Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/302.jpg" pagenum="274"/>
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                  tur eadem per datam arcus Cycloidis partem
                    <emph type="italics"/>
                  CO,
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                  & ſumatur ar­
                    <lb/>
                  cus
                    <emph type="italics"/>
                  Od
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                  in ratione ad arcum
                    <emph type="italics"/>
                  CD
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                  quam habet arcus
                    <emph type="italics"/>
                  OB
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                  ad arcum
                    <lb/>
                    <emph type="italics"/>
                  CB:
                    <emph.end type="italics"/>
                  & vis qua corpus in
                    <emph type="italics"/>
                  d
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                  urgetur in Medio reſiſtente, cum ſit ex­
                    <lb/>
                  ceſſus vis
                    <emph type="italics"/>
                  Cd
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                  ſupra reſiſtentiam
                    <emph type="italics"/>
                  CO,
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                  exponetur per arcum
                    <emph type="italics"/>
                  Od,
                    <emph.end type="italics"/>
                  ad­
                    <lb/>
                  eoque erit ad vim qua corpus
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  urgetur in Medio non reſiſtente,
                    <lb/>
                  in loco
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                  ut arcus
                    <emph type="italics"/>
                  Od
                    <emph.end type="italics"/>
                  ad arcum
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ; & propterea etiam in lo­
                    <lb/>
                  co
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ut arcus
                    <emph type="italics"/>
                  OB
                    <emph.end type="italics"/>
                  ad arcum
                    <emph type="italics"/>
                  CB.
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                  Proinde ſi corpora duo,
                    <emph type="italics"/>
                  D, d
                    <emph.end type="italics"/>
                    <lb/>
                  exeant de loco
                    <emph type="italics"/>
                  B,
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                  & his viribus urgeantur: cum vires ſub initio
                    <lb/>
                  ſint ut arcus
                    <emph type="italics"/>
                  CB
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                  &
                    <emph type="italics"/>
                  OB,
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                  erunt velocitates primæ & arcus primo
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                  deſcripti in eadem ratione. </s>
                  <s>Sunto arcus illi
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Bd,
                    <emph.end type="italics"/>
                  & arcus
                    <lb/>
                  reliqui
                    <emph type="italics"/>
                  CD, Od
                    <emph.end type="italics"/>
                  erunt in eadem ratione. </s>
                  <s>Proinde vires, ipſis
                    <lb/>
                    <emph type="italics"/>
                  CD, Od
                    <emph.end type="italics"/>
                  proportionales, manebunt in eadem ratione ac ſub initio,
                    <lb/>
                  & propterea corpora pergent arcus in eadem ratione ſimul deſcri­
                    <lb/>
                  bere. </s>
                  <s>Igitur vires &
                    <lb/>
                    <figure id="id.039.01.302.1.jpg" xlink:href="039/01/302/1.jpg" number="176"/>
                    <lb/>
                  velocitates & arcus re­
                    <lb/>
                  liqui
                    <emph type="italics"/>
                  CD, Od
                    <emph.end type="italics"/>
                  ſemper
                    <lb/>
                  erunt ut arcus toti
                    <emph type="italics"/>
                  CB,
                    <lb/>
                  OB,
                    <emph.end type="italics"/>
                  & propterea ar­
                    <lb/>
                  cus illi reliqui ſimul
                    <lb/>
                  deſcribentur. </s>
                  <s>Quare
                    <lb/>
                  corpora duo
                    <emph type="italics"/>
                  D, d
                    <emph.end type="italics"/>
                  ſi­
                    <lb/>
                  mul pervenient ad loca
                    <lb/>
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  O,
                    <emph.end type="italics"/>
                  alterum qui­
                    <lb/>
                  dem in Medio non re­
                    <lb/>
                  ſiſtente ad locum
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  alterum in Medio reſiſtente ad locum
                    <emph type="italics"/>
                  O.
                    <emph.end type="italics"/>
                  Cum autem velocitates in
                    <lb/>
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  O
                    <emph.end type="italics"/>
                  ſint ut arcus
                    <emph type="italics"/>
                  CB, OB
                    <emph.end type="italics"/>
                  ; erunt arcus quos corpora ulterius
                    <lb/>
                  pergendo ſimul deſcribunt, in eadem ratione. </s>
                  <s>Sunto illi
                    <emph type="italics"/>
                  CE
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <emph type="italics"/>
                  Oe.
                    <emph.end type="italics"/>
                  Vis qua corpus
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  in Medio non reſiſtente retardatur in
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                    <lb/>
                  eſt ut
                    <emph type="italics"/>
                  CE,
                    <emph.end type="italics"/>
                  & vis qua corpus
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  in Medio reſiſtente retardatur in
                    <emph type="italics"/>
                  e
                    <emph.end type="italics"/>
                    <lb/>
                  eſt ut ſumma vis
                    <emph type="italics"/>
                  Ce
                    <emph.end type="italics"/>
                  & reſiſtentiæ
                    <emph type="italics"/>
                  CO,
                    <emph.end type="italics"/>
                  id eſt ut
                    <emph type="italics"/>
                  Oe
                    <emph.end type="italics"/>
                  ; ideoque vi­
                    <lb/>
                  res, quibus corpora retardantur, ſunt ut arcubus
                    <emph type="italics"/>
                  CE, Oe
                    <emph.end type="italics"/>
                  propor­
                    <lb/>
                  tionales arcus
                    <emph type="italics"/>
                  CB, OB
                    <emph.end type="italics"/>
                  ; proindeque velocitates, in data illa ratio­
                    <lb/>
                  ne retardatæ, manent in eadem illa data ratione. </s>
                  <s>Velocitates igitur
                    <lb/>
                  & arcus iiſdem deſcripti ſemper ſunt ad invicem in data illa ratio­
                    <lb/>
                  ne arcuum
                    <emph type="italics"/>
                  CB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  OB
                    <emph.end type="italics"/>
                  ; & propterea ſi ſumantur arcus toti
                    <emph type="italics"/>
                  AB,
                    <lb/>
                  aB
                    <emph.end type="italics"/>
                  in eadem ratione, corpora
                    <emph type="italics"/>
                  D, d
                    <emph.end type="italics"/>
                  ſimul deſcribent hos arcus, &
                    <lb/>
                  in locis
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  motum omnem ſimul amittent. </s>
                  <s>Iſochronæ ſunt
                    <lb/>
                  igitur oſcillationes totæ, & arcubus totis
                    <emph type="italics"/>
                  BA, Ba
                    <emph.end type="italics"/>
                  proportionales
                    <lb/>
                  ſunt arcuum partes quælibet
                    <emph type="italics"/>
                  BD, Bd
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  BE, Be
                    <emph.end type="italics"/>
                  quæ ſimul de­
                    <lb/>
                  ſcribuntur.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
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