Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/146.jpg" pagenum="118"/>
                    <arrow.to.target n="note94"/>
                  puncta
                    <emph type="italics"/>
                  b, c
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                  perpetuo tangunt; deque puncto
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  ad lineam
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  eri­
                    <lb/>
                  gatur perpendiculum
                    <emph type="italics"/>
                  Vad
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                  abſcindens areas curvilineas
                    <emph type="italics"/>
                  VDba,
                    <lb/>
                  VDcd,
                    <emph.end type="italics"/>
                  & erigantur etiam ordinatæ
                    <emph type="italics"/>
                  Ez, Ex:
                    <emph.end type="italics"/>
                  quoniam rectan­
                    <lb/>
                  gulum
                    <emph type="italics"/>
                  DbXIN
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  DbzE
                    <emph.end type="italics"/>
                  æquale eſt dimidio rectanguli
                    <lb/>
                  AX
                    <emph type="italics"/>
                  KN,
                    <emph.end type="italics"/>
                  ſeu triangulo
                    <emph type="italics"/>
                  ICK
                    <emph.end type="italics"/>
                  ; & rectangulum
                    <emph type="italics"/>
                  DcXIN
                    <emph.end type="italics"/>
                  ſeu
                    <lb/>
                    <emph type="italics"/>
                  DcxE
                    <emph.end type="italics"/>
                  æquale eſt dimidio rectanguli
                    <emph type="italics"/>
                  YXXXC,
                    <emph.end type="italics"/>
                  ſeu triangulo
                    <lb/>
                    <emph type="italics"/>
                  XCY;
                    <emph.end type="italics"/>
                  hoc eſt, quoniam arearum
                    <emph type="italics"/>
                  VDba, VIC
                    <emph.end type="italics"/>
                  æquales ſemper
                    <lb/>
                  ſunt naſcentes particulæ
                    <emph type="italics"/>
                  DbzE, ICK,
                    <emph.end type="italics"/>
                  & arearum
                    <emph type="italics"/>
                  VDcd,
                    <lb/>
                  VCX
                    <emph.end type="italics"/>
                  æquales ſemper ſunt naſcentes particulæ
                    <emph type="italics"/>
                  DcxE, XCY,
                    <emph.end type="italics"/>
                    <lb/>
                  erit area genita
                    <emph type="italics"/>
                  VDba
                    <emph.end type="italics"/>
                  æqualis areæ genitæ
                    <emph type="italics"/>
                  VIC,
                    <emph.end type="italics"/>
                  adeoque tem­
                    <lb/>
                  pori proportionalis, & area genita
                    <emph type="italics"/>
                  VDcd
                    <emph.end type="italics"/>
                  æqualis Sectori ge­
                    <lb/>
                  nito
                    <emph type="italics"/>
                  VCX.
                    <emph.end type="italics"/>
                  Dato igitur tempore quovis ex quo corpus diſceſ­
                    <lb/>
                  ſit de loco
                    <emph type="italics"/>
                  V,
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                  dabitur area ipſi proportionalis
                    <emph type="italics"/>
                  VDba,
                    <emph.end type="italics"/>
                  & inde
                    <lb/>
                  dabitur corporis altitudo
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  CI
                    <emph.end type="italics"/>
                  ; & area
                    <emph type="italics"/>
                  VDcd,
                    <emph.end type="italics"/>
                  eique
                    <lb/>
                  æqualis Sector
                    <emph type="italics"/>
                  VCX
                    <emph.end type="italics"/>
                  una cum ejus angulo
                    <emph type="italics"/>
                  VCI.
