Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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lineola illa
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Dd:
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at ſecundum lineam
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PS
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ad centrum
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S
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tendentem
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minor, in ratione
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PD
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ad
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PE,
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adeoque ut
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PDXDd.
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Dividi
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jam intelligatur linea
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DF
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in particulas innumeras æquales, quæ
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ſingulæ nominentur
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Dd
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; & ſuperficies
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FE
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dividetur in totidem
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æquales annulos, quorum vires erunt ut ſumma omnium
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PDXDd,
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hoc eſt, ut 1/2
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PFq
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-1/2
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PDq,
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adeoque ut
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DE quad.
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Ducatur
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<
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jam ſuperficies
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FE
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in altitudinem
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Ef
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; & fiet ſolidi
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EFfe
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vis ex
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ercita in corpuſculum
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P
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ut
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DEqXFf:
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puta ſi detur vis quam
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particula aliqua data
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Ff
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in diſtantia
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PF
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exercet in corpuſculum
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P.
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At ſi vis illa non detur, fiet vis ſolidi
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EFfe
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ut ſolidum
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DEqXFf
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& vis illa non data conjunctim.
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<
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E. D.
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DE MOTU
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CORPORUM</
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PROPOSITIO LXXX. THEOREMA XL.
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Si ad Sphæræ alicujus
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ABE,
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centro
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S
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deſcriptæ, particulas ſingu
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las æquales tendant æquales vires centripetæ, & ad Sphæræ
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axem
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AB,
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in quo corpuſculum aliquod
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P
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locatur, erigantur de
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punctis ſingulis
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D
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perpendicula
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DE,
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Sphæræ occurrentia in
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E,
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<
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& in ipſis capiantur longitudines
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DN,
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quæ ſint ut quantitas
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(DE
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q
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XPS/PE)
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& vis quam Sphæræ particula ſita in axe ad di
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ſtantiam
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PE
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exercet in corpuſculum
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P
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conjunctim: dico quod
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Vis tota, qua corpuſculum
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P
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trahitur verſus Sphæram, est ut
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area comprehenſa ſub axe Sphæræ
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AB
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& linea curva
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ANB,
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quam punctum
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N
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perpetuo tangit.
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