Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  <s>
                    <emph type="italics"/>
                  Corol.
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                  4. Unde cum quadrata temporum, cæteris paribus, ſint ut
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                    <arrow.to.target n="note249"/>
                  longitudines pendulorum; ſi & tempora & quantitates materiæ æ­
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                  qualia ſunt, pondera erunt ut longitudines pendulorum. </s>
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                  LIBER
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                  SECUNDUS.</s>
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                  <s>
                    <emph type="italics"/>
                  Corol.
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                  5. Et univerſaliter, quantitas materiæ pendulæ eſt ut pon­
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                  dus & quadratum temporis directe, & longitudo penduli inverſe. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  6. Sed & in Medio non reſiſtente quantitas materiæ pen­
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                  dulæ eſt ut pondus comparativum & quadratum temporis directe
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                  & longitudo penduli inverſe. </s>
                  <s>Nam pondus comparativum eſt vis
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                  motrix corporis in Medio quovis gravi, ut ſupra explicui; adeoque
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                  idem præſtat in tali Medio non reſiſtente atque pondus abſolutum
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                  in vacuo. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  7. Et hinc liquet ratio tum comparandi corpora inter ſe,
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                  quoad quantitatem materiæ in ſingulis; tum comparandi pondera
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                  ejuſdem corporis in diverſis locis, ad cognoſcendam variationem
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                  gravitatis. </s>
                  <s>Factis autem experimentis quam accuratiſſimis inveni
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                  ſemper quantitatem materiæ in corporibus ſingulis eorum ponderi
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                  proportionalem eſſe. </s>
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                    <emph type="center"/>
                  PROPOSITIO XXV. THEOREMA XX:
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                  </s>
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                  <s>
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                  Corpora Funependula quibus, in Medio quovis, reſiſtitur in ratione
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                  momentorum temporis, & corpora Funependula quæ in ejuſdem
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                  gravitatis ſpecificæ Medio non reſiſtente moventur, oſcillatio­
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                  nes in Cycloide eodem tempore peragunt, & arcuum partes pro­
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                  portionales ſimul deſcribunt.
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                  </s>
                </p>
                <p type="main">
                  <s>Sit
                    <emph type="italics"/>
                  AB
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                  Cycloidis
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                  arcus, quem corpus
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                    <emph type="italics"/>
                  D
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                  tempore quovis in
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                  Medio non reſiſtente
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                  oſcillando deſcribit. </s>
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                  Biſecetur idem in
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                  C,
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                    <lb/>
                  ita ut
                    <emph type="italics"/>
                  C
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                  ſit infimum
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                  ejus punctum; & erit
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                  vis acceleratrix qua
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                  corpus urgetur in lo­
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                  co quovis
                    <emph type="italics"/>
                  D
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                  vel
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  vel
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                    <emph type="italics"/>
                  E
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                  ut longitudo arcus
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                    <emph type="italics"/>
                  CD
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                  vel
                    <emph type="italics"/>
                  Cd
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                  vel
                    <emph type="italics"/>
                  CE.
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                  Exponatur vis illa per eundem arcum; &
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                  cum reſiſtentia ſit ut momentum temporis, adeoQ.E.D.tur, expona-</s>
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