Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  DE MOTU
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                  CORPORUM</s>
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                  PROPOSITIO LXXVIII. THEOREMA XXXVIII.
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                  Si Sphæræ in progreſſu a centro ad circumferentiam ſint utcunque
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                  diſſimilares & inæquabiles, in progreſſu vero per circuitum ad
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                  datam omnem a centro diſtantiam ſint undique ſimilares; &
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                  vis attractiva puncti cujuſque ſit ut diſtantia corporis attracti:
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                  dico quod vis tota qua hujuſmodi Sphæræ duæ ſe mutuo trahunt
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                  ſit proportionalis diſtantiæ inter centra Sphærarum.
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                  <s>Demonſtratur ex Propoſitione præcedente, eodem modo quo
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                  Propoſitio LXXVI ex Propoſitione LXXV demonſtrata fuit. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  Quæ ſuperius in Propoſitionibus X & LXIV de motu
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                  corporum circa centra Conicarum Sectionum demonſtrata ſunt,
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                  valent ubi attractiones omnes fiunt vi Corporum Sphærieorum
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                  conditionis jam deſcriptæ, ſuntque corpora attracta Sphæræ con­
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                  ditionis ejuſdem. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
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                  Scholium.
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                    <emph.end type="center"/>
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                  <s>Attractionum Caſus duos inſigniores jam dedi expoſitos; nimi­
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                  rum ubi Vires centripetæ decreſcunt in duplicata diſtantiarum ra­
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                  tione, vel creſcunt in diſtantiarum ratione ſimplici; efficientes
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                  in utroque Caſu ut corpora gyrentur in Conicis Sectionibus, &
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                  componentes corporum Sphærieorum Vires centripetas eadem Lege,
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                  in receſſu a centro, decreſcentes vel creſcentes cum ſeipſis: Quod
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                  eſt notatu dignum. </s>
                  <s>Caſus cæteros, qui concluſiones minus ele­
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                  gantes exhibent, ſigillatim percurrere longum eſſet. </s>
                  <s>Malim
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                  cunctos methodo generali ſimul comprehendere ac determinare,
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                  ut ſequitur. </s>
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                  LEMMA XXIX.
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                  Si deſcribantur centro
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                  S
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                  circulus quilibet
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                  AEB,
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                  & centro
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                  P
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                  cir­
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                  culi duo
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                  EF, ef,
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                  ſecantes priorem in
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                  E, e,
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                  lineamque
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                  PS
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                  in
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                  F, f;
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                  & ad
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                  PS
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                  demittantur perpendicula
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                  ED, ed:
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                  dico quod,
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                  fi diſtantia arcuum
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                  EF, ef
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                  in infinitum minui intelligatur, ra­
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                  tio ultima lineæ evaneſcentis
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                  Dd
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                  ad lineam evaneſcentem
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                  Ff
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                    <emph type="italics"/>
                  ea ſit, quæ lineæ
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                  PE
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                  ad lineam
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                  PS. </s>
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