Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  Globi inverſe, & ſubduplicata ratione Vis abſolutæ Globi etiam
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                  inverſe.
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                    <expan abbr="q.">que</expan>
                  E. I.
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                  </s>
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                  <s>
                    <margin.target id="note118"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Hinc etiam Oſcillantium, Cadentium & Revolventium
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                  corporum tempora poſſunt inter ſe conferri. </s>
                  <s>Nam ſi Rotæ, qua Cy­
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                  clois intra globum deſcribitur, diameter conſtituatur æqualis ſemi­
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                  diametro globi, Cyclois evadet Linea recta per centrum globi tran­
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                  ſiens, & Oſcillatio jam erit deſcenſus & ſubſequens aſcenſus in hac
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                  recta. </s>
                  <s>Unde datur tum tempus deſcenſus de loco quovis ad
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                  centrum, tum tempus huic æquale quo corpus uniformiter cir­
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                  ca centrum globi ad diſtantiam quamvis revolvendo arcum qua­
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                  drantalem deſcribit. </s>
                  <s>Eſt enim hoc tempus (per Caſum ſecun­
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                  dum) ad tempus ſemioſcillationis in Cycloide quavis
                    <emph type="italics"/>
                  QRS
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                  ut
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                  1 ad √(
                    <emph type="italics"/>
                  AR/AC
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                  ). </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. Hinc etiam conſectantur quæ
                    <emph type="italics"/>
                  Wrennus
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                  &
                    <emph type="italics"/>
                  Hugenius
                    <emph.end type="italics"/>
                  de
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                  Cycloide vulgari adinvenerunt. </s>
                  <s>Nam ſi Globi diameter augeatur
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                  in infinitum: mutabitur ejus ſuperficies ſphærica in planum, Viſque
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                  centripeta aget uniformiter ſecundum lineas huic plano perpendi­
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                  culares, & Cyclois noſtra abibit in Cycloidem vulgi. </s>
                  <s>Iſto autem
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                  in caſu longitudo arcus Cycloidis, inter planum illud & punctum
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                  deſcribens, æqualis evadet quadruplicato ſinui verſo dimidii arcus
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                  Rotæ inter idem planum & punctum deſcribens; ut invenit
                    <emph type="italics"/>
                  Wren­
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                  nus:
                    <emph.end type="italics"/>
                  Et Pendulum inter duas ejuſmodi Cycloides in ſimili & æ­
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                  quali Cycloide temporibus æqualibus Oſcillabitur, ut demonſtravit
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                    <emph type="italics"/>
                  Hugenius.
                    <emph.end type="italics"/>
                  Sed & Deſcenſus gravium, tempore Oſcillationis unius,
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                  is erit quem
                    <emph type="italics"/>
                  Hugenius
                    <emph.end type="italics"/>
                  indicavit. </s>
                </p>
                <p type="main">
                  <s>Aptantur autem Propoſitiones a nobis demonſtratæ ad veram
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                  conſtitutionem Terræ, quatenus Rotæ eundo in ejus circulis maxi­
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                  mis deſcribunt motu Clavorum, perimetris ſuis infixorum, Cycloi­
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                  des extra globum; & Pendula inferius in fodinis & cavernis Terra
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                  ſuſpenſa, in Cycloidibus intra globos Oſcillari debent, ut Oſcilla­
                    <lb/>
                  tiones omnes evadant Iſochronæ. </s>
                  <s>Nam Gravitas (ut in Libro
                    <lb/>
                  tertio docebitur) decreſcit in progreſſu a ſuperficie Terræ, ſur­
                    <lb/>
                  ſum quidem in duplicata ratione diſtantiarum a centro ejus, de
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                  orſum vero in ratione ſimplici. </s>
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