Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/254.jpg" pagenum="226"/>
                    <arrow.to.target n="note202"/>
                  una cum (1/A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ) in
                    <emph type="italics"/>
                  na
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  erit nihil. </s>
                  <s>Et propterea momentum ip­
                    <lb/>
                  ſius (1/A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ) ſeu A
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                  -
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  erit-(
                    <emph type="italics"/>
                  na
                    <emph.end type="italics"/>
                  /A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  +1).
                    <emph type="italics"/>
                  q.ED.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note202"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  5. Et cum A
                    <emph type="sup"/>
                  1/2
                    <emph.end type="sup"/>
                  in A
                    <emph type="sup"/>
                  1/2
                    <emph.end type="sup"/>
                  ſit A, momentum ipſius A
                    <emph type="sup"/>
                  1/2
                    <emph.end type="sup"/>
                  ductum in
                    <lb/>
                  2A
                    <emph type="sup"/>
                  1/2
                    <emph.end type="sup"/>
                  erit
                    <emph type="italics"/>
                  a,
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                  per Cas. </s>
                  <s>3: ideoque momentum ipſius A
                    <emph type="sup"/>
                  1/2
                    <emph.end type="sup"/>
                  erit (
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  /2A 1/2)
                    <lb/>
                  ſive 1/2
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                  -1/2
                    <emph.end type="sup"/>
                  . </s>
                  <s>Et generaliter ſi ponatur A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m/n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  æquale B, erit A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  æ­
                    <lb/>
                  quale B
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  , ideoque
                    <emph type="italics"/>
                  ma
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  æquale
                    <emph type="italics"/>
                  nb
                    <emph.end type="italics"/>
                  B
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1,
                    <emph.end type="sup"/>
                  &
                    <emph type="italics"/>
                  ma
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                  -1
                    <emph.end type="sup"/>
                  æqua­
                    <lb/>
                  le
                    <emph type="italics"/>
                  nb
                    <emph.end type="italics"/>
                  B
                    <emph type="sup"/>
                  -1
                    <emph.end type="sup"/>
                  ſeu
                    <emph type="italics"/>
                  nb
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                  -
                    <emph type="italics"/>
                  m/n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  , adeoque
                    <emph type="italics"/>
                  m/n a
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                  (
                    <emph type="italics"/>
                  m-n/n
                    <emph.end type="italics"/>
                  )
                    <emph.end type="sup"/>
                  æquale
                    <emph type="italics"/>
                  b,
                    <emph.end type="italics"/>
                  id eſt, æquale
                    <lb/>
                  momento ipſius A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m/n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ,
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  6. Igitur Genitæ cujuſeunque A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  B
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  momentum eſt mo­
                    <lb/>
                  mentum ipſius A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ductum in B
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  , una cum momento ipſius B
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  du­
                    <lb/>
                  cto in A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  , id eſt
                    <emph type="italics"/>
                  ma
                    <emph.end type="italics"/>
                  A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  B
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  +
                    <emph type="italics"/>
                  nb
                    <emph.end type="italics"/>
                  B
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  -1
                    <emph.end type="sup"/>
                  A
                    <emph type="sup"/>
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ; idque ſive dignita­
                    <lb/>
                  tum indices
                    <emph type="italics"/>
                  m
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  ſint integri numeri vel fracti, ſive affirmati­
                    <lb/>
                  vi vel negativi. </s>
                  <s>Et par eſt ratio contenti ſub pluribus dignitati­
                    <lb/>
                  bus.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc in continue proportionalibus, ſi terminus unus
                    <lb/>
                  datur, momenta terminorum reliquorum erunt ut iidem termini
                    <lb/>
                  multiplicati per numerum intervallorum inter ipſos & terminum
                    <lb/>
                  datum. </s>
                  <s>Sunto A, B, C, D, E, F continue proportionales; & ſi
                    <lb/>
                  detur terminus C, momenta reliquorum terminorum erunt inter
                    <lb/>
                  ſe ut-2A, -B, D, 2E, 3F. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et ſi in quatuor proportionalibus duæ mediæ dentur,
                    <lb/>
                  momenta extremarum erunt ut eædem extremæ. </s>
                  <s>Idem intelligen­
                    <lb/>
                  dum eſt de lateribus rectanguli cujuſcunQ.E.D.ti. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Et ſi ſumma vel differentia duorum quadratorum detur,
                    <lb/>
                  momenta laterum erunt reciproce ut latera. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>In literis quæ mihi cum Geometra peritiſſimo
                    <emph type="italics"/>
                  G.G. Leibnitio
                    <emph.end type="italics"/>
                  an­
                    <lb/>
                  nis abhinc decem intercedebant, cum ſignificarem me compotem
                    <lb/>
                  eſſe methodi determinandi Maximas & Minimas, ducendi Tangen­
                    <lb/>
                  tes, & ſimilia peragendi, quæ in terminis ſurdis æque ac in ratio­
                    <lb/>
                  nalibus procederet, & literis tranſpoſitis hanc ſententiam involven-</s>
                </p>
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          </chap>
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