Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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Corol.
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1. Hinc ſi agatur
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BC
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ſecans
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PQ
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in
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r,
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& in
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PT
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capiatur
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Pt
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in ratione ad
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Pr
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quam habet
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PT
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ad
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PR:
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erit
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Bt
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tangens
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Conicæ ſectionis ad punctum
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B.
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Nam concipe punctum
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D
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coire
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cum puncto
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B
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ita ut, chorda
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BD
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evaneſcente,
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BT
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tangens eva
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dat; &
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CD
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ac
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BT
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coincident cum
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CB
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&
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Bt.
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Corol.
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2. Et vice verſa ſi
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<
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Bt
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fit tangens, & ad quod
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vis Conicæ ſectionis punc
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tum
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D
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conveniant
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BD,
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CD
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; erit
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PR
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ad
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PT
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ut
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ut
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Pr
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ad
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Pt.
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Et contra,
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ſi ſit
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PR
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ad
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PT
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ut
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Pr
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ad
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Pt:
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convenient
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BD, CD
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ad Conicæ Sectionis punc
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um aliquod
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D.
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Corol.
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3. Conica ſectio
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non ſecat Conicam ſectio
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nem in punctis pluribus quam quatuor. </
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<
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eant duæ Conicæ ſectiones per quinque puncta
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A, B, C, P, O
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; eaſ
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que ſecet recta
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BD
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in punctis
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D, d,
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& ipſam
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PQ
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ſecet recta
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Cd
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in r. </
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<
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>Ergo
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PR
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eſt ad
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PT
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ut
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P
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r ad
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PT
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; unde
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PR
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&
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P
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r ſibi
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invicem æquantur, contra Hypotheſin. </
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LEMMA XXI.
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Si rectæ duæ mobiles & infinitæ
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BM, CM
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per data puncta
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B, C,
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ceu
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polos ductæ, concurſu ſuo
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M
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deſcribant tertiam poſitione da
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tam rectam
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MN;
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& aliæ duæ infinitæ rectæ
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BD, CD
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cum
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prioribus duabus ad puncta illa data
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B, C
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datos angulos
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MBD, MCD
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efficientes ducantur; dico quod hæ duæ
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BD,
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CD
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concurſu ſuo
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D
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deſcribent ſectionem Conicam per puncta
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B, C
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tranſeuntem. </
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BD, CD
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concurſu
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ſuo
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D
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deſcribant Sectionem Conicam per data puncta
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B, C, A
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tranſeuntem, & ſit angulus
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DBM
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ſemper æqualis angulo dato
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ABC,
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anguluſque
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DCM
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ſemper æqualis angulo dato
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ACB:
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<
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punctum
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M
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continget rectam poſitione datam.
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