Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/225.jpg" pagenum="197"/>
                  tervallo
                    <emph type="italics"/>
                  AD
                    <emph.end type="italics"/>
                  deſcribitur, trahunt corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  eſt ut area
                    <lb/>
                    <arrow.to.target n="note173"/>
                  tota
                    <emph type="italics"/>
                  AHIKL
                    <emph.end type="italics"/>
                  ducta in
                    <emph type="italics"/>
                  AP.
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note173"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſi vires punctorum decreſcunt in duplicata di­
                    <lb/>
                  ſtantiarum ratione, hoc eſt, ſi ſit
                    <emph type="italics"/>
                  FK
                    <emph.end type="italics"/>
                  ut (1/
                    <emph type="italics"/>
                  PFquad.
                    <emph.end type="italics"/>
                  ), atque adeo a­
                    <lb/>
                  rea
                    <emph type="italics"/>
                  AHIKL
                    <emph.end type="italics"/>
                  ut (1/
                    <emph type="italics"/>
                  PA
                    <emph.end type="italics"/>
                  -1/
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  ); erit attractio corpuſculi
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in Circu­
                    <lb/>
                  lum ut (1-
                    <emph type="italics"/>
                  PA/PH
                    <emph.end type="italics"/>
                  ), id eſt, ut (
                    <emph type="italics"/>
                  AH/PH
                    <emph.end type="italics"/>
                  ). </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Et univerſaliter, ſi vires punctorum ad diſtantias D ſint
                    <lb/>
                  reciproce ut diſtantiarum dignitas quælibet D
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  , hoc eſt, ſi ſit
                    <emph type="italics"/>
                  FK
                    <emph.end type="italics"/>
                    <lb/>
                  ut (1/D
                    <emph type="sup"/>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                    <emph.end type="sup"/>
                  ), adeoque area
                    <emph type="italics"/>
                  AHIKL
                    <emph.end type="italics"/>
                  ut (1/
                    <emph type="italics"/>
                  PA
                    <emph type="sup"/>
                  n-1
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  -1/
                    <emph type="italics"/>
                  PH
                    <emph type="sup"/>
                  n-1
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  ); erit attra­
                    <lb/>
                  ctio corpuſculi
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in Circulum ut (1/
                    <emph type="italics"/>
                  PA
                    <emph type="sup"/>
                  n-2
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  -
                    <emph type="italics"/>
                  PA/PH
                    <emph type="sup"/>
                  n-1
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  ). </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol
                    <emph.end type="italics"/>
                  3. Et ſi diameter Circuli augeatur in infinitum, & nume­
                    <lb/>
                  rus
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  ſit unitate major; attractio corpuſculi
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in planum totum
                    <lb/>
                  infinitum erit reciproce ut
                    <emph type="italics"/>
                  PA
                    <emph type="sup"/>
                  n-2
                    <emph.end type="sup"/>
                  ,
                    <emph.end type="italics"/>
                  propterea quod terminus al­
                    <lb/>
                  ter (
                    <emph type="italics"/>
                  PA/PH
                    <emph type="sup"/>
                  n-1
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  ) evaneſcet. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XCI. PROBLEMA XLV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Invenire attractionem corpuſculi ſiti in axe Solidi rotundi, ad cujus
                    <lb/>
                  puncta ſingula tendunt vires æquales centripetæ in quacunque
                    <lb/>
                  diſtantiarum ratione decreſcentes.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>In Solidum
                    <emph type="italics"/>
                  ADEFG
                    <emph.end type="italics"/>
                  tra­
                    <lb/>
                    <figure id="id.039.01.225.1.jpg" xlink:href="039/01/225/1.jpg" number="128"/>
                    <lb/>
                  hatur corpuſculum
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ſitum in
                    <lb/>
                  ejus axe
                    <emph type="italics"/>
                  AB.
                    <emph.end type="italics"/>
                  Circulo quoli­
                    <lb/>
                  bet
                    <emph type="italics"/>
                  RFS
                    <emph.end type="italics"/>
                  ad hunc axem per­
                    <lb/>
                  pendiculari ſecetur hoc Solidum,
                    <lb/>
                  & in ejus diametro
                    <emph type="italics"/>
                  FS,
                    <emph.end type="italics"/>
                  in pla­
                    <lb/>
                  no aliquo
                    <emph type="italics"/>
                  PALKB
                    <emph.end type="italics"/>
                  per axem
                    <lb/>
                  tranſeunte, capiatur (per Prop. </s>
                  <s>
                    <lb/>
                  XC) longitudo
                    <emph type="italics"/>
                  FK
                    <emph.end type="italics"/>
                  vi qua cor­
                    <lb/>
                  puſculum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in circulum illum
                    <lb/>
                  attrahitur proportionalis. </s>
                  <s>Tangat autem punctum
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  curvam line­
                    <lb/>
                  am
                    <emph type="italics"/>
                  LKI,
                    <emph.end type="italics"/>
                  planis extimorum circulorum
                    <emph type="italics"/>
                  AL
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  BI
                    <emph.end type="italics"/>
                  occurrentem in
                    <lb/>
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  ; & erit attractio corpuſculi
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in Solidum ut area
                    <emph type="italics"/>
                  LABI.
                    <lb/>
                    <expan abbr="q.">que</expan>
                  E. I.
                    <emph.end type="italics"/>
                  </s>
                </p>
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