Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  LIBER
                    <lb/>
                  TERTIUS.</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XI.
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Cometa motu omni privatus de altitudine
                    <emph.end type="italics"/>
                  SN
                    <emph type="italics"/>
                  ſeu
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                  S
                    <foreign lang="grc">μ</foreign>
                  +1/3I
                    <foreign lang="grc">μ</foreign>
                    <lb/>
                    <emph type="italics"/>
                  demitteretur, ut caderet in Solem, & ea ſemper vi uniformiter
                    <lb/>
                  continuata urgeretur in Solem, qua urgetur ſub initio; idem ſe­
                    <lb/>
                  miſſe temporis quo in Orbe ſuo deſcribat arcum
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                  AC,
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                  deſcenſu
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                  ſuo deſcriberet ſpatium longitudini
                    <emph.end type="italics"/>
                  I
                    <foreign lang="grc">μ</foreign>
                    <emph type="italics"/>
                  æquale.
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                <p type="main">
                  <s>Nam Cometa quo tempore deſcribat arcum Parabolicum
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                    <lb/>
                  eodem tempore ea cum velocitate quam habet in altitudine
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                    <lb/>
                  (per Lemma noviſſimum) deſcribet chordam
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                  adeoque (per
                    <lb/>
                  Corol. </s>
                  <s>7. Prop. </s>
                  <s>XVI. Lib. </s>
                  <s>I.) eodem tempore in Circulo cujus ſemi­
                    <lb/>
                  diameter eſſet
                    <emph type="italics"/>
                  SP,
                    <emph.end type="italics"/>
                  vi gravitatis ſuæ revolvendo, deſcriberet arcum
                    <lb/>
                  cujus longitudo eſſet ad arcus Parabolici chordam
                    <emph type="italics"/>
                  AC,
                    <emph.end type="italics"/>
                  in ſubdu­
                    <lb/>
                  plicata ratione unius ad duo. </s>
                  <s>Et propterea eo cum pondere quod
                    <lb/>
                  habet in Solem in altitudine
                    <emph type="italics"/>
                  SP,
                    <emph.end type="italics"/>
                  cadendo de altitudine illa in
                    <lb/>
                  Solem, deſcriberet ſemiſſe temporis illius (per Corol.9. Prop. </s>
                  <s>IV.
                    <lb/>
                  Lib. </s>
                  <s>I.) ſpatium æquale quadrato ſemiſſis chordæ illius applicato
                    <lb/>
                  ad quadruplum altitudinis
                    <emph type="italics"/>
                  SP,
                    <emph.end type="italics"/>
                  id eſt, ſpatium (
                    <emph type="italics"/>
                  AIq/4SP
                    <emph.end type="italics"/>
                  ). Unde cum
                    <lb/>
                  pondus Cometæ in Solem in altitudine
                    <emph type="italics"/>
                  SN,
                    <emph.end type="italics"/>
                  ſit ad ipſius pondus
                    <lb/>
                  in Solem in altitudine
                    <emph type="italics"/>
                  SP,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  : Cometa pondere
                    <lb/>
                  quod habet in altitudine
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  eodem tempore, in Solem caden­
                    <lb/>
                  do, deſcribet ſpatium (
                    <emph type="italics"/>
                  AIq/4S
                    <foreign lang="grc">μ</foreign>
                    <emph.end type="italics"/>
                  ), id eſt, ſpatium longitudini
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  vel
                    <lb/>
                    <emph type="italics"/>
                  M
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  æquale.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XLI. PROBLEMA XXI.
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                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Cometæ in Parabola moti Trajectoriam ex datis tribus
                    <lb/>
                  Obſervationibus determinare.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
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                <p type="main">
                  <s>Problema hocce longe difficillimum multimode aggreſſus, com­
                    <lb/>
                  poſui Problemata quædam in Libro primo quæ ad ejus ſolutio­
                    <lb/>
                  nem ſpectant. </s>
                  <s>Poſtea ſolutionem ſequentem paulo ſimpliciorem
                    <lb/>
                  excogitavi. </s>
                </p>
                <p type="main">
                  <s>Seligantur tres obſervationes æqualibus temporum intervallis ab
                    <lb/>
                  invicem quamproxime diſtantes. </s>
                  <s>Sit autem temporis intervallum
                    <lb/>
                  illud ubi Cometa tardius movetur paulo majus altero, ita videlicet </s>
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