Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/339.jpg" pagenum="311"/>
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                  </s>
                </p>
                <p type="main">
                  <s>Et (per Cor. 10, Prop.XXXVI) ſi vaſis latitudo ſit infinita, ut li­
                    <lb/>
                    <arrow.to.target n="note287"/>
                  neola
                    <emph type="italics"/>
                  HI
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                  evaneſcat & altitudines
                    <emph type="italics"/>
                  IG, HG
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                  æquentur: vis aquæ
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                  defluentis in circellum erit ad pondus Cylindri cujus baſis eſt cir­
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                  cellus ille & altitudo eſt 1/2
                    <emph type="italics"/>
                  IG,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EFq
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                  -1/2
                    <emph type="italics"/>
                  PQq
                    <emph.end type="italics"/>
                  quam
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                  proxime. </s>
                  <s>Nam vis aquæ, uniformi motu defluentis per totum ca­
                    <lb/>
                  nalem, eadem erit in circellum
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  in quacunque canalis parte
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                  locatum.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note287"/>
                  LIBER
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                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>Claudantur jam canalis orificia
                    <emph type="italics"/>
                  EF, ST,
                    <emph.end type="italics"/>
                  & aſcendat circellus in
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                  fluido undique compreſſo & aſcenſu ſuo cogat aquam ſuperiorem
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                  deſcendere per ſpatium annulare inter circellum & latera cana­
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                  lis: & velocitas circelli aſcendentis erit ad velocitatem aquæ
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                  deſcendentis ut differentia circulorum
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  &
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                  PQ
                    <emph.end type="italics"/>
                  ad circulum
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                    <emph type="italics"/>
                  PQ,
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                  & velocitas circelli aſcendentis ad ſummam velocitatum,
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                  hoc eſt, ad velocitatem relativam aquæ deſcendentis qua præ­
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                  terfluit circellum aſcendentem, ut differentia circulorum
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad circulum
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  ſive ut
                    <emph type="italics"/>
                  EFq-PQq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EFq.
                    <emph.end type="italics"/>
                  Sit illa
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                  velocitas relativa æqualis velocitati qua ſupra oſtenſum eſt
                    <lb/>
                  aquam tranſire per idem ſpatium annulare dum circellus interea
                    <lb/>
                  immotus manet, id eſt, velocitati quam aqua cadendo & caſu ſuo
                    <lb/>
                  deſcribendo altitudinem
                    <emph type="italics"/>
                  IG
                    <emph.end type="italics"/>
                  acquirere poteſt: & vis aquæ in cir­
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                  cellum aſcendentem eadem erit ac prius, per Legum Cor. 5, id eſt,
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                  Reſiſtentia circelli aſcendentis erit ad pondus Cylindri aquæ cujus
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                  baſis eſt circellus ille & altitudo eſt 1/2
                    <emph type="italics"/>
                  IG,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  -1/2
                    <emph type="italics"/>
                  PQq
                    <emph.end type="italics"/>
                    <lb/>
                  quamproxime. </s>
                  <s>Velocitas autem circelli erit ad velocitatem quam
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                  aqua cadendo & caſu ſuo deſcribendo altitudinem
                    <emph type="italics"/>
                  IG
                    <emph.end type="italics"/>
                  acquirit,
                    <lb/>
                  ut
                    <emph type="italics"/>
                  EFq-PQq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EFq.
                    <emph.end type="italics"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>Augeatur amplitudo canalis in infinitum: & rationes illæ inter
                    <lb/>
                    <emph type="italics"/>
                  EFq-PQq
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EFq,
                    <emph.end type="italics"/>
                  interque
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  -1/2
                    <emph type="italics"/>
                  PQq
                    <emph.end type="italics"/>
                  acce­
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                  dent ultimo ad rationes æqualitatis. </s>
                  <s>Et propterea Velocitas cir­
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                  celli ea nunc erit quam aqua cadendo & caſu ſuo deſcribendo al­
                    <lb/>
                  titudinem
                    <emph type="italics"/>
                  IG
                    <emph.end type="italics"/>
                  acquirere poteſt, Reſiſtentia vero ejus æqualis eva­
                    <lb/>
                  det ponderi Cylindri cujus baſis eſt circellus ille & altitudo di­
                    <lb/>
                  midium eſt altitudinis
                    <emph type="italics"/>
                  IG,
                    <emph.end type="italics"/>
                  a qua Cylindrus cadere debet ut velo­
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                  citatem circelli aſcendentis acquirat; & hac velocitate Cylindrus,
                    <lb/>
                  tempore cadendi, quadruplum longitudinis ſuæ deſcribet. </s>
                  <s>Reſi­
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                  ſtentia autem Cylindri, hac velocitate ſecundum longitudinem ſuam
                    <lb/>
                  progredientis, eadem eſt cum Reſiſtentia circelli per Lemma IV;
                    <lb/>
                  ideoque æqualis eſt Vi qua motus ejus, interea dum quadruplum
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                  longitudinis ſuæ deſcribit, generari poteſt quamproxime. </s>
                </p>
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