                    <emph.end type="italics"/>
                  Datis autem
                    <lb/>
                  angulo
                    <emph type="italics"/>
                  VCI
                    <emph.end type="italics"/>
                  & altitudine
                    <emph type="italics"/>
                  CI
                    <emph.end type="italics"/>
                  datur locus
                    <emph type="italics"/>
                  I,
                    <emph.end type="italics"/>
                  in quo corpus com­
                    <lb/>
                  pleto illo tempore reperietur.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note94"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc maximæ minimæque corporum altitudines, id eſt
                    <lb/>
                  Apſides Trajectoriarum expedite inveniri poſſunt. </s>
                  <s>Sunt enim
                    <lb/>
                  Apſides puncta illa in quibus recta
                    <emph type="italics"/>
                  IC
                    <emph.end type="italics"/>
                  per centrum ducta incidit
                    <lb/>
                  perpendiculariter in Trajectoriam
                    <emph type="italics"/>
                  VIK:
                    <emph.end type="italics"/>
                  id quod ſit ubi rectæ
                    <emph type="italics"/>
                  IK
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  NK
                    <emph.end type="italics"/>
                  æquantur, adeoque ubi area
                    <emph type="italics"/>
                  ABFD
                    <emph.end type="italics"/>
                  æqualis eſt ZZ. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Sed & angulus
                    <emph type="italics"/>
                  KIN,
                    <emph.end type="italics"/>
                  in quo Trajectoria alibi ſecat
                    <lb/>
                  lineam illam
                    <emph type="italics"/>
                  IC,
                    <emph.end type="italics"/>
                  ex data corporis altitudine
                    <emph type="italics"/>
                  IC
                    <emph.end type="italics"/>
                  expedite inveNI­
                    <lb/>
                  tur; nimirum capiendo ſinum ejus ad radium ut
                    <emph type="italics"/>
                  KN
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  IK,
                    <emph.end type="italics"/>
                  id
                    <lb/>
                  eſt, ut Z ad latus quadratum areæ
                    <emph type="italics"/>
                  ABFD.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Si centro
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  & vertice principali
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  deſcribatur Sectio quæ­
                    <lb/>
                  libet Conica
                    <emph type="italics"/>
                  VRS,
                    <emph.end type="italics"/>
                  & a quovis ejus puncto
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  agatur Tangens
                    <emph type="italics"/>
                  RT
                    <emph.end type="italics"/>
                    <lb/>
                  occurrens axi infinite producto
                    <emph type="italics"/>
                  CV
                    <emph.end type="italics"/>
                  in puncto
                    <emph type="italics"/>
                  T;
                    <emph.end type="italics"/>
                  dein juncta
                    <emph type="italics"/>
                  CR
                    <emph.end type="italics"/>
                    <lb/>
                  ducatur recta
                    <emph type="italics"/>
                  CP,
                    <emph.end type="italics"/>
                  quæ æqualis ſit abſciſſæ
                    <emph type="italics"/>
                  CT,
                    <emph.end type="italics"/>
                  angulumque
                    <emph type="italics"/>
                  VCP
                    <emph.end type="italics"/>
                    <lb/>
                  Sectori
                    <emph type="italics"/>
                  VCR
                    <emph.end type="italics"/>
                  proportionalem conſtituat; tendat autem ad centrum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                    <lb/>
                  Vis centripeta Cubo diſtantiæ loeorum a centro reciproce propor­
                    <lb/>
                  tionalis, & exeat corpus de loco
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  juſta cum Velocitate ſecundum
                    <lb/>
                  lineam rectæ
                    <emph type="italics"/>
                  CV
                    <emph.end type="italics"/>
                  perpendicularem: progredietur corpus illud in
                    <lb/>
                  Trajectoria quam punctum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  perpetuo tangit; adeoque ſi Conica
                    <lb/>
                  ſectio
                    <emph type="italics"/>
                  CVRS
                    <emph.end type="italics"/>
                  Hyperbola ſit, deſcendet idem ad centrum: Sin
                    <lb/>
                  ea Ellipſis ſit, aſcendet illud perpetuo & abibit in infinitum. </s>
                  <s>Et con­
                    <lb/>
                  tra, ſi corpus quacunque cum Velocitate exeat de loco
                    <emph type="italics"/>
                  V,
                    <emph.end type="italics"/>
                  & perin­
                    <lb/>
                  de ut incæperit vel obliQ.E.D.ſcendere ad centrum, vel ab eo ob-</s>
                </p>
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