Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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<
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>Nam ſi linea
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Pe
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ſecet arcum
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EF
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in
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q
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; & recta
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Ee,
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quæ cum
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arcu evaneſcente
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Ee
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coincidit, producta occurrat rectæ
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PS
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in
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;
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& ab
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demittatur in
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PE
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normalis
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SG:
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ob ſimilia triangula
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DTE, dTe, DES
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; erit
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Dd
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ad
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Ee,
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ut
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DT
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ad
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TE,
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ſeu
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DE
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ad
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ES
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; & ob triangula
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Eeq, ESG
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(per Lem. </
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>VIII, & Corol. </
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Lem. </
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>VII) ſimilia, erit
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Ee
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ad
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eq
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ſeu
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Ff,
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ut
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ES
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ad
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SG
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; & ex
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æquo,
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Dd
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ad
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Ff
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ut
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DE
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ad
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SG
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; hoc eſt (ob ſimilia triangula
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PDE, PGS
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) ut
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PE
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ad
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PS.
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E. D.
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LIBER
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PRIMUS.</
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PROPOSITIO LXXIX. THEOREMA XXXIX.
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Si ſuperficies ob latitudinem infinite diminutam jamjam evaneſcens
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EF fe,
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convolutione ſui circa axem
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PS,
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deſcribat ſolidum
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Sphæricum concavo convexum, ad cujus particulas ſingulas æqua
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les tendant æquales vires centripetæ: dico quod Vis, qua ſoli
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dum illud trahit corpuſculum ſitum in
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P,
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est in ratione compo
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ta ex ratione ſolidi
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DE
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q
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XFf
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& ratione vis qua particula
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data in loco
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Ff
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traheret idem corpuſculum.
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>Nam ſi primo conſideremus vim ſuperficiei Sphæricæ
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FE,
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quæ
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convolutione arcus
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FE
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generatur, & a linea
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de
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ubivis ſecatur in
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r
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;
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erit ſuperficiei pars annularis, convolutione arcus
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rE
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genita, ut
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lineola
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Dd,
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manente Sphæræ radio
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PE,
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(uti demonſtravit
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Ar
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chimedes
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in Lib. </
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<
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>de
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Sphæra
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&
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Cylindro.
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) Et hujus vis ſecundum li
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neas
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PE
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vel
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Pr
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undiQ.E.I. ſuperficie conica ſitas exercita, ut
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hæc ipſa ſuperficiei pars annularis; hoc eſt, ut lineola
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Dd
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vel,
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quod perinde eſt, ut rectangulum ſub dato Sphæræ radio
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PE
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& </
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