Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/429.jpg" pagenum="401"/>
                  anguli
                    <emph type="italics"/>
                  CTp
                    <emph.end type="italics"/>
                  ad angulum
                    <emph type="italics"/>
                  CTP.
                    <emph.end type="italics"/>
                  Quæ quidem rationes ex ſinu­</s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note430"/>
                  bus angulorum contactus ac differentiarum angulorum facile colli­
                    <lb/>
                  guntur. </s>
                  <s>His autem inter ſe collatis, prodit curvatura Figuræ
                    <emph type="italics"/>
                  Cpa
                    <emph.end type="italics"/>
                    <lb/>
                  in
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  ad ipſius curvaturam in
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AT cub
                    <emph.end type="italics"/>
                  +(16824/100000)
                    <emph type="italics"/>
                  CTqXAT
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  CT cub
                    <emph.end type="italics"/>
                  +(16824/100000)
                    <emph type="italics"/>
                  ATqXCT.
                    <emph.end type="italics"/>
                  Ubi numerus (16824/100000) deſignat
                    <lb/>
                  differentiam quadratorum angulorum
                    <emph type="italics"/>
                  CTP
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CTp
                    <emph.end type="italics"/>
                  appli­
                    <lb/>
                  catam ad quadratum anguli minoris
                    <emph type="italics"/>
                  CTP,
                    <emph.end type="italics"/>
                  ſeu (quod per­
                    <lb/>
                  inde eſt) differentiam quadratorum temporum 27
                    <emph type="sup"/>
                  d.
                    <emph.end type="sup"/>
                  7
                    <emph type="sup"/>
                  h.
                    <emph.end type="sup"/>
                  43′, &
                    <lb/>
                  29
                    <emph type="sup"/>
                  d.
                    <emph.end type="sup"/>
                  12
                    <emph type="sup"/>
                  h.
                    <emph.end type="sup"/>
                  44′, applicatam ad quadratum temporis 27
                    <emph type="sup"/>
                  d.
                    <emph.end type="sup"/>
                  7
                    <emph type="sup"/>
                  h.
                    <emph.end type="sup"/>
                  43′, </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note430"/>
                  LIBER
                    <lb/>
                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>Igitur cum
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  deſignet Syzygiam Lunæ, &
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  ipſius Quadratu­
                    <lb/>
                  ram, proportio jam inventa eadem eſſe debet cum proportione
                    <lb/>
                  curvaturæ Orbis Lunæ in Syzygiis ad ejuſdem curvaturam in
                    <lb/>
                  Quadraturis, quam ſupra invenimus. </s>
                  <s>Proinde ut inveniatur pro­
                    <lb/>
                  portio
                    <emph type="italics"/>
                  CT
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AT,
                    <emph.end type="italics"/>
                  duco extrema & media in ſe invicem. </s>
                  <s>Et
                    <lb/>
                  termini prodeuntes ad
                    <emph type="italics"/>
                  ATXCT
                    <emph.end type="italics"/>
                  applicati, fiunt 2062, 79
                    <emph type="italics"/>
                  CTqq
                    <emph.end type="italics"/>
                    <lb/>
                  -2151969 NX
                    <emph type="italics"/>
                  CTcub
                    <emph.end type="italics"/>
                  +368676 NX
                    <emph type="italics"/>
                  ATXCTq
                    <emph.end type="italics"/>
                  +36342
                    <emph type="italics"/>
                  ATq
                    <lb/>
                  XCTq
                    <emph.end type="italics"/>
                  -362047 NX
                    <emph type="italics"/>
                  ATqXCT
                    <emph.end type="italics"/>
                  +2191371 NX
                    <emph type="italics"/>
                  AT cub
                    <emph.end type="italics"/>
                  +
                    <lb/>
                  4051, 4
                    <emph type="italics"/>
                  ATqq
                    <emph.end type="italics"/>
                  =0. Hic pro terminorum
                    <emph type="italics"/>
                  AT
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CT
                    <emph.end type="italics"/>
                  ſemiſum­
                    <lb/>
                  ma N ſcribo 1, & pro eorundem ſemidifferentia ponendo
                    <emph type="italics"/>
                  x,
                    <emph.end type="italics"/>
                  fit
                    <lb/>
                    <emph type="italics"/>
                  CT
                    <emph.end type="italics"/>
                  =1+
                    <emph type="italics"/>
                  x,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  AT
                    <emph.end type="italics"/>
                  =1-
                    <emph type="italics"/>
                  x
                    <emph.end type="italics"/>
                  : quibus in æquatione ſcriptis, &
                    <lb/>
                  æquatione prodeunte reſoluta, obtinetur
                    <emph type="italics"/>
                  x
                    <emph.end type="italics"/>
                  æqualis 0,00719, &
                    <lb/>
                  inde ſemidiameter
                    <emph type="italics"/>
                  CT
                    <emph.end type="italics"/>
                  fit 1,00719, & ſemidiameter
                    <emph type="italics"/>
                  AT
                    <emph.end type="italics"/>
                  0,99281,
                    <lb/>
                  qui numeri ſunt ut (70 1/24) & (69 1/24) quam proxime. </s>
                  <s>Eſt igitur di­
                    <lb/>
                  ſtantia Lunæ a Terra in Syzygiis ad ipſius diſtantiam in Quadra­
                    <lb/>
                  turis (ſepoſita ſcilicet Eccentricitatis conſideratione) ut (69 1/24) ad
                    <lb/>
                  (70 1/24), vel numeris rotundis ut 69 ad 70. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXIX. PROBLEMA X.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Invenire Variationem Lunæ.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Oritur hæc inæqualitas partim ex forma Elliptica orbis Luna­
                    <lb/>
                  ris, partim ex inæqualitate momentorum areæ, quam Luna radio
                    <lb/>
                  ad Terram ducto deſcribit. </s>
                  <s>Si Luna
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in Ellipſi
                    <emph type="italics"/>
                  DBCA
                    <emph.end type="italics"/>
                  circa
                    <lb/>
                  Terram in centro Ellipſeos quieſcentem moveretur, & radio
                    <emph type="italics"/>
                  TP
                    <emph.end type="italics"/>
                    <lb/>
                  ad Terram ducto deſcriberet aream
                    <emph type="italics"/>
                  CTP
                    <emph.end type="italics"/>
                  tempori proportiona­
                    <lb/>
                  lem; eſſet autem Ellipſeos ſemidiameter maxima
                    <emph type="italics"/>
                  CT
                    <emph.end type="italics"/>
                  ad ſemi­
                    <lb/>
                  diametrum minimam
                    <emph type="italics"/>
                  TA
                    <emph.end type="italics"/>
                  ut 70 ad 69: foret tangens anguli
                    <lb/>
                    <emph type="italics"/>
                  CTP
                    <emph.end type="italics"/>
                  ad tangentem anguli motus medii a Quadratura
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  compu­
                    <lb/>
                  tati, ut Ellipſeos ſemidiameter
                    <emph type="italics"/>
                  TA
                    <emph.end type="italics"/>
                  ad ejuſdem ſemidiametrum </s>
                </p>
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