Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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methodo ſive dentur duo puncta
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P, p,
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ſive duæ tangentes
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TR,
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tr,
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ſive punctum
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P
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& tangens
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TR,
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deſcribendi ſunt circuli duo. </
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Sit
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H
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eorum interſectio com
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munis, & umbilicis
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S, H,
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axe illo
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dato deſcribatur Trajectoria. </
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Dico factum. </
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ctoria deſcripta (eo quod
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PH
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+SP
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in Ellipſi, &
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PH-SP
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in Hyperbola æquatur axi)
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tranſibit per punctum
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P,
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&
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(per Lemma ſuperius) tanget
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rectam
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TR.
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Et eodem argu
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mento vel tranſibit eadem per
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puncta duo
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P, p,
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vel tanget re
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ctas duas
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TR, tr. </
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DE MOTU
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CORPORUM</
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PROPOSITIO XIX. PROBLEMA XI.
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Circa datum umbilicum Trajectoriam Parabolicam deſcribere, quæ
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tranſibit per puncta data, & rectas poſitione datas continget.
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<
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S
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umbilicus,
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P
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punctum &
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TR
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tangens Trajectoriæ deſcri
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bendæ. </
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<
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P,
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intervallo
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PS
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deſcribe cir
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culum
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FG.
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Ab umbilico ad tangentem demit
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te perpendicularem
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ST,
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& produc eam ad
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V,
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ut ſit
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TV
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æqualis
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ST.
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Eodem modo deſcri
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bendus eſt alter circulus
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fg,
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ſi datur alterum
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punctum
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p
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; vel inveniendum alterum punctum
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v,
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ſi datur altera tangens
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tr
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; dein ducenda re
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cta
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IF
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quæ tangat duos circulos
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FG, fg
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ſi
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dantur duo puncta
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P, p,
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vel tranſeat per duo
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puncta
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V, v,
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ſi dantur duæ tangentes
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TR, tr,
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vel
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tangat circulum
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FG
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& tranſeat per punctum
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V,
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ſi datur punctum
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P
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& tangens
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TR.
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Ad
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FI
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demitte perpendicula
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rem
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SI,
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eamque biſeca in
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K
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; & axe
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SK,
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vertice principali
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K
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de
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ſcribatur Parabola. </
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<
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>Nam Parabola, ob æquales
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SK
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&
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IK, SP
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&
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FP,
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tranſibit per punctum
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P
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; & (per Lem
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matis XIV. Corol. </
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ST
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&
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TV
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& angulum rectum
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STR,
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tanget rectam
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TR. q.E.F.
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