Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  Prioris autem generis reſiſtentiæ ſunt ad invicem ut vires totæ mo­
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                  trices a quibus oriuntur, id eſt, ut vires totæ acceleratrices & quan­
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                  titates materiæ in partibus correſpondentibus; hoc eſt (per Hy­
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                  potheſin) ut quadrata velocitatum directe & diſtantiæ particula­
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                  rum correſpondentium inverſe & quantitates materiæ in partibus
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                  correſpondentibus directe: ideoque (cum diſtantiæ particularum Sy­
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                  ſtematis unius ſint ad diſtantias correſpondentes particularum alte­
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                  rius, ut diameter particulæ vel partis in Syſtemate priore ad dia­
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                  metrum particulæ vel partis correſpondentis in altero, & quantita­
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                  tes materiæ ſint ut denſitates partium & cubi diametrorum) reſi­
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                  ſtentiæ ſunt ad invicem ut quadrata velocitatum & quadrata dia­
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                  metrorum & denſitates partium Syſtematum.
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                  Q.E.D.
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                  Poſte­
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                  rioris generis reſiſtentiæ ſunt ut reflexionum correſpondentium nu­
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                  meri & vires conjunctim. </s>
                  <s>Numeri autem reflexionum ſunt ad in­
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                  vicem ut velocitates partium correſpondentium directe, & ſpatia
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                  inter earum reflexiones inverſe. </s>
                  <s>Et vires reflexionum ſunt ut ve­
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                  locitates & magnitudines & denſitates partium correſpondentium
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                  conjunctim; id eſt, ut velocitates & diametrorum cubi & denſita­
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                  tes partium. </s>
                  <s>Et conjunctis his omnibus rationibus, reſiſtentiæ
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                  partium correſpondentium ſunt ad invicem ut quadrata veloci­
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                  tum & quadrata diametrorum & denſitates partium conjunctim.
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                  Q.E.D.
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                  DE MOTU
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                  CORPORUM</s>
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                    <emph type="italics"/>
                  Corol.
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                  1. Igitur ſi Syſtemata illa ſint Fluida duo Elaſtica ad
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                  modum Aeris, & partes eorum quieſcant inter ſe: corpora autem
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                  duo ſimilia & partibus fluidorum quoad magnitudinem & denſita­
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                  tem proportionalia, & inter partes illas ſimiliter poſita, ſecundum
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                  lineas ſimiliter poſitas utcunque projiciantur; vires autem acce­
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                  leratrices, quibus particulæ Fluidorum ſe mutuo agitant, ſint ut
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                  corporum projectorum diametri inverſe, & quadrata velocitatum
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                  directe: corpora illa temporibus proportionalibus ſimiles excita­
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                  bunt motus in Fluidis, & ſpatia ſimilia ac diametris ſuis propor­
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                  tionalia deſcribent.
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                    <emph type="italics"/>
                  Corol.
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                  2. Proinde in eodem Fluido projectile velox reſiſtentiam pa­
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                  titur quæ eſt in duplicata ratione velocitatis quam proxime. </s>
                  <s>Nam
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                  ſi vires, quibus particulæ diſtantes ſe mutuo agitant, augerentur in
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                  duplicata ratione velocitatis, reſiſtentia foret in eadem ratione du­
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                  plicata accurate; ideoQ.E.I. Medio, cujus partes ab invicem diſtan­
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                  tes ſeſe viribus nullis agitant, reſiſtentia eſt in duplicata ratione ve­
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                  locitatis accurate. </s>
                  <s>Sunto igitur Media tria
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                  A, B, C
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                  ex partibus
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                  ſimilibus & æqualibus & ſecundum diſtantias æquales regulariter </s>
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