Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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anguli
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CTp
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ad angulum
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CTP.
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Quæ quidem rationes ex ſinu</
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bus angulorum contactus ac differentiarum angulorum facile colli
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guntur. </
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>His autem inter ſe collatis, prodit curvatura Figuræ
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Cpa
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in
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a
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ad ipſius curvaturam in
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C,
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ut
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AT cub
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+(16824/100000)
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CTqXAT
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ad
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CT cub
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+(16824/100000)
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ATqXCT.
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Ubi numerus (16824/100000) deſignat
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differentiam quadratorum angulorum
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CTP
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&
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CTp
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appli
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catam ad quadratum anguli minoris
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CTP,
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ſeu (quod per
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inde eſt) differentiam quadratorum temporum 27
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d.
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7
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h.
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43′, &
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29
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d.
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12
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h.
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44′, applicatam ad quadratum temporis 27
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d.
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7
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h.
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43′, </
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LIBER
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TERTIUS.</
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>Igitur cum
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a
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deſignet Syzygiam Lunæ, &
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C
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ipſius Quadratu
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ram, proportio jam inventa eadem eſſe debet cum proportione
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curvaturæ Orbis Lunæ in Syzygiis ad ejuſdem curvaturam in
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Quadraturis, quam ſupra invenimus. </
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<
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>Proinde ut inveniatur pro
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portio
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CT
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ad
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AT,
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duco extrema & media in ſe invicem. </
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<
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>Et
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termini prodeuntes ad
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ATXCT
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applicati, fiunt 2062, 79
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CTqq
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-2151969 NX
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CTcub
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+368676 NX
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ATXCTq
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+36342
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ATq
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XCTq
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-362047 NX
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ATqXCT
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+2191371 NX
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AT cub
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+
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4051, 4
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ATqq
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=0. Hic pro terminorum
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AT
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&
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CT
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ſemiſum
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ma N ſcribo 1, & pro eorundem ſemidifferentia ponendo
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x,
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fit
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CT
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=1+
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x,
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&
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AT
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=1-
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x
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: quibus in æquatione ſcriptis, &
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æquatione prodeunte reſoluta, obtinetur
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x
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æqualis 0,00719, &
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inde ſemidiameter
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CT
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fit 1,00719, & ſemidiameter
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AT
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0,99281,
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qui numeri ſunt ut (70 1/24) & (69 1/24) quam proxime. </
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>Eſt igitur di
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ſtantia Lunæ a Terra in Syzygiis ad ipſius diſtantiam in Quadra
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turis (ſepoſita ſcilicet Eccentricitatis conſideratione) ut (69 1/24) ad
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(70 1/24), vel numeris rotundis ut 69 ad 70. </
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PROPOSITIO XXIX. PROBLEMA X.
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Invenire Variationem Lunæ.
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>Oritur hæc inæqualitas partim ex forma Elliptica orbis Luna
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ris, partim ex inæqualitate momentorum areæ, quam Luna radio
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ad Terram ducto deſcribit. </
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<
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>Si Luna
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P
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in Ellipſi
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DBCA
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circa
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Terram in centro Ellipſeos quieſcentem moveretur, & radio
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TP
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ad Terram ducto deſcriberet aream
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CTP
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tempori proportiona
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lem; eſſet autem Ellipſeos ſemidiameter maxima
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CT
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ad ſemi
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diametrum minimam
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TA
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ut 70 ad 69: foret tangens anguli
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<
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CTP
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ad tangentem anguli motus medii a Quadratura
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C
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compu
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tati, ut Ellipſeos ſemidiameter
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TA
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ad ejuſdem ſemidiametrum </
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