Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Page concordance

< >
Scan Original
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/099.jpg" pagenum="71"/>
                    <arrow.to.target n="note47"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note47"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XX.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Parallelogrammum quodvis
                    <emph.end type="italics"/>
                  ASPQ
                    <emph type="italics"/>
                  angulis duobus oppoſitis
                    <emph.end type="italics"/>
                  A
                    <emph type="italics"/>
                  &
                    <emph.end type="italics"/>
                    <lb/>
                  P
                    <emph type="italics"/>
                  tangit ſectionem quamvis Conicam in punctis
                    <emph.end type="italics"/>
                  A
                    <emph type="italics"/>
                  &
                    <emph.end type="italics"/>
                  P;
                    <emph type="italics"/>
                  &, lateri­
                    <lb/>
                  bus unius angulorum illorum infinite productis
                    <emph.end type="italics"/>
                  AQ, AS,
                    <emph type="italics"/>
                  occurrit
                    <lb/>
                  eidem ſectioni Conicæ in
                    <emph.end type="italics"/>
                  B
                    <emph type="italics"/>
                  &
                    <emph.end type="italics"/>
                  C;
                    <emph type="italics"/>
                  a punctis autem occurſuum
                    <emph.end type="italics"/>
                  B
                    <emph type="italics"/>
                  &
                    <emph.end type="italics"/>
                    <lb/>
                  C
                    <emph type="italics"/>
                  ad quintum quodvis ſectionis Conicæ punctum
                    <emph.end type="italics"/>
                  D
                    <emph type="italics"/>
                  agantur rec­
                    <lb/>
                  tæ duæ
                    <emph.end type="italics"/>
                  BD, CD
                    <emph type="italics"/>
                  occurrentes alteris duobus infinite productis pa­
                    <lb/>
                  rallelogrammi lateribus
                    <emph.end type="italics"/>
                  PS, PQ
                    <emph type="italics"/>
                  in
                    <emph.end type="italics"/>
                  T
                    <emph type="italics"/>
                  &
                    <emph.end type="italics"/>
                  R:
                    <emph type="italics"/>
                  erunt ſemper abſciſſæ
                    <lb/>
                  laterum partes
                    <emph.end type="italics"/>
                  PR
                    <emph type="italics"/>
                  &
                    <emph.end type="italics"/>
                  PT
                    <emph type="italics"/>
                  adinvicem in data ratione. </s>
                  <s>Et contra, ſi
                    <lb/>
                  partes illæ abſciſſæ ſunt ad invicem in data ratione, punctum
                    <emph.end type="italics"/>
                  D
                    <emph type="italics"/>
                  tan­
                    <lb/>
                  get Sectionem Conicam per puncta quatuor
                    <emph.end type="italics"/>
                  A, B, C, P
                    <emph type="italics"/>
                  tranſeuntem.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  1. Jungantur
                    <emph type="italics"/>
                  BP, CP
                    <emph.end type="italics"/>
                  & a puncto
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  agantur rectæ duæ
                    <lb/>
                    <emph type="italics"/>
                  DG, DE,
                    <emph.end type="italics"/>
                  quarum prior
                    <lb/>
                    <figure id="id.039.01.099.1.jpg" xlink:href="039/01/099/1.jpg" number="45"/>
                    <lb/>
                    <emph type="italics"/>
                  DG
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  parallela ſit &
                    <lb/>
                  occurrat
                    <emph type="italics"/>
                  PB, PQ, CA
                    <emph.end type="italics"/>
                  in
                    <lb/>
                    <emph type="italics"/>
                  H, I, G
                    <emph.end type="italics"/>
                  ; altera
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  paral­
                    <lb/>
                  lela ſit ipfi
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  & occurrat
                    <lb/>
                    <emph type="italics"/>
                  PC, PS, AB
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  F, K, E:
                    <emph.end type="italics"/>
                    <lb/>
                  & erit (per Lemma XVII.) re­
                    <lb/>
                  ctangulum
                    <emph type="italics"/>
                  DEXDF
                    <emph.end type="italics"/>
                  ad re­
                    <lb/>
                  ctangulum
                    <emph type="italics"/>
                  DGXDH
                    <emph.end type="italics"/>
                  in ra­
                    <lb/>
                  tione data. </s>
                  <s>Sed eſt
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  (ſeu
                    <emph type="italics"/>
                  IQ
                    <emph.end type="italics"/>
                  ) ut
                    <emph type="italics"/>
                  PB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  HB,
                    <emph.end type="italics"/>
                    <lb/>
                  adeoque ut
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DH
                    <emph.end type="italics"/>
                  ; &
                    <lb/>
                  viciſſim
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DH.
                    <emph.end type="italics"/>
                  Eſt &
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  RC
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  DC,
                    <emph.end type="italics"/>
                  adeoque ut (
                    <emph type="italics"/>
                  IG
                    <emph.end type="italics"/>
                  vel)
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DG,
                    <emph.end type="italics"/>
                  & viciſſim
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                    <lb/>
                  ut
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DG
                    <emph.end type="italics"/>
                  ; & conjunctis rationibus fit rectangulum
                    <emph type="italics"/>
                  PQXPR
                    <emph.end type="italics"/>
                    <lb/>
                  ad rectangulum
                    <emph type="italics"/>
                  PSXPT
                    <emph.end type="italics"/>
                  ut rectangulum
                    <emph type="italics"/>
                  DEXDF
                    <emph.end type="italics"/>
                  ad rectan­
                    <lb/>
                  gulum
                    <emph type="italics"/>
                  DGXDH,
                    <emph.end type="italics"/>
                  atque adeo in data ratione. </s>
                  <s>Sed dantur
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  & propterea ratio
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  datur.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Quod ſi
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ponantur in data ratione ad invi­
                    <lb/>
                  cem, tum ſimili ratiocinio regrediendo, ſequetur eſſe rectangulum
                    <lb/>
                    <emph type="italics"/>
                  DEXDF
                    <emph.end type="italics"/>
                  ad rectangulum
                    <emph type="italics"/>
                  DGXDH
                    <emph.end type="italics"/>
                  in ratione data, adeoque
                    <lb/>
                  punctum
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  (per Lemma XVIII.) contingere Conicam ſectionem
                    <lb/>
                  tranſeuntem per puncta
                    <emph type="italics"/>
                  A, B, C, P. Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum