Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/131.jpg" pagenum="103"/>
                  noſcatur quantitas areæ abſcindendæ tempori proportionalis. </s>
                  <s>Sit ea
                    <lb/>
                    <arrow.to.target n="note79"/>
                  A, & fiat conjectura de poſitione rectæ
                    <emph type="italics"/>
                  SP,
                    <emph.end type="italics"/>
                  quæ aream
                    <emph type="italics"/>
                  APS
                    <emph.end type="italics"/>
                    <lb/>
                  abſcindat veræ proximam. </s>
                  <s>Jun­
                    <lb/>
                    <figure id="id.039.01.131.1.jpg" xlink:href="039/01/131/1.jpg" number="77"/>
                    <lb/>
                  gatur
                    <emph type="italics"/>
                  OP,
                    <emph.end type="italics"/>
                  & ab
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  Aſymptoton agantur
                    <emph type="italics"/>
                  AI, PK
                    <emph.end type="italics"/>
                    <lb/>
                  Aſymptoto alteri parallelæ, & per
                    <lb/>
                  Tabulam Logarithmorum dabi­
                    <lb/>
                  tur Area
                    <emph type="italics"/>
                  AIKP,
                    <emph.end type="italics"/>
                  eique æqualis
                    <lb/>
                  area
                    <emph type="italics"/>
                  OPA,
                    <emph.end type="italics"/>
                  quæ ſubducta de tri­
                    <lb/>
                  angulo
                    <emph type="italics"/>
                  OPS
                    <emph.end type="italics"/>
                  relinquet aream ab­
                    <lb/>
                  ſciſſam
                    <emph type="italics"/>
                  APS.
                    <emph.end type="italics"/>
                  Applicando areæ
                    <lb/>
                  abſcindendæ A & abſciſſæ
                    <emph type="italics"/>
                  APS
                    <emph.end type="italics"/>
                    <lb/>
                  differentiam duplam 2
                    <emph type="italics"/>
                  APS
                    <emph.end type="italics"/>
                  -2 A
                    <lb/>
                  vel 2 A-2
                    <emph type="italics"/>
                  APS
                    <emph.end type="italics"/>
                  ad lineam
                    <emph type="italics"/>
                  SN,
                    <emph.end type="italics"/>
                  quæ ab umbilico
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  in tangentem
                    <lb/>
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  perpendicularis eſt, orietur longitudo chordæ
                    <emph type="italics"/>
                    <expan abbr="Pq.">Pque</expan>
                    <emph.end type="italics"/>
                  Inſcri­
                    <lb/>
                  batur autem chorda illa
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  inter
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ſi area abſciſſa
                    <emph type="italics"/>
                  APS
                    <emph.end type="italics"/>
                    <lb/>
                  major ſit area abſcindenda A, ſecus ad puncti
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  contrarias partes:
                    <lb/>
                  & punctum
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  erit locus corporis accuratior. </s>
                  <s>Et computatione
                    <lb/>
                  repetita invenietur idem accuratior in perpetuum. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note79"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>Atque his calculis Problema generaliter confit Analytice. </s>
                  <s>Ve­
                    <lb/>
                  rum uſibus Aſtronomicis accommodatior eſt calculus particularis
                    <lb/>
                  qui ſequitur. </s>
                  <s>Exiſtentibus
                    <emph type="italics"/>
                  AO, OB, OD
                    <emph.end type="italics"/>
                  ſemiaxibus Ellipſeos, &
                    <lb/>
                  L ipſius latere recto, ac D differentia inter ſemiaxem minorem
                    <emph type="italics"/>
                  OD
                    <emph.end type="italics"/>
                    <lb/>
                  & lateris recti ſemiſſem 1/2 L; quære tum angulum Y, cujus ſinus
                    <lb/>
                  ſit ad Radium ut eſt rectangu­
                    <lb/>
                    <figure id="id.039.01.131.2.jpg" xlink:href="039/01/131/2.jpg" number="78"/>
                    <lb/>
                  lum ſub differentia illa D, &
                    <lb/>
                  ſemiſumma axium
                    <emph type="italics"/>
                  AO+OD
                    <emph.end type="italics"/>
                    <lb/>
                  ad quadratum axis majoris
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  tum angulum Z, cujus ſinus
                    <lb/>
                  ſit ad Radium ut eſt duplum
                    <lb/>
                  rectangulum ſub umbilieorum
                    <lb/>
                  diſtantia
                    <emph type="italics"/>
                  SH
                    <emph.end type="italics"/>
                  & differentia
                    <lb/>
                  illa D ad triplum quadratum
                    <lb/>
                  ſemiaxis majoris
                    <emph type="italics"/>
                  AO.
                    <emph.end type="italics"/>
                  His
                    <lb/>
                  angulis ſemel inventis; locus corporis ſic deinceps determinabitur. </s>
                  <s>
                    <lb/>
                  Sume angulum T proportionalem tempori quo arcus
                    <emph type="italics"/>
                  BP
                    <emph.end type="italics"/>
                  deſcrip­
                    <lb/>
                  tus eſt, ſcu motui medio (ut loquuntur) æqualem; & angulum
                    <lb/>
                  V (primam medii motus æquationem) ad angulum Y (æquatio­
                    <lb/>
                  nem maximam primam) ut eſt ſinus dupli anguli T ad Radium; </s>
                </p>
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