Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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hac figura tangentes illæ duæ evadent ſibi invicem parallelæ, & tan
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gens tertia fiet parallela rectæ per
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puncta duo data tranſeunti. </
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hi, kl
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tangentes illæ duæ parallelæ,
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ik
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tangens tertia, &
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hl
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recta huic
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parallela tranſiens per puncta illa
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a, b,
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per quæ Conica ſectio in hac
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figura nova tranſire debet, & pa
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rallelogrammum
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hikl
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complens. </
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Secentur rectæ
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hi, ik, kl
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in
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c, d, e,
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ita ut ſit
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hc
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ad latus quadratum
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rectanguli
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ahb, ic
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ad
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id,
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&
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ke
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ad
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kd
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ut eſt ſumma rectarum
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hi
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&
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kl
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ad ſummam trium linea
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rum quarum prima eſt recta
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ik,
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& alteræ duæ ſunt latera quadrata
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rectangulorum
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ahb
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&
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alb
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& erunt
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c, d, e
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puncta contactuum. </
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enim, ex Conicis, ſunt
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hc
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quadratum ad rectangulum
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ahb,
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&
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ic
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quadratum ad
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id
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quadratum, &
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ke
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quadratum ad
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kd
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quadratum,
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&
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el
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quadratum ad rectangulum
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alb
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in eadem ratione; & propter
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ea
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hc
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ad latus quadratum ipſius
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ahb, ic
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ad
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id, ke
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ad
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kd,
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&
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el
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ad
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latus quadratum ipſius
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alb
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ſunt in ſubduplicata illa ratione, &
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compoſite, in data ratione omnium antecedentium
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hi
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&
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kl
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ad
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omnes conſequentes, quæ ſunt latus quadratum rectanguli
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ahb
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&
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recta
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ik
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& latus quadratum rectanguli
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alb.
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Habentur igitur ex
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data illa ratione puncta contactuum
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c, d, e,
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in figura nova. </
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<
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inverſas operationes Lemmatis noviſſimi transferantur hæc pun
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cta in figuram primam & ibi, per Probl. </
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Trajectoria.
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q.E.F.
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Ceterum perinde ut puncta
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a, b
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ja
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cent vel inter puncta
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h, l,
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vel extra, debent puncta
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c, d, e
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vel
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inter puncta
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h, i, k, l
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capi, vel extra. </
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<
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a, b
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al
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terutrum cadit inter puncta
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h, l,
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& alterum extra, Problema im
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poſſibile eſt. </
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DE MOTU
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CORPORUM</
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PROPOSITIO XXVI. PROBLEMA XVIII.
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Trajectoriam deſcribere quæ tranſibit per punctum datum & rectas
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quatuor poſitione datas continget.
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<
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>Ab interſectione communi duarum quarumlibet tangentium ad
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interſectionem communem reliquarum duarum agatur recta infini-</
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