Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  <s>
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                  DE MUNDI
                    <lb/>
                  SYSTEMATE</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA X.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si producatur
                    <emph.end type="italics"/>
                  S
                    <foreign lang="grc">μ</foreign>
                    <emph type="italics"/>
                  ad
                    <emph.end type="italics"/>
                  N & P,
                    <emph type="italics"/>
                  ut
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  N
                    <emph type="italics"/>
                  ſit pars tertia ipſius
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  I,
                    <lb/>
                  & SP
                    <emph type="italics"/>
                  ſit ad
                    <emph.end type="italics"/>
                  SN
                    <emph type="italics"/>
                  ut
                    <emph.end type="italics"/>
                  SN
                    <emph type="italics"/>
                  ad
                    <emph.end type="italics"/>
                  S
                    <foreign lang="grc">μ</foreign>
                  .
                    <emph type="italics"/>
                  Cometa, quo tempore deſcri­
                    <lb/>
                  bit arcum
                    <emph.end type="italics"/>
                  A
                    <foreign lang="grc">μ</foreign>
                  C,
                    <emph type="italics"/>
                  ſi progrederetur ea ſemper cum velocitate
                    <lb/>
                  quam habet in altitudine ipſi
                    <emph.end type="italics"/>
                  SP
                    <emph type="italics"/>
                  æquali, deſcriberet longitudi­
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                  nem æqualem chordæ
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                  AC. </s>
                </p>
                <p type="main">
                  <s>Nam ſi Cometa velocitate quam habet in
                    <foreign lang="grc">μ</foreign>
                  , eodem tempore
                    <lb/>
                  progrederetur uniformiter in recta quæ Parabolam tangit in
                    <foreign lang="grc">μ</foreign>
                  ;
                    <lb/>
                  area quam radio ad punctum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ducto deſcriberet, æqualis eſſet
                    <lb/>
                  areæ Parabolicæ
                    <emph type="italics"/>
                  ASC
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ. </foreign>
                  </s>
                  <s>Ideoque contentum ſub longitudine in
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                  tangente deſcripta & longitudine
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  , eſſet ad contentum ſub
                    <lb/>
                  longitudinibus
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SM,
                    <emph.end type="italics"/>
                  ut area
                    <emph type="italics"/>
                  ASC
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  ad triangulum
                    <lb/>
                    <emph type="italics"/>
                  ASCM,
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                  id eſt, ut
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SM.
                    <emph.end type="italics"/>
                  Quare
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  eſt ad longitudi­
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                  nem in tangente deſcriptam, ut
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  ad
                    <emph type="italics"/>
                  SN.
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                  Cum autem velocitas
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                    <figure id="id.039.01.478.1.jpg" xlink:href="039/01/478/1.jpg" number="230"/>
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                  Cometæ in altitudine
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  ſit (per Corol. </s>
                  <s>6. Prop. </s>
                  <s>XVI. Lib. </s>
                  <s>I.)
                    <lb/>
                  ad velocitatem in altitudine
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  , in ſubduplicata ratione
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  inverſe, id eſt, in ratione
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  ad
                    <emph type="italics"/>
                  SN
                    <emph.end type="italics"/>
                  ; longitudo hac velo­
                    <lb/>
                  citate eodem tempore deſcripta, erit ad longitudinem in tangente
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                  deſcriptam, ut
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  ad
                    <emph type="italics"/>
                  SN,
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                  Igitur
                    <emph type="italics"/>
                  AC
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                  & longitudo hac nova ve­
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                  locitate deſcripta, cum ſint ad longitudinem in tangente deſcrip­
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                  tam in eadem ratione, æquantur inter ſe.
                    <emph type="italics"/>
                  Q.E.D.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  Cometa igitur ea cum velocitate, quam habet in altitudine
                    <lb/>
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  +2/3
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  , eodem tempore deſcriberet chordam
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  quamproxime. </s>
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