Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/272.jpg" pagenum="244"/>
                    <arrow.to.target n="note220"/>
                  Circulum ſemel deſcribere, deinde regulam interminatam
                    <emph type="italics"/>
                  CH
                    <emph.end type="italics"/>
                  ita ap­
                    <lb/>
                  plicare ad punctum
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  ut ejus pars
                    <emph type="italics"/>
                  FH,
                    <emph.end type="italics"/>
                  Circulo & rectæ
                    <emph type="italics"/>
                  FK
                    <emph.end type="italics"/>
                  interje­
                    <lb/>
                  cta, æqualis ſit ejus parti
                    <emph type="italics"/>
                  CE
                    <emph.end type="italics"/>
                  inter punctum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  & rectam
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  ſitæ. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note219"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note220"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Quæ de Hyperbolis dicta ſunt fa­
                    <lb/>
                    <figure id="id.039.01.272.1.jpg" xlink:href="039/01/272/1.jpg" number="159"/>
                    <lb/>
                  cile applicantur ad Parabolas. </s>
                  <s>Nam
                    <lb/>
                  ſi
                    <emph type="italics"/>
                  XAGK
                    <emph.end type="italics"/>
                  Parabolam deſignet quam
                    <lb/>
                  recta
                    <emph type="italics"/>
                  XV
                    <emph.end type="italics"/>
                  tangat in vertice
                    <emph type="italics"/>
                  X,
                    <emph.end type="italics"/>
                  ſintque
                    <lb/>
                  ordinatim applicatæ
                    <emph type="italics"/>
                  IA, VG
                    <emph.end type="italics"/>
                  ut quæ­
                    <lb/>
                  libet abſciſſarum
                    <emph type="italics"/>
                  XI, XV
                    <emph.end type="italics"/>
                  dignitates
                    <lb/>
                    <emph type="italics"/>
                  XI
                    <emph type="sup"/>
                  n
                    <emph.end type="sup"/>
                  , XV
                    <emph type="sup"/>
                  n
                    <emph.end type="sup"/>
                  ;
                    <emph.end type="italics"/>
                  agantur
                    <emph type="italics"/>
                  XT, GT, AH,
                    <emph.end type="italics"/>
                    <lb/>
                  quarum
                    <emph type="italics"/>
                  XT
                    <emph.end type="italics"/>
                  parallela ſit
                    <emph type="italics"/>
                  VG,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  GT,
                    <lb/>
                  AH
                    <emph.end type="italics"/>
                  Parabolam tangant in
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  A:
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  corpus de loco quovis
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  ſecundum
                    <lb/>
                  rectam
                    <emph type="italics"/>
                  AH
                    <emph.end type="italics"/>
                  productam, juſta cum
                    <lb/>
                  velocitate projectum, deſcribet hanc
                    <lb/>
                  Parabolam, ſi modo denſitas Medii,
                    <lb/>
                  in locis ſingulis
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  ſit reciproce ut
                    <lb/>
                  tangens
                    <emph type="italics"/>
                  GT.
                    <emph.end type="italics"/>
                  Velocitas autem in
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  ea erit quacum Projectile per­
                    <lb/>
                  geret, in ſpatio non reſiſtente, in Parabola Conica verticem
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  dia­
                    <lb/>
                  metrum
                    <emph type="italics"/>
                  VG
                    <emph.end type="italics"/>
                  deorſum productam, & latus rectum (
                    <emph type="italics"/>
                  2GTq./nn-nXVG
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  habente. </s>
                  <s>Et reſiſtentia in
                    <emph type="italics"/>
                  G
                    <emph.end type="italics"/>
                  erit ad vim gravitatis ut
                    <emph type="italics"/>
                  GT
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  (2nn-2n/n-2) VG.
                    <emph.end type="italics"/>
                  Unde ſi
                    <emph type="italics"/>
                  NAK
                    <emph.end type="italics"/>
                  lineam horizontalem deſignet, &
                    <lb/>
                  manente tum denſitate Medii in
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  tum velocitate quacum corpus
                    <lb/>
                  projicitur, mutetur utcunque angulus
                    <emph type="italics"/>
                  NAH;
                    <emph.end type="italics"/>
                  manebunt longitu­
                    <lb/>
                  dines
                    <emph type="italics"/>
                  AH, AI, HX,
                    <emph.end type="italics"/>
                  & inde datur Parabolæ vertex
                    <emph type="italics"/>
                  X,
                    <emph.end type="italics"/>
                  & poſitio
                    <lb/>
                  rectæ
                    <emph type="italics"/>
                  XI,
                    <emph.end type="italics"/>
                  & ſumendo
                    <emph type="italics"/>
                  VG
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  IA
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  XV
                    <emph type="sup"/>
                  n
                    <emph.end type="sup"/>
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  XI
                    <emph type="sup"/>
                  n
                    <emph.end type="sup"/>
                  ,
                    <emph.end type="italics"/>
                  dantur om­
                    <lb/>
                  nia Parabolæ puncta
                    <emph type="italics"/>
                  G,
                    <emph.end type="italics"/>
                  per quæ Projectile tranſibit. </s>
                </p>
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