Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/311.jpg" pagenum="283"/>
                  cum Figura
                    <emph type="italics"/>
                  BKVTa
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                  in puncto medio
                    <emph type="italics"/>
                  V,
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                  hæc ſi ad partem al­</s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note259"/>
                  terutram
                    <emph type="italics"/>
                  BRV
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                  vel
                    <emph type="italics"/>
                  VSa
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                  excedit Figuram illam, deficiet ab eadem
                    <lb/>
                  ad partem alteram, & ſic eidem æquabitur quam proxime. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note259"/>
                  LIBER
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                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXXI. THEOREMA XXV.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Corporis oſcillantis reſiſtentia in ſingulis arcuum deſcriptorum
                    <lb/>
                  partibus proportionalibus augeatur vel minuatur in data ratio­
                    <lb/>
                  ne; differentia inter arcum deſcenſu deſcriptum & arcum ſub­
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                  ſequente aſcenſu deſcriptum, augebitur vel diminuetur in eadem
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                  ratione.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Oritur enim differentia illa ex retardatione Penduli per reſi­
                    <lb/>
                  ſtentiam Medii, adeoque eſt ut retardatio tota eique proportio­
                    <lb/>
                  nalis reſiſtentia retardans. </s>
                  <s>In ſuperiore Propoſitione rectangu­
                    <lb/>
                  lum ſub recta 1/2
                    <emph type="italics"/>
                  aB
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                  & arcuum illorum
                    <emph type="italics"/>
                  CB, Ca
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                  differentia
                    <emph type="italics"/>
                  Aa,
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                    <lb/>
                  æqualis erat areæ
                    <emph type="italics"/>
                  BKT.
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                  Et area illa, ſi maneat longitudo
                    <emph type="italics"/>
                  aB,
                    <emph.end type="italics"/>
                    <lb/>
                  augetur vel diminuitur in ratione ordinatim applicatarum
                    <emph type="italics"/>
                  DK
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  hoc eſt, in ratione reſiſtentiæ, adeoque eſt ut longitudo
                    <emph type="italics"/>
                  aB
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  reſiſtentia conjunctim. </s>
                  <s>Proindeque rectangulum ſub
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  & 1/2
                    <emph type="italics"/>
                  aB
                    <emph.end type="italics"/>
                    <lb/>
                  eſt ut
                    <emph type="italics"/>
                  aB
                    <emph.end type="italics"/>
                  & reſiſtentia conjunctim, & propterea
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  ut reſiſten­
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                  tia.
                    <emph type="italics"/>
                  Q.E.D.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Unde ſi reſiſtentia ſit ut velocitas, differentia arcuum
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                  in eodem Medio erit ut arcus totus deſcriptus: & contra. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Si reſiſtentia ſit in duplicata ratione velocitatis, diffe­
                    <lb/>
                  rentia illa erit in duplicata ratione arcus totius: & contra. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Et univerſaliter, ſi reſiſtentia ſit in triplicata vel alia
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                  quavis ratione velocitatis, differentia erit in eadem ratione arcus
                    <lb/>
                  totius: & contra. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Et ſi reſiſtentia ſit partim in ratione ſimplici velocita­
                    <lb/>
                  tis, partim in ejuſdem ratione duplicata, differentia erit partim in
                    <lb/>
                  ratione arcus totius & partim in ejus ratione duplicata: & contra. </s>
                  <s>
                    <lb/>
                  Eadem erit lex & ratio reſiſtentiæ pro velocitate, quæ eſt differen­
                    <lb/>
                  tiæ illius pro longitudine arcus. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Ideoque ſi, pendulo inæquales arcus ſucceſſive deſcri­
                    <lb/>
                  bente, inveniri poteſt ratio incrementi ac decrementi differentiæ hu­
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                  jus pro longitudine arcus deſcripti; habebitur etiam ratio incrementi
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                  ac decrementi reſiſtentiæ pro velocitate majore vel minore. </s>
                </p>
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