Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  conjunctim. </s>
                  <s>Igitur ut partes illæ ſint totis proportionales, debe­
                    <lb/>
                    <arrow.to.target n="note199"/>
                  bit reſiſtentia & tempus conjunctim eſſe ut motus. </s>
                  <s>Proinde tem­
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                  pus erit ut motus directe & reſiſtentia inverſe. </s>
                  <s>Quare temporam
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                  particulis in ea ratione ſumptis, corpora amittent ſemper parti­
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                  culas motuum proportionales totis, adeoque retinebunt velocita­
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                  tes in ratione prima. </s>
                  <s>Et ob datam velocitatum rationem, deſcri­
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                  bent ſemper ſpatia quæ ſunt ut velocitates primæ & tempora con­
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                  junctim.
                    <emph type="italics"/>
                  Q.E.D.
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                  </s>
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                <p type="margin">
                  <s>
                    <margin.target id="note199"/>
                  LIBER
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                  SECUNDUS.</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Igitur ſi æquivelocibus corporibus reſiſtitur in duplicata
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                  ratione diametrorum: Globi homogenei quibuſcunque cum velocita­
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                  tibus moti, deſcribendo ſpatia diametris ſuis proportionalia, amit­
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                  tent partes motuum proportionales totis. </s>
                  <s>Motus enim Globi cu­
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                  juſque erit ut ejus velocitas & Maſſa conjunctim, id eſt, ut veloci­
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                  tas & cubus diametri; reſiſtentia (per Hypotheſin) erit ut quadra­
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                  tum diametri & quadratum velocitatis conjunctim; & tempus (per
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                  hanc Propoſitionem) eſt in ratione priore directe & ratione poſte­
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                  riore inverſe, id eſt, ut diameter directe & velocitas inverſe; ad­
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                  eoque ſpatium (tempori & velocitati proportionale) eſt ut dia­
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                  meter. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Si æquivelocibus corporibus reſiſtitur in ratione ſeſquial­
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                  tera diametrorum: Globi homogenei quibuſcunque cum velocitati­
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                  bus moti, deſcribendo ſpatia in ſeſquialtera ratione diametrorum,
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                  amittent partes motuum proportionales totis. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Et univerſaliter, ſi æquivelocibus corporibus reſiſtitur in
                    <lb/>
                  ratione dignitatis cujuſcunQ.E.D.ametrorum: ſpatia quibus Globi
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                  homogenei, quibuſcunque cum velocitatibus moti, amittent partes
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                  motuum proportionales totis, erunt ut cubi diametrorum ad digNI­
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                  tatem illam applicati. </s>
                  <s>Sunto diametri D & E; & ſi reſiſtentiæ,
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                  ubi velocitates æquales ponuntur, ſint ut D
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
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                    <emph.end type="sup"/>
                  & E
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  : ſpatia quibus
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                  Globi quibuſcunque cum velocitatibus moti, amitteus partes mo­
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                  tuum proportionales totis, erunt ut D
                    <emph type="sup"/>
                  3-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  & E
                    <emph type="sup"/>
                  3-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  . </s>
                  <s>Igitur deſcri­
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                  bendo ſpatia ipſis D
                    <emph type="sup"/>
                  3-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  & E
                    <emph type="sup"/>
                  3-
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  proportionalia, retinebunt veloci­
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                  tates in eadem ratione ad invicem ac ſub initio. </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Quod ſi Globi non ſint homogenei, ſpatium a Globo
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                  denſiore deſcriptum augeri debet in ratione denſitatis. </s>
                  <s>Motus
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                  enim, ſub pari velocitare, major eſt in ratione denſitatis, & tempus
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                  (per hanc Propoſitionem) augetur in ratione motus directe, ac
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                  ſpatium deſcriptum in ratione temporis. </s>
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