Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
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                  SECTIO II.
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                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  De motu Corporum quibus reſiſtitur in duplicata ra­
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                  tione Velocitatum.
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                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO V. THEOREMA III.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Corpori reſiſiitur in velocitatis ratione duplicata, & idem ſola
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                  vi inſita per Medium ſimilare movetur; tempora vero ſuman­
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                  tur in progreſſione Geometrica a minoribus terminis ad majores
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                  pergente: dico quod velocitates initio ſingulorum temporum
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                  ſunt in eadem progreſſione Geometrica inverſe, & quod ſpatia
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                  ſunt æqualia quæ ſingulis temporibus deſcribuntur.
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                <p type="main">
                  <s>Nam quoniam quadrato velocita­
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                    <figure id="id.039.01.248.1.jpg" xlink:href="039/01/248/1.jpg" number="149"/>
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                  tis proportionalis eſt reſiſtentia Me­
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                  dii, & reſiſtentiæ proportionale eſt
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                  decrementum velocitatis; ſi tempus
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                  in particulas innumeras æquales divi­
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                  datur, quadrata velocitatum ſingulis
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                  temporum initiis erunt velocitatum
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                  earundem differentiis proportionalia. </s>
                  <s>
                    <lb/>
                  Sunto temporis particulæ illæ
                    <emph type="italics"/>
                  AK,
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                  KL, LM,
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                  &c. </s>
                  <s>in recta
                    <emph type="italics"/>
                  CD
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                  ſumptæ,
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                  & erigantur perpendicula
                    <emph type="italics"/>
                  AB, Kk,
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                  Ll, Mm,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Hyperbolæ
                    <emph type="italics"/>
                  BklmG,
                    <emph.end type="italics"/>
                    <lb/>
                  centro
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  Aſymptotis rectangulis
                    <emph type="italics"/>
                  CD, CH
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                  deſcriptæ, occurrentia
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                  in
                    <emph type="italics"/>
                  B, k, t, m,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>& erit
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Kk
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CA,
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                  & diviſim
                    <lb/>
                    <emph type="italics"/>
                  AB-Kk
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Kk
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CA,
                    <emph.end type="italics"/>
                  & viciſſim
                    <emph type="italics"/>
                  AB-Kk
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  Kk
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CA,
                    <emph.end type="italics"/>
                  adeoque ut
                    <emph type="italics"/>
                  ABXKk
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ABXCA.
                    <emph.end type="italics"/>
                  Unde, cum
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                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ABXCA
                    <emph.end type="italics"/>
                  dentur, erit
                    <emph type="italics"/>
                  AB-Kk
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  ABXKk
                    <emph.end type="italics"/>
                  ; & ultimo,
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                  ubi coeunt
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Kk,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                    <expan abbr="ABq.">ABque</expan>
                    <emph.end type="italics"/>
                  Et ſimili argumento erunt
                    <emph type="italics"/>
                  Kk-Ll,
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                  Ll-Mm,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ut
                    <emph type="italics"/>
                  Kkq, Llq,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Linearum igitur
                    <emph type="italics"/>
                  AB, Kk, Ll, Mm
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                  </s>
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