Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/263.jpg" pagenum="235"/>
                    <emph type="italics"/>
                  CH,
                    <emph.end type="italics"/>
                  (ut moris eſt) & valor ordinatim applicatæ reſolvatur in ſe­
                    <lb/>
                    <arrow.to.target n="note211"/>
                  riem convergentem: Problema per primos ſeriei terminos expe­
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                  dite ſolvetur, ut in exemplis ſequentibus. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note211"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Exempl.
                    <emph.end type="italics"/>
                  1. Sit Linea
                    <emph type="italics"/>
                  PFHQ
                    <emph.end type="italics"/>
                  Semicirculus ſuper diametro
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                    <lb/>
                  deſcriptus, & requiratur Medii denſitas quæ faciat ut Projectile
                    <lb/>
                  in hac linea moveatur. </s>
                </p>
                <p type="main">
                  <s>Biſecetur diameter
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  dic
                    <emph type="italics"/>
                  AQ n, AC a, CH e,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  CD o
                    <emph.end type="italics"/>
                  : & erit
                    <emph type="italics"/>
                  DIq
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  AQq-ADq=nn-aa-2ao-oo,
                    <emph.end type="italics"/>
                  ſeu
                    <lb/>
                    <emph type="italics"/>
                  ee-2ao-oo,
                    <emph.end type="italics"/>
                  & radice per methodum noſtram extracta, fiet
                    <lb/>
                    <emph type="italics"/>
                  DI=e-(ao/e)-(oo/2e)-(aaoo/2e
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  )-(ao
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  /2e
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  )-(a
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  o
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  /2e
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  )
                    <emph.end type="italics"/>
                  -&c. </s>
                  <s>Hic ſcribatur
                    <emph type="italics"/>
                  nn
                    <emph.end type="italics"/>
                    <lb/>
                  pro
                    <emph type="italics"/>
                  ee+aa,
                    <emph.end type="italics"/>
                  & evadet
                    <emph type="italics"/>
                  DI=e-(ao/e)-(nnoo/2e
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  )-(anno
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  /2e
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                  )
                    <emph.end type="italics"/>
                  -&c. </s>
                </p>
                <p type="main">
                  <s>Hujuſmodi ſeries diſtinguo in terminos ſucceſſivos in hunc mo­
                    <lb/>
                  dum. </s>
                  <s>Terminum primum appello in quo quantitas infinite par­
                    <lb/>
                  va
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                  non extat; ſecundum in quo quantitas illa eſt unius dimen­
                    <lb/>
                  ſionis, tertium in quo extat
                    <lb/>
                    <figure id="id.039.01.263.1.jpg" xlink:href="039/01/263/1.jpg" number="154"/>
                    <lb/>
                  duarum, quartum in quo
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                  trium eſt, & ſic in infiNI­
                    <lb/>
                  tum. </s>
                  <s>Et primus terminus
                    <lb/>
                  qui hic eſt
                    <emph type="italics"/>
                  e,
                    <emph.end type="italics"/>
                  denotabit ſem­
                    <lb/>
                  per longitudinem Ordinatæ
                    <lb/>
                    <emph type="italics"/>
                  CH
                    <emph.end type="italics"/>
                  inſiſtentis ad initium
                    <lb/>
                  indefinitæ quantitatis
                    <emph type="italics"/>
                  o
                    <emph.end type="italics"/>
                  ; ſe­
                    <lb/>
                  cundus terminus qui hic eſt
                    <lb/>
                  (
                    <emph type="italics"/>
                  ao/e
                    <emph.end type="italics"/>
                  ), denotabit differentiam
                    <lb/>
                  inter
                    <emph type="italics"/>
                  CH
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DN,
                    <emph.end type="italics"/>
                  id eſt, lineolam
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  quæ abſcinditur com­
                    <lb/>
                  plendo parallelogrammum
                    <emph type="italics"/>
                  HCDM,
                    <emph.end type="italics"/>
                  atque adeo poſitionem tan­
                    <lb/>
                  gentis
                    <emph type="italics"/>
                  HN
                    <emph.end type="italics"/>
                  ſemper determinat: ut in hoc caſu capiendo
                    <emph type="italics"/>
                  MN
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  HM
                    <emph.end type="italics"/>
                  ut eſt (
                    <emph type="italics"/>
                  ao/e
                    <emph.end type="italics"/>
                  ) ad
                    <emph type="italics"/>
                  o,
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  e.
                    <emph.end type="italics"/>
                  Terminus tertius qui hic eſt
                    <lb/>
                  (
                    <emph type="italics"/>
                  nnoo/2e
                    <emph type="sup"/>
                  3
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  ) deſignabit lineolam
                    <emph type="italics"/>
                  IN
                    <emph.end type="italics"/>
                  quæ jacet inter tangentem & cur­
                    <lb/>
                  vam, adeoQ.E.D.terminat angulum contactus
                    <emph type="italics"/>
                  IHN
                    <emph.end type="italics"/>
                  ſeu curvatu­
                    <lb/>
                  ram quam curva linea habet in
                    <emph type="italics"/>
                  H.
                    <emph.end type="italics"/>
                  Si lineola illa
                    <emph type="italics"/>
                  IN
                    <emph.end type="italics"/>
                  finitæ eſt
                    <lb/>
                  magnitudinis, deſignabitur per terminum tertium una cum ſe­
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                  quentibus in infinitum. </s>
                  <s>At ſi lineola illa minuatur in infinitum, </s>
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