Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  æqualibus, vel deſcribent Ellipſes in plano illo circa centrum
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                  C,
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                  vel periodos movendi ultro citroQ.E.I. lineis rectis per centrum
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                  C
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                  in plano illo ductis, complebunt.
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                    <expan abbr="q.">que</expan>
                  E. D.
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                  DE MOTU
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                  CORPORUM</s>
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                  Scholium.
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                  <s>His affines ſunt aſcenſus ac deſcenſus corporum in ſuperficiebus
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                  curvis. </s>
                  <s>Concipe lineas curvas in plano deſcribi, dein circa axes
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                  quoſvis datos per centrum Virium tranſeuntes revolvi, & ea revo­
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                  lutione ſuperficies curvas deſcribere; tum corpora ita moveri ut
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                  eorum centra in his ſuperficiebus perpetuo reperiantur. </s>
                  <s>Si cor­
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                  pora illa oblique aſcendendo & deſcendendo currant ultro citroque
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                  peragentur eorum motus in planis per axem tranſeuntibus, atque
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                  adeo in lineis curvis quarum revolutione curvæ illæ ſuperficies ge­
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                  nitæ ſunt. </s>
                  <s>Iſtis igitur in caſibus ſufficit motum in his lineis cur­
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                  vis conſiderare. </s>
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                  PROPOSITIO XLVIII. THEOREMA XVI.
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                  Si Rota Globo extrinſecus ad angulos rectos inſiſtat, & more ro­
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                  tarum revolvendo progrediatur in circulo maximo; longitudo
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                  Itineris curvilinei, quod punctum quodvis in Rotæ perimetro da­
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                  tum, ex quo Globum tetigit, confecit, (quodque Cycloidem vel
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                  Epicycloidem nominare licet) erit ad duplicatum ſinum verſum
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                  arcus dimidii qui Globum ex eo tempore inter eundum tetigit,
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                  ut ſumma diametrorum Globi & Rotæ ad ſemidiametrum Globi.
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                  PROPOSITIO XLIX. THEOREMA XVII.
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                  Si Rota Globo concavo ad rectos angulos intrinſecus inſiſtat & re­
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                  volvendo progrediatur in circulo maximo; longitudo Itineris
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                  curvilinei quod punctum quodvis in Rotæ perimetro datum, ex
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                  quo Globum tetigit, confecit, erit ad duplicatum ſinum verſum
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                  arcus dimidii qui Globum toto hoc tempore inter eundum teti­
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                  git, ut differentia diametrorum Globi & Rotæ ad ſemidiame­
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                  trum Globi.
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