Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/314.jpg" pagenum="286"/>
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                  & centrum Globi eſſet 126 digitorum, arcus quem centrum Globi
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                  deſcripſit erat (124 1/31) digitorum. </s>
                  <s>Quoniam corporis oſcillantis ve­
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                  locitas maxima, ob reſiſtentiam Aeris, non incidit in punctum infi­
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                  mum arcus deſcripti, ſed in medio fere loco arcus totius verſatur:
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                  hæc eadem erit circiter ac ſi Globus deſcenſu ſuo toto in Medio
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                  non reſiſtente deſcriberet arcus illius partem dimidiam digitorum
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                  (62 1/62), idQ.E.I. Cycloide, ad quam motum Penduli ſupra reduxi­
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                  mus: & propterea velocitas illa æqualis erit velocitati quam Glo­
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                  bus, perpendiculariter cadendo & caſu ſuo deſcribendo altitudinem
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                  arcus illius ſinui verſo æqualem, acquirere poſſet. </s>
                  <s>Eſt autem ſinus
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                  ille verſus in Cycloide ad arcum iſtum (62 1/62) ut arcus idem ad pen­
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                  duli longitudinem duplam 252, & propterea æqualis digitis 15,278.
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                  Quare velocitas ea ipſa eſt quam corpus cadendo & caſu ſuo ſpa­
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                  tium 15,278 digitorum deſcribendo acquirere poſſet. </s>
                  <s>Tali igitur
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                  cum velocitate Globus reſiſtentiam patitur, quæ ſit ad ejus pondus
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                  ut 0,61675 ad 121, vel (ſi reſiſtentiæ pars illa ſola ſpectetur quæ
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                  eſt in velocitatis ratione duplicata) ut 0,56752 ad 121. </s>
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                    <margin.target id="note262"/>
                  DE MOTU
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                  CORPORUM</s>
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                  <s>Experimento autem Hydroſtatico inveni quod pondus Globi hu­
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                  jus lignei eſſet ad pondus Globi aquei magnitudinis ejuſdem, ut 55
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                  ad 97: & propterea cum 121 ſit ad 213,4 in eadem ratione, erit
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                  reſiſtentia Globi aquei præfata cum velocitate progredientis ad ip­
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                  ſius pondus, ut 0,56752 ad 213,4 id eſt, ut 1 ad (376 1/50). Unde cum
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                  pondus Globi aquei, quo tempore Globus cum velocitate unifor­
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                  miter continuata deſcribat longitudinem digitorum 30,556, veloci­
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                  tatem illam omnem in Globo cadente generare poſſet; manifeſtum
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                  eſt quod vis reſiſtentiæ eodem tempore uniformiter continuata tol­
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                  lere poſſet velocitatem minorem in ratione 1 ad (376 1/50), hoc eſt, ve­
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                  locitatis totius partem (1/(376 1/50)). Et propterea quo tempore Globus,
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                  ea cum velocitate uniformiter continuata, longitudinem ſemidiame­
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                  tri ſuæ, ſeu digitorum (3 7/16), deſcribere poſſet, eodem amitteret mo­
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                  tus ſui partem (1/3342). </s>
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                  <s>Numerabam etiam oſcillationes quibus Pendulum quartam mo­
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                  tus ſui partem amiſit. </s>
                  <s>In ſequente Tabula numeri ſupremi deno­
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                  tant longitudinem arcus deſcenſu primo deſcripti, in digitis & par­
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                  tibus digiti expreſſam: numeri medii ſignificant longitudinem ar­
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                  cus aſcenſu ultimo deſcripti; & loco infimo ſtant numeri oſcilla­
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                  tionum. </s>
                  <s>Experimentum deſcripſi tanquam magis accuratum quam
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                  cum motus pars tantum octava amitteretur. </s>
                  <s>Calculum tentet qui
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                  volet. </s>
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