Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/063.jpg" pagenum="35"/>
                  eodem plano cum triangulo
                    <emph type="italics"/>
                  ASB.
                    <emph.end type="italics"/>
                  Junge
                    <emph type="italics"/>
                  SC
                    <emph.end type="italics"/>
                  ; & triangulum
                    <emph type="italics"/>
                  SBC,
                    <emph.end type="italics"/>
                    <lb/>
                  ob parallelas
                    <emph type="italics"/>
                  SB, Cc,
                    <emph.end type="italics"/>
                  æquale erit triangulo
                    <emph type="italics"/>
                  SBc,
                    <emph.end type="italics"/>
                  atque adeo etiam
                    <lb/>
                  triangulo
                    <emph type="italics"/>
                  SAB.
                    <emph.end type="italics"/>
                  Simili argumento ſi vis centripeta ſucceſſive agat
                    <lb/>
                  in
                    <emph type="italics"/>
                  C, D, E,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>faciens ut corpus ſingulis temporis particulis ſin­
                    <lb/>
                  gulas deſeribat rectas
                    <emph type="italics"/>
                  CD, DE, EF,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>jacebunt hæ omnes in
                    <lb/>
                  eodem plano; & triangulum
                    <emph type="italics"/>
                  SCD
                    <emph.end type="italics"/>
                  triangulo
                    <emph type="italics"/>
                  SBC,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SDE
                    <emph.end type="italics"/>
                  ipſi
                    <lb/>
                    <emph type="italics"/>
                  SCD,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SEF
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  SDE
                    <emph.end type="italics"/>
                  æquale erit. </s>
                  <s>Æqualibus igitur tempori­
                    <lb/>
                  bus æquales areæ in plano immoto deſcribuntur: & componendo,
                    <lb/>
                  ſunt arearum ſummæ quævis
                    <emph type="italics"/>
                  SADS, SAFS
                    <emph.end type="italics"/>
                  inter ſe, ut ſunt tem­
                    <lb/>
                  pora deſcriptionum. </s>
                  <s>Augeatur jam numerus & minuatur latitudo
                    <lb/>
                  triangulorum in infinitum; & eorum ultima perimeter
                    <emph type="italics"/>
                  ADF,
                    <emph.end type="italics"/>
                  (per
                    <lb/>
                  Corollarium quartum Lemmatis tertii) erit linea curva: adeoque vis
                    <lb/>
                  centripeta, qua corpus a tangente hujus curvæ perpetuo retrahitur,
                    <lb/>
                  aget indeſinenter; areæ vero quævis deſcriptæ
                    <emph type="italics"/>
                  SADS, SAFS
                    <emph.end type="italics"/>
                    <lb/>
                  temporibus deſcriptionum ſemper proportionales, erunt iiſdem tem­
                    <lb/>
                  poribus in hoc caſu proportionales.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Velocitas corporis in centrum immobile attracti eſt in
                    <lb/>
                  ſpatiis non reſiſtentibus reciproce ut perpendiculum a centro illo in
                    <lb/>
                  Orbis tangentem rectilineam demiſſum. </s>
                  <s>Eſt enim velocitas in locis
                    <lb/>
                  illis
                    <emph type="italics"/>
                  A, B, C, D, E,
                    <emph.end type="italics"/>
                  ut ſunt baſes æqualium triangulorum
                    <emph type="italics"/>
                  AB, BC,
                    <lb/>
                  CD, DE, EF
                    <emph.end type="italics"/>
                  ; & hæ baſes ſunt reciproce ut perpendicula in ipſas
                    <lb/>
                  demiſſa. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Si arcuum duorum æqualibus temporibus in ſpatiis non
                    <lb/>
                  reſiſtentibus ab eodem corpore ſucceſſive deſcriptorum chordæ
                    <emph type="italics"/>
                  AB,
                    <lb/>
                  BC
                    <emph.end type="italics"/>
                  compleantur in parallelogrammum
                    <emph type="italics"/>
                  ABCU,
                    <emph.end type="italics"/>
                  & hujus diagona­
                    <lb/>
                  lis
                    <emph type="italics"/>
                  BU
                    <emph.end type="italics"/>
                  in ea poſitione quam ultimo habet ubi arcus illi in infiNI­
                    <lb/>
                  tum diminuuntur, producatur utrinque; tranſibit eadem per cen­
                    <lb/>
                  trum virium. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Si arcuum æqualibus temporibus in ſpatiis non reſiſten­
                    <lb/>
                  tibus deſcriptorum chordæ
                    <emph type="italics"/>
                  AB, BC
                    <emph.end type="italics"/>
                  ac
                    <emph type="italics"/>
                  DE, EF
                    <emph.end type="italics"/>
                  compleantur in
                    <lb/>
                  parallelogramma
                    <emph type="italics"/>
                  ABCU, DEFZ
                    <emph.end type="italics"/>
                  ; vires in
                    <emph type="italics"/>
                  B
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  ſunt ad invi­
                    <lb/>
                  cem in ultima ratione diagonalium
                    <emph type="italics"/>
                  BU, EZ,
                    <emph.end type="italics"/>
                  ubi arcus iſti in infi­
                    <lb/>
                  nitum diminuuntur. </s>
                  <s>Nam corporis motus
                    <emph type="italics"/>
                  BC
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  componun­
                    <lb/>
                  tur (per Legum Corol. </s>
                  <s>1.) ex motibus
                    <emph type="italics"/>
                  Bc, BU
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Ef, EZ:
                    <emph.end type="italics"/>
                  at­
                    <lb/>
                  qui
                    <emph type="italics"/>
                  BU
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  EZ,
                    <emph.end type="italics"/>
                  ipſis
                    <emph type="italics"/>
                  Cc
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Ff
                    <emph.end type="italics"/>
                  æquales, in Demonſtratione Pro­
                    <lb/>
                  poſitionis hujus generabantur ab impulſibus vis centripetæ in B &
                    <lb/>
                    <emph type="italics"/>
                  E,
                    <emph.end type="italics"/>
                  ideoque ſunt his impulſibus proportionales. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Vires quibus corpora quælibet in ſpatiis non reſiſtenti­
                    <lb/>
                  bus a motibus rectilineis retrahuntur ac detorquentur in orbes cur­
                    <lb/>
                  vos ſunt inter ſe ut arcuum æqualibus temporibus deſcriptorum ſa­
                    <lb/>
                  gittæ illæ quæ convergunt ad centrum virium, & chordas biſecant </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
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    </archimedes>
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