Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/477.jpg" pagenum="449"/>
                <p type="main">
                  <s>Jungatur enim
                    <emph type="italics"/>
                  EO
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                  ſecans arcum Parabolicum
                    <emph type="italics"/>
                  ABC
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  Y,
                    <emph.end type="italics"/>
                  & aga­
                    <lb/>
                    <arrow.to.target n="note478"/>
                  tur
                    <foreign lang="grc">μ</foreign>
                    <emph type="italics"/>
                  X
                    <emph.end type="italics"/>
                  quæ tangat eundem arcum in vertice
                    <foreign lang="grc">μ</foreign>
                  & actæ
                    <emph type="italics"/>
                  EO
                    <emph.end type="italics"/>
                  occur­
                    <lb/>
                  rat in
                    <emph type="italics"/>
                  X
                    <emph.end type="italics"/>
                  ; & erit area curvilinea
                    <emph type="italics"/>
                  AEX
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                  ad aream curvilineam
                    <lb/>
                    <emph type="italics"/>
                  ACY
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC.
                    <emph.end type="italics"/>
                  Ideoque cum triangulum
                    <emph type="italics"/>
                  ASE
                    <emph.end type="italics"/>
                  ſit
                    <lb/>
                  ad triangulum
                    <emph type="italics"/>
                  ASC
                    <emph.end type="italics"/>
                  in eadem ratione, erit area tota
                    <emph type="italics"/>
                  ASEX
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                    <lb/>
                  ad aream totam
                    <emph type="italics"/>
                  ASCY
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC.
                    <emph.end type="italics"/>
                  Cum autem
                    <foreign lang="grc">ξ</foreign>
                    <emph type="italics"/>
                  O
                    <emph.end type="italics"/>
                    <lb/>
                  ſit ad
                    <emph type="italics"/>
                  SO
                    <emph.end type="italics"/>
                  ut 3 ad 1, &
                    <emph type="italics"/>
                  EO
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  XO
                    <emph.end type="italics"/>
                  in eadem ratione, erit
                    <emph type="italics"/>
                  SX
                    <emph.end type="italics"/>
                    <lb/>
                  ipſi
                    <emph type="italics"/>
                  EB
                    <emph.end type="italics"/>
                  parallela: & propterea ſi jungatur
                    <emph type="italics"/>
                  BX,
                    <emph.end type="italics"/>
                  erit triangulum
                    <lb/>
                    <emph type="italics"/>
                  SEB
                    <emph.end type="italics"/>
                  triangulo
                    <emph type="italics"/>
                  XEB
                    <emph.end type="italics"/>
                  æquale. </s>
                  <s>Unde ſi ad aream
                    <emph type="italics"/>
                  ASEX
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                    <lb/>
                  addatur triangulum
                    <emph type="italics"/>
                  EXB,
                    <emph.end type="italics"/>
                  & de ſumma auferatur triangulum
                    <lb/>
                    <emph type="italics"/>
                  SEB,
                    <emph.end type="italics"/>
                  manebit area
                    <emph type="italics"/>
                  ASBX
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                  areæ
                    <emph type="italics"/>
                  ASEX
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                  æqualis,
                    <lb/>
                  atque adeo ad aream
                    <emph type="italics"/>
                  ASCY
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC.
                    <emph.end type="italics"/>
                  Sed areæ
                    <lb/>
                    <emph type="italics"/>
                  ASBX
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                  æqualis eſt area
                    <emph type="italics"/>
                  ASBY
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                  quamproxime, & hæc
                    <lb/>
                  area
                    <emph type="italics"/>
                  ASBY
                    <foreign lang="grc">μ</foreign>
                  A
                    <emph.end type="italics"/>
                  eſt ad aream
                    <emph type="italics"/>
                  ASCY
                    <foreign lang="grc">μ</foreign>
                  A,
                    <emph.end type="italics"/>
                  ut tempus deſcripti
                    <lb/>
                  arcus
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad tempus deſcripti arcus totius
                    <emph type="italics"/>
                  AC.
                    <emph.end type="italics"/>
                  Ideoque
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                    <lb/>
                  eſt ad
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  in ratione temporum quamproxime.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note478"/>
                  LIBER
                    <lb/>
                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Ubi punctum
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  incidit in Parabolæ verticem
                    <foreign lang="grc">μ</foreign>
                  , eſt
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  in ratione temporum accurate. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Si jungatur
                    <foreign lang="grc">μξ</foreign>
                  ſecans
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  in
                    <foreign lang="grc">δ</foreign>
                  & in ea capiatur
                    <foreign lang="grc">ξ</foreign>
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  quæ ſit
                    <lb/>
                  ad
                    <foreign lang="grc">μ</foreign>
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  ut 27
                    <emph type="italics"/>
                  MI
                    <emph.end type="italics"/>
                  ad 16
                    <emph type="italics"/>
                  M
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  : acta
                    <emph type="italics"/>
                  Bn
                    <emph.end type="italics"/>
                  ſecabit chordam
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  in
                    <lb/>
                  ratione temporum magis accurate quam prius. </s>
                  <s>Jaceat autem
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  n
                    <emph.end type="italics"/>
                  ultra punctum
                    <foreign lang="grc">ξ</foreign>
                  , ſi punctum
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  magis diſtat a vertice
                    <lb/>
                  principali Parabolæ quam punctum
                    <foreign lang="grc">μ</foreign>
                  ; & citra, ſi minus diſtat ab
                    <lb/>
                  eodem vertice. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA IX.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Rectæ
                    <emph.end type="italics"/>
                  I
                    <foreign lang="grc">μ</foreign>
                  &
                    <foreign lang="grc">μ</foreign>
                  M
                    <emph type="italics"/>
                  & longitudo (AIC/4S
                    <foreign lang="grc">μ</foreign>
                  ) æquantur inter ſe.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam 4
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <foreign lang="grc">μ</foreign>
                  eſt latus rectum Parabolæ pertinens ad verti­
                    <lb/>
                  cem
                    <foreign lang="grc">μ</foreign>
                  . </s>
                </p>
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