Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/435.jpg" pagenum="407"/>
                    <emph type="italics"/>
                  PDXAZ
                    <emph.end type="italics"/>
                  proportionalis, & conjunctis rationibus,
                    <emph type="italics"/>
                  PKXPH
                    <emph.end type="italics"/>
                    <lb/>
                    <arrow.to.target n="note436"/>
                  eſt ut contentum
                    <emph type="italics"/>
                  KkXPDXAZ,
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                  &
                    <emph type="italics"/>
                  PKXPHXAZ
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                    <emph type="italics"/>
                  KkXPDXAZ qu.
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                  id eſt, ut area
                    <emph type="italics"/>
                  PDdM
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                  &
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  con­
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                  junctim.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note436"/>
                  LIBER
                    <lb/>
                  TIRTIUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol
                    <emph.end type="italics"/>
                  2. In data quavis Nodorum poſitione, motus horarius
                    <lb/>
                  mediocris eſt ſemiſſis motus horarii in Syzygiis Lunæ, ideoque eſt
                    <lb/>
                  ad 16″. </s>
                  <s>35′. </s>
                  <s>16
                    <emph type="sup"/>
                  iv
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                  . </s>
                  <s>36
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>ut quadratum ſinus diſtantiæ Nodorum a
                    <lb/>
                  Syzygiis ad quadratum Radii, five ut
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  AD
                    <emph type="italics"/>
                  AT.qu.
                    <emph.end type="italics"/>
                  Nam
                    <lb/>
                  ſi Luna uniformi cum motu perambulet ſemicirculum
                    <emph type="italics"/>
                  QAq,
                    <emph.end type="italics"/>
                  ſum­
                    <lb/>
                  ma omnium arearum
                    <emph type="italics"/>
                  PDdM,
                    <emph.end type="italics"/>
                  quo tempore Luna pergit a
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  M,
                    <emph.end type="italics"/>
                  erit area
                    <emph type="italics"/>
                  QMdE
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                  quæ ad circuli tangentem
                    <emph type="italics"/>
                  QE
                    <emph.end type="italics"/>
                  termina­
                    <lb/>
                  tur; & quo tempore Luna attingit punctum
                    <emph type="italics"/>
                  n,
                    <emph.end type="italics"/>
                  ſumma illa erit
                    <lb/>
                  area tota
                    <emph type="italics"/>
                  EQAn
                    <emph.end type="italics"/>
                  quam linea
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  deſcribit, dein Luna pergente
                    <lb/>
                  ab
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  q,
                    <emph.end type="italics"/>
                  linea
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  cadet extra circulum, & aream
                    <emph type="italics"/>
                  nqe
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  circuli tangentem
                    <emph type="italics"/>
                  qe
                    <emph.end type="italics"/>
                  terminatam deſcribet; quæ, quoniam Nodi
                    <lb/>
                  prius regrediebantur, jam vero progrediuntur, ſubduci debet de
                    <lb/>
                  area priore, & cum æqualis ſit areæ
                    <emph type="italics"/>
                  QEN,
                    <emph.end type="italics"/>
                  relinquet ſemicircu­
                    <lb/>
                  lum
                    <emph type="italics"/>
                  NQAn.
                    <emph.end type="italics"/>
                  Igitur ſumma omnium arearum
                    <emph type="italics"/>
                  PDdM,
                    <emph.end type="italics"/>
                  quo
                    <lb/>
                  tempore Luna ſemicirculum deſcribit, eſt area ſemicirculi; &
                    <lb/>
                  ſumma omnium quo tempore Luna circulum deſcribit eſt area cir­
                    <lb/>
                  culi totius. </s>
                  <s>At area
                    <emph type="italics"/>
                  PDdM,
                    <emph.end type="italics"/>
                  ubi Luna verſatur in Syzygiis, eſt
                    <lb/>
                  rectangulum ſub arcu
                    <emph type="italics"/>
                  PM
                    <emph.end type="italics"/>
                  & radic
                    <emph type="italics"/>
                  MT
                    <emph.end type="italics"/>
                  ; & ſumma omnium huic
                    <lb/>
                  æqualium arearum, quo tempore Luna circulum deſcribit, eſt
                    <lb/>
                  rectangulum ſub circumferentia tota & radio circuli; & hoc
                    <lb/>
                  rectangulum, cum ſit æquale duobus circulis, duplo majus eſt
                    <lb/>
                  quam rectangulum prius. </s>
                  <s>Proinde Nodi, ea cum velocitate uNI­
                    <lb/>
                  formiter continuata quam habent in Syzygiis Lunaribus, ſpatium
                    <lb/>
                  duplo majus deſcriberent quam revera deſcribunt; & propterea
                    <lb/>
                  motus mediocris quocum, ſi uniformiter continuaretur, ſpatium
                    <lb/>
                  a ſe inæquabili cum motu revera confectum deſcribere poſſent, eſt
                    <lb/>
                  ſemiſſis motus quem habent in Syzygiis Lunæ. </s>
                  <s>Unde cum mo­
                    <lb/>
                  tus horarius maximus, ſi Nodi in Quadraturis verſantur, ſit
                    <lb/>
                  33″. </s>
                  <s>10′. </s>
                  <s>33
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>12
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  , motus mediocris horarius in hoc caſu erit
                    <lb/>
                  16″. </s>
                  <s>35′. </s>
                  <s>16
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>36
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>Et cum motus horarius Nodorum ſemper ſit
                    <lb/>
                  ut
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  & area
                    <emph type="italics"/>
                  PDdM
                    <emph.end type="italics"/>
                  conjunctim, & propterea motus ho­
                    <lb/>
                  rarius Nodorum in Syzygiis Lunæ ut
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  & area
                    <emph type="italics"/>
                  PDdM
                    <emph.end type="italics"/>
                    <lb/>
                  conjunctim, id eſt (ob datam aream
                    <emph type="italics"/>
                  PDdM
                    <emph.end type="italics"/>
                  in Syzygiis de­
                    <lb/>
                  ſcriptam) ut
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  erit etiam motus mediocris ut
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  atque
                    <lb/>
                  adeo hic motus, ubi Nodi extra Quadraturas verſantur, erit ad
                    <lb/>
                  16″. </s>
                  <s>35′. </s>
                  <s>16
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>36
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>ut
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ATqu. </s>
                  <s>Q.E.D.
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                  </s>
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