motum medium Luna
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rem, vel (quod eodem fere recidit) per angulum
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CTP,
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vel
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etiam per arcum
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CP.
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Ad
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CT
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erigatur normalis
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CG
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ipſi
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CT
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æqualis. </
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<
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>Et diviſo arcu quadrantali
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AC
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in particulas innumeras
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æquales
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Pp,
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&c. </
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<
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>per quas æquales totidem particulæ temporis
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exponi poſſint, ductaque
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pk
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perpendiculari ad
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CT,
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jungatur
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TG
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ipſis
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KP, kp
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productis occurrens in
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F
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&
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f
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; & erit
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Kk
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ad
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<
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PK
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ut
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Pp
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ad
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Tp,
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hoc eſt in data ratione, adeoque
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FKXKk
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<
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ſeu area
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FKkf,
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ut (
<
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3PKXTK/TP
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), id eſt, ut
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EL
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; & compoſite,
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area tota
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GCKF
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ut ſumma omnium virium
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EL
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tempore toto
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<
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CP
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impreſſarum in Lunam, atque adeo etiam ut velocitas hac </
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