Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  oritur ab attritu canalis, hic non conſidero. </s>
                  <s>Deſignent igitur
                    <emph type="italics"/>
                  AB,
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                    <arrow.to.target n="note343"/>
                  CD
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                  mediocrem altitudinem aquæ in crure utroque; & ubi aqua
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                  in crure
                    <emph type="italics"/>
                  KL
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                  aſcendit ad altitudinem
                    <emph type="italics"/>
                  EF,
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                  deſcenderit aqua in
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                  crure
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                  MN
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                  ad altitudinem
                    <emph type="italics"/>
                  GH.
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                  Sit autem
                    <emph type="italics"/>
                  P
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                  corpus pendulum,
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                    <emph type="italics"/>
                  VP
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                  filum,
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                  V
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                  punctum ſuſpenſionis,
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                  SPQR
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                  Cyclois quam Pen­
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                  dulum deſcribat,
                    <emph type="italics"/>
                  P
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                  ejus punctum infimum,
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                  PQ
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                  arcus altitudini
                    <lb/>
                    <emph type="italics"/>
                  AE
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                  æqualis. </s>
                  <s>Vis, qua motus aquæ alternis vicibus acceleratur
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                  & retardatur, eſt exceſſus ponderis aquæ in alterutro crure ſupra
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                  pondus in altero, ideoque, ubi aqua in crure
                    <emph type="italics"/>
                  KL
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                  aſcendit ad
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                  EF,
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                    <lb/>
                  & in crure altero deſcendit ad
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                  GH,
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                  vis illa eſt pondus duplica­
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                  tum aquæ
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                  EABF,
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                  & propterea eſt ad pondus aquæ totius ut
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                    <emph type="italics"/>
                  AE
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                  ſeu
                    <emph type="italics"/>
                  PQ
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                  ad
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                  VP
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                  ſeu
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                  PR.
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                  Vis etiam, qua pondus
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                  P
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                  in
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                  loco quovis
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                  Q
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                  acceleratur & retardatur in Cycloide, (per Corol. </s>
                  <s>
                    <lb/>
                  Prop. </s>
                  <s>LI.) eſt ad ejus pondus totum, ut ejus diſtantia
                    <emph type="italics"/>
                  YQ
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                  a loco
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                  infimo
                    <emph type="italics"/>
                  P,
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                  ad Cycloidis longitudinem
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                  PR.
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                  Quare aquæ & pen­
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                  duli, æqualia ſpatia
                    <emph type="italics"/>
                  AE, PQ
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                  deſcribentium, vires motrices ſunt
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                  ut pondera movenda; ideoque, ſi aqua & pendulum in princi­
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                  pio quieſcunt, vires illæ movebunt eadem æqualiter tempori­
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                  bus æqualibus, efficientque ut motu reciproco ſimul eant & re­
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                  deant.
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                  Q.E.D.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note343"/>
                  LIBER
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                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Igitur aquæ aſcendentis & deſcendentis, ſive motus in­
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                  tenſior ſit ſive remiſſior, vices omnes ſunt Iſochronæ. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. Si longitudo aquæ totius in canali ſit pedum
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                  Pariſien­
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                  ſium
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                  6 1/9: aqua tempore minuti unius ſecundi deſcendet, & tem­
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                  pore minuti alterius ſecundi aſcendet; & ſic deinceps vicibus al­
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                  ternis in infinitum. </s>
                  <s>Nam pendulum pedum (3 1/18) longitudinis,
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                  tempore minuti unius ſecundi oſcillatur. </s>
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