Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <margin.target id="note172"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XC. PROBLEMA XLIV.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si ad ſingula Circuli cujuſcunque puncta tendant vires æquales cen­
                    <lb/>
                  tripetæ, decreſcentes in quacunQ.E.D.ſtantiarum ratione: inve­
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                  nire vim qua corpuſculum attrahitur ubivis poſitum in recta
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                  quæ plano Circuli ad centrum ejus perpendiculariter inſiſtit.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Centro
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  intervallo quovis
                    <emph type="italics"/>
                  AD,
                    <emph.end type="italics"/>
                  in plano cui recta
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  per­
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                  pendicularis eſt, deſcribi intelligatur Circulus; & invenienda ſit vis
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                  qua corpuſculum quodvis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in eundem attrahitur. </s>
                  <s>A Circuli puncto
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                  quovis
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  ad corpuſculum attractum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  agatur recta
                    <emph type="italics"/>
                  PE:
                    <emph.end type="italics"/>
                  In re­
                    <lb/>
                  cta
                    <emph type="italics"/>
                  PA
                    <emph.end type="italics"/>
                  capiatur
                    <emph type="italics"/>
                  PF
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  æ­
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                    <figure id="id.039.01.224.1.jpg" xlink:href="039/01/224/1.jpg" number="127"/>
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                  qualis, & erigatur normalis
                    <emph type="italics"/>
                  FK,
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                    <lb/>
                  quæ ſit ut vis qua punctum
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  tra­
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                  hit corpuſculum
                    <emph type="italics"/>
                  P.
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                  Sitque
                    <emph type="italics"/>
                  IKL
                    <emph.end type="italics"/>
                    <lb/>
                  curva linea quam punctum
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  per­
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                  petuo tangit. </s>
                  <s>Occurrat eadem Cir­
                    <lb/>
                  culi plano in
                    <emph type="italics"/>
                  L.
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                  In
                    <emph type="italics"/>
                  PA
                    <emph.end type="italics"/>
                  capiatur
                    <lb/>
                    <emph type="italics"/>
                  PH
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                  æqualis
                    <emph type="italics"/>
                  PD,
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                  & erigatur per­
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                  pendiculum
                    <emph type="italics"/>
                  HI
                    <emph.end type="italics"/>
                  curvæ prædictæ
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                  occurrens in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  ; & erit corpuſ­
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                  culi
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  attractio in Circulum ut area
                    <lb/>
                    <emph type="italics"/>
                  AHIL
                    <emph.end type="italics"/>
                  ducta in altitudinem
                    <emph type="italics"/>
                  AP.
                    <lb/>
                    <expan abbr="q.">que</expan>
                  E. I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Etenim in
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  capiatur linea quam minima
                    <emph type="italics"/>
                  Ee.
                    <emph.end type="italics"/>
                  Jungatur
                    <emph type="italics"/>
                  Pe,
                    <emph.end type="italics"/>
                    <lb/>
                  & in
                    <emph type="italics"/>
                  PE, PA
                    <emph.end type="italics"/>
                  capiantur
                    <emph type="italics"/>
                  PC, Pf
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  Pe
                    <emph.end type="italics"/>
                  æquales. </s>
                  <s>Et quoniam vis,
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                  qua annuli punctum quodvis
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  trahit ad ſe corpus
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ponitur eſſe
                    <lb/>
                  ut
                    <emph type="italics"/>
                  FK,
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                  & inde vis qua punctum illud trahit corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  eſt ut
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                  (
                    <emph type="italics"/>
                  APXFK/PE
                    <emph.end type="italics"/>
                  ), & vis qua annulus totus trahit corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  ut
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                  annulus & (
                    <emph type="italics"/>
                  APXFK/PE
                    <emph.end type="italics"/>
                  ) conjunctim; annulus autem iſte eſt ut rectan­
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                  gulum ſub radio
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  & latitudine
                    <emph type="italics"/>
                  Ee,
                    <emph.end type="italics"/>
                  & hoc rectangulum (ob pro­
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                  portionales
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  AE, Ee
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CE
                    <emph.end type="italics"/>
                  ) æquatur rectangulo
                    <emph type="italics"/>
                  PEXCE
                    <emph.end type="italics"/>
                    <lb/>
                  ſeu
                    <emph type="italics"/>
                  PEXFf
                    <emph.end type="italics"/>
                  ; erit vis qua annulus iſte trahit corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  verſus
                    <lb/>
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PEXFf
                    <emph.end type="italics"/>
                  & (
                    <emph type="italics"/>
                  APXFK/PE
                    <emph.end type="italics"/>
                  ) conjunctim, id eſt, ut contentum
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                    <emph type="italics"/>
                  FfXFKXAP,
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                  ſive ut area
                    <emph type="italics"/>
                  FKkf
                    <emph.end type="italics"/>
                  ducta in
                    <emph type="italics"/>
                  AP.
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                  Et propterea
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                  ſumma virium, quibus annuli omnes in Circulo, qui centro
                    <emph type="italics"/>
                  A
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                  & in-</s>
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