Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/228.jpg" pagenum="200"/>
                    <arrow.to.target n="note176"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note176"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XCII. PROBLEMA XLVI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Dato Corpore attractivo, invenire rationem decrementi virium cen­
                    <lb/>
                  tripetarum in ejus puncta ſingula tendentium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>E Corpore dato formanda eſt Sphæra vel Cylindrus aliave figu­
                    <lb/>
                  ra regularis, cujus lex attractionis, cuivis decrementi rationi con­
                    <lb/>
                  gruens (per Prop. </s>
                  <s>LXXX, LXXXI, & XCI) inveniri poteſt. </s>
                  <s>Dein fa­
                    <lb/>
                  ctis experimentis invenienda eſt vis attractionis in diverſis diſtan­
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                  tiis, & lex attractionis in totum inde patefacta dabit rationem de­
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                  crementi virium partium ſingularum, quam invenire oportuit. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XCIII. THEOREMA XLVII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Solidum ex una parte planum, ex reliquis autem partibus infiNI­
                    <lb/>
                  tum, conſtet ex particulis æqualibus æqualiter attractivis, qua­
                    <lb/>
                  rum vires in receſſu a Solido decreſcunt in ratione poteſtatis cu­
                    <lb/>
                  juſvis diſtantiarum pluſquam quadraticæ, & vi Solidi totius cor­
                    <lb/>
                  puſculum ad utramvis plani partem conſtitutum trahatur: dico
                    <lb/>
                  quod Solidi vis illa attractiva, in receſſu ab ejus ſuperficie pla­
                    <lb/>
                  na, decreſcet in ratione poteſtatis, cujus latus est diſtantia cor­
                    <lb/>
                  puſculi a plano, & Index ternario minor quam Index poteſta­
                    <lb/>
                  tis diſtantiarum.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  1. Sit
                    <emph type="italics"/>
                  LGl
                    <emph.end type="italics"/>
                  planum
                    <lb/>
                    <figure id="id.039.01.228.1.jpg" xlink:href="039/01/228/1.jpg" number="132"/>
                    <lb/>
                  quo Solidum terminatur. </s>
                  <s>
                    <lb/>
                  Jaceat Solidum autem ex
                    <lb/>
                  parte plani hujus verſus
                    <lb/>
                    <emph type="italics"/>
                  I,
                    <emph.end type="italics"/>
                  inque plana innumera
                    <lb/>
                    <emph type="italics"/>
                  mHM, nIN,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ipſi
                    <emph type="italics"/>
                  GL
                    <emph.end type="italics"/>
                    <lb/>
                  parallela reſolvatur. </s>
                  <s>Et
                    <lb/>
                  primo collocetur corpus at­
                    <lb/>
                  tractum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  extra Solidum. </s>
                  <s>
                    <lb/>
                  Agatur autem
                    <emph type="italics"/>
                  CGHI
                    <emph.end type="italics"/>
                  pla­
                    <lb/>
                  nis illis innumeris perpendicularis, & decreſcant vires attractivæ
                    <lb/>
                  punctorum Solidi in ratione poteſtatis diſtantiarum, cujus index ſit
                    <lb/>
                  numerus
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  ternario non minor. </s>
                  <s>Ergo (per Corol. </s>
                  <s>3. Prop. </s>
                  <s>XC) </s>
                </p>
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Impressum