Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  fecundum) compoſitæ, ſimiles habebunt determinationes, perin­
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                    <arrow.to.target n="note271"/>
                  de ac ſi centra inter particulas ſimiliter ſita reſpicerent; & erunt
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                  vires illæ totæ ad invicem ut vires ſingulæ componentes, hoc eſt,
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                  ut correſpondentium particularum diametri inverſe, & quadrata
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                  velocitatum directe: & propterea efficient ut correſpondentes par­
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                  ticulæ figuras ſimiles deſcribere pergant. </s>
                  <s>Hæc ita ſe habebunt per
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                  Corol. 1, & 8 Prop. IV, Lib. 1. ſi modo centra illa quieſcant.
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                  Sin moveantur, quoniam ob tranſlationum ſimilitudinem, ſimiles
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                  manent eorum ſitus inter Syſtematum particulas; ſimiles indu­
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                  centur mutationes in figuris quas particulæ deſcribunt. </s>
                  <s>Similes igi­
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                  tur erunt correſpondentium & ſimilium particularum motus uſ­
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                  que ad occurſus ſuos primos, & propterea ſimiles occurſus, & ſi­
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                  miles reflexiones, & ſubinde (per jam oſtenſa) ſimiles motus in­
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                  ter ſe donec iterum in ſe mutuo inciderint, & ſic deinceps in in­
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                  finitum.
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                  Q.E.D.
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                  LIBER
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                  SECUNDUS.</s>
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                    <emph type="italics"/>
                  Corol.
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                  1. Hinc ſi corpora duo quævis, quæ ſimilia ſint & ad
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                  Syſtematum particulas correſpondentes ſimiliter ſita, inter ipſas
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                  temporibus proportionalibus ſimiliter moveri incipiant, ſintque
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                  eorum magnitudines ac denſitates ad invicem ut magnitudines ac
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                  denſitates correſpondentium particularum: hæc pergent tempori­
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                  bus proportionalibus ſimiliter moveri. </s>
                  <s>Eſt enim eadem ratio par­
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                  tium majorum Syſtematis utriuſque atque particularum.
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                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. Et ſi ſimiles & ſimiliter poſitæ Syſtematum partes om­
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                  nes quieſcant inter ſe: & earum duæ, quæ cæteris majores ſint, &
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                  ſibi mutuo in utroque Syſtemate correſpondeant, ſecundum lineas
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                  ſimiliter ſitas ſimili cum motu utcunque moveri incipiant: hæ ſi­
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                  miles in reliquis Syſtematum partibus excitabunt motus, & pergent
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                  inter ipſas temporibus proportionalibus ſimiliter moveri; atque
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                  adeo ſpatia diametris ſuis proportionalia deſcribere.
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                    <emph type="center"/>
                  PROPOSITIO XXXIII. THEOREMA XXVII.
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                  Iiſdem poſitis, dico quod Syſtematum partes majores reſiſtituntur
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                  in ratione compoſita ex duplicata ratione velocitatum ſuarum &
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                  duplicata ratione diametrorum & ratione denſitatis partium
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                  Syſtematum.
                    <emph.end type="italics"/>
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                  </s>
                </p>
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                  <s>Nam reſiſtentia oritur partim ex viribus centripetis vel centri­
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                  fugis quibus particulæ Syſtematum ſe mutuo agitant, partim ex
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                  occurſibus & reflexionibus particularum & partium majorum. </s>
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