Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/172.jpg" pagenum="144"/>
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                  <s>
                    <margin.target id="note120"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Nam ſi vis, qua corpus trahitur de
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  C,
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                  exponatur per
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                  rectam
                    <emph type="italics"/>
                  TZ
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                  captam ipſi proportionalem, reſolvetur hæc in vires
                    <lb/>
                    <emph type="italics"/>
                  TY, YZ
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                  ; quarum
                    <emph type="italics"/>
                  YZ
                    <emph.end type="italics"/>
                  trahendo corpus ſecundum longitudinem
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                  Fili
                    <emph type="italics"/>
                  PT,
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                  motum ejus nil mutat, vis autem altera
                    <emph type="italics"/>
                  TY
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                  motum ejus
                    <lb/>
                  in curva
                    <emph type="italics"/>
                  STRQ
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                  directe accelerat vel directe retardat. </s>
                  <s>Proinde
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                  cum hæc ſit ut via deſcribenda
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                  TR,
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                  accelerationes corporis vel re­
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                  tardationes in Oſcillationum duarum (majoris & minoris) parti­
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                  bus proportionalibus deſcribendis, erunt ſemper ut partes illæ, &
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                  propterea facient ut partes illæ ſimul deſcribantur. </s>
                  <s>Corpora autem
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                  quæ partes totis ſemper proportionales ſimul deſcribunt, ſimul de­
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                  ſcribent totas.
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                    <expan abbr="q.">que</expan>
                  E. D.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Hinc ſi corpus
                    <emph type="italics"/>
                  T
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                  Filo rectilineo
                    <emph type="italics"/>
                  AT
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                  a centro
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                  A
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                  pen­
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                  dens, deſcribat arcum circularem
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                  STRQ,
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                  & interea urgeatur ſe­
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                  cundum lineas parallelas deorſum a vi aliqua, quæ ſit ad vim uNI­
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                  formem Gravitatis, ut arcus
                    <emph type="italics"/>
                  TR
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                  ad ejus ſinum
                    <emph type="italics"/>
                  TN:
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                  æqualia e­
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                  runt Oſcillationum ſingularum tempora. </s>
                  <s>Etenim ob parallelas
                    <lb/>
                    <emph type="italics"/>
                  TZ, AR,
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                  ſimilia erunt triangula
                    <emph type="italics"/>
                  ATN, ZTY
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                  ; & propterea
                    <lb/>
                    <emph type="italics"/>
                  TZ
                    <emph.end type="italics"/>
                  erit ad
                    <emph type="italics"/>
                  AT
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  TY
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  TN
                    <emph.end type="italics"/>
                  ; hoc eſt, (ſi Gravitatis vis unifor­
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                  mis exponatur per longitudinem datam
                    <emph type="italics"/>
                  AT
                    <emph.end type="italics"/>
                  ) vis
                    <emph type="italics"/>
                  TZ,
                    <emph.end type="italics"/>
                  qua Oſcil­
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                  lationes evadent Iſochronæ, erit ad vim Gravitatis
                    <emph type="italics"/>
                  AT,
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                  ut arcus
                    <lb/>
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  TY
                    <emph.end type="italics"/>
                  æqualis ad arcus illius ſinum
                    <emph type="italics"/>
                  TN.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Igitur in Horologiis, ſi vires a Machina in Pendulum
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                  ad motum conſervandum impreſſæ ita cum vi Gravitatis componi
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                  poſſint, ut vis tota deorſum ſemper ſit ut linea quæ oritur appli­
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                  cando rectangulum ſub arcu
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  & radio
                    <emph type="italics"/>
                  AR
                    <emph.end type="italics"/>
                  ad ſinum
                    <emph type="italics"/>
                  TN,
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                    <lb/>
                  Oſcillationes omnes erunt Iſochronæ. </s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LIV. PROBLEMA XXXVI.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Conceſſis Figurarum curvilinearum quadraturis, invenire Tempora
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                  quibus corpora Vi qualibet centripeta in lineis quibuſcunque cur­
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                  vis, in plano per centrum Virium tranſeunte deſcriptis, deſcen­
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                  dent & aſcendent.
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                  </s>
                </p>
                <p type="main">
                  <s>Deſcendat corpus de loco quovis
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                  S
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                  per lineam quamvis curvam
                    <lb/>
                    <emph type="italics"/>
                  STtR,
                    <emph.end type="italics"/>
                  in plano per virium centrum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  tranſeunte datam. </s>
                  <s>Junga­
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                  tur
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                  CS
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                  & dividatur eadem in partes innumeras æquales, ſitque
                    <emph type="italics"/>
                  Dd
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                  </s>
                </p>
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