Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Eſt igitur reſiſtentia in loco infimo
                    <emph type="italics"/>
                  C
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                  ad vim gravitatis,
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                  ut area
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                  (OP/OQ) IEF
                    <emph.end type="italics"/>
                  ad aream
                    <emph type="italics"/>
                  PINM.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  2. Fit autem maxima, ubi area
                    <emph type="italics"/>
                  PIHR
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                  eſt ad aream
                    <lb/>
                    <emph type="italics"/>
                  IEF
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  OR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                    <expan abbr="Oq.">Oque</expan>
                    <emph.end type="italics"/>
                  Eo enim in caſu momentum ejus (nimirum
                    <lb/>
                    <emph type="italics"/>
                  PIGR
                    <emph.end type="italics"/>
                  -Y) evadit nullum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Hinc etiam innoteſcit velocitas in locis ſingulis: quippe
                    <lb/>
                  quæ eſt in ſubduplicata ratione reſiſtentiæ, & ipſo motus initio æ­
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                  quatur velocitati corporis in eadem Cycloide abſque omni reſiſten­
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                  tia oſcillantis. </s>
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                <p type="main">
                  <s>Cæterum ob difficilem calculum quo reſiſtentia & velocitas per
                    <lb/>
                  hanc Propoſitionem inveniendæ ſunt, viſum eſt Propoſitionem ſe­
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                  quentem ſubjungere, quæ & generalior ſit & ad uſus Philoſophi­
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                  cos abunde ſatis accurata. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXX. THEOREMA XXIV.
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                  </s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si recta
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                  aB
                    <emph type="italics"/>
                  æqualis ſit Cycloidis arcui quem corpus oſcillando de­
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                  ſcribit, & ad ſingula ejus puncta
                    <emph.end type="italics"/>
                  D
                    <emph type="italics"/>
                  erigantur perpendicula
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                  DK,
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                    <emph type="italics"/>
                  quæ ſint ad longitudinem Penduli ut reſiſtentia corporis in ar­
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                  cus punctis correſpondentibus ad vim gravitatis: dico quod
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                  differentia inter arcum deſcenſu toto deſcriptum, & arcum
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                  aſcenſu toto ſubſequente deſcriptum, ducta in arcuum eorundem
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                  ſemiſummam, æqualis erit areæ
                    <emph.end type="italics"/>
                  BKaB
                    <emph type="italics"/>
                  a perpendiculis omnibus
                    <emph.end type="italics"/>
                    <lb/>
                  DK
                    <emph type="italics"/>
                  occupatæ.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Exponatur enim tum Cycloidis arcus, oſcillatione integra de­
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                  ſcriptus, per rectam illam ſibi æqualem
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                  aB,
                    <emph.end type="italics"/>
                  tum arcus qui deſcribe­
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                  retur in vacuo per longitudinem
                    <emph type="italics"/>
                  AB.
                    <emph.end type="italics"/>
                  Biſecetur
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  & pun­
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                  ctum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  repræſentabit infimum Cycloidis punctum, & erit
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ut
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                  vis a gravitate oriunda, qua corpus in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  ſecundum tangentem
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                  Cycloidis urgetur, eamque habebit rationem ad longitudinem Pen­
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                  duli quam habet vis in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  ad vim gravitatis. </s>
                  <s>Exponatur igitur vis
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                  illa per longitudinem
                    <emph type="italics"/>
                  CD,
                    <emph.end type="italics"/>
                  & vis gravitatis per longitudinem pen­
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                  duli, & ſi in
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  capiatur
                    <emph type="italics"/>
                  DK
                    <emph.end type="italics"/>
                  in ea ratione ad longitudinem </s>
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