Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Page concordance

< >
Scan Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/097.jpg" pagenum="69"/>
                  vertetur in geminas Rectas, quarum una eſt recta illa in quam pun­
                    <lb/>
                    <arrow.to.target n="note45"/>
                  ctum
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  incidit, & altera eſt recta qua alia duo ex punctis quatuor jun­
                    <lb/>
                  guntur. </s>
                  <s>Si Trapezii anguli duo oppoſiti ſimul ſumpti æquentur
                    <lb/>
                  duobus rectis, & lineæ quatuor
                    <emph type="italics"/>
                  PQ, PR, PS, PT
                    <emph.end type="italics"/>
                  ducantur ad
                    <lb/>
                  latera ejus vel perpendiculariter vel in angulis quibuſvis æqualibus,
                    <lb/>
                  ſitque rectangulum ſub duabus ductis
                    <emph type="italics"/>
                  PQXPR
                    <emph.end type="italics"/>
                  æquale rectangu­
                    <lb/>
                  lo ſub duabus aliis
                    <emph type="italics"/>
                  PSXPT,
                    <emph.end type="italics"/>
                  Sectio conica evadet Circulus. </s>
                  <s>Idem
                    <lb/>
                  fiet ſi lineæ quatuor ducantur in angulis quibuſvis & rectangulum
                    <lb/>
                  ſub duabus ductis
                    <emph type="italics"/>
                  PQXPR
                    <emph.end type="italics"/>
                  ſit ad rectangulum ſub aliis duabus
                    <lb/>
                    <emph type="italics"/>
                  PSXPT
                    <emph.end type="italics"/>
                  ut rectangulum ſub ſinubus angulorum
                    <emph type="italics"/>
                  S, T,
                    <emph.end type="italics"/>
                  in quibus
                    <lb/>
                  duæ ultimæ
                    <emph type="italics"/>
                  PS, PT
                    <emph.end type="italics"/>
                  ducuntur, ad rectangulum ſub ſinubus angu­
                    <lb/>
                  lorum
                    <emph type="italics"/>
                  Q, R,
                    <emph.end type="italics"/>
                  in quibus duæ primæ
                    <emph type="italics"/>
                  PQ, PR
                    <emph.end type="italics"/>
                  ducuntur. </s>
                  <s>Cæteris
                    <lb/>
                  in caſibus Locus puncti
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  erit aliqua trium figurarum quæ vulgo
                    <lb/>
                  nominantur Sectiones Conicæ. </s>
                  <s>Vice autem Trapezii
                    <emph type="italics"/>
                  ABCD
                    <emph.end type="italics"/>
                  ſub­
                    <lb/>
                  ſtitui poteſt Quadrilaterum cujus latera duo oppoſita ſe mutuo in­
                    <lb/>
                  ſtar diagonalium decuſſant. </s>
                  <s>Sed & e punctis quatuor
                    <emph type="italics"/>
                  A, B, C, D
                    <emph.end type="italics"/>
                    <lb/>
                  poſſunt unum vel duo abire ad infinitum, eoque pacto latera fi­
                    <lb/>
                  guræ quæ ad puncta illa convergunt, evadere parallela: quo in
                    <lb/>
                  caſu Sectio Conica tranſibit per cætera puncta, & in plagas paralle­
                    <lb/>
                  larum abibit in infinitum. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note45"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XIX.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Invenire
                    <expan abbr="punctũ">punctum</expan>
                    <emph.end type="italics"/>
                  P,
                    <emph type="italics"/>
                  a quo ſi rectæ
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.097.1.jpg" xlink:href="039/01/097/1.jpg" number="42"/>
                    <lb/>
                    <emph type="italics"/>
                  quatuor
                    <emph.end type="italics"/>
                  PQ, PR, PS, PT,
                    <lb/>
                    <emph type="italics"/>
                  ad alias totidem poſitione da
                    <lb/>
                  tas rectas
                    <emph.end type="italics"/>
                  AB, CD, AC, BD,
                    <lb/>
                    <emph type="italics"/>
                  ſingulæ ad ſingulas in datis
                    <lb/>
                  angulis ducantur,
                    <expan abbr="rectangulũ">rectangulum</expan>
                    <lb/>
                  ſub duabus ductis,
                    <emph.end type="italics"/>
                  PQXPR,
                    <lb/>
                    <emph type="italics"/>
                  ſit ad rectangulum ſub aliis
                    <lb/>
                  duabus,
                    <emph.end type="italics"/>
                  PSXPT,
                    <emph type="italics"/>
                  in data ra­
                    <lb/>
                  tione.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Lineæ
                    <emph type="italics"/>
                  AB, CD,
                    <emph.end type="italics"/>
                  ad quas rectæ duæ
                    <emph type="italics"/>
                  PQ, PR,
                    <emph.end type="italics"/>
                  unum rectan­
                    <lb/>
                  gulorum continentes ducuntur, conveniant cum aliis duabus poſi­
                    <lb/>
                  tione datis lineis in punctis
                    <emph type="italics"/>
                  A, B, C, D.
                    <emph.end type="italics"/>
                  Ab eorum aliquo
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  age
                    <lb/>
                  rectam quamlibet
                    <emph type="italics"/>
                  AH,
                    <emph.end type="italics"/>
                  in qua velis punctum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  reperiri. </s>
                  <s>Secet ea
                    <lb/>
                  lineas oppoſitas
                    <emph type="italics"/>
                  BD, CD,
                    <emph.end type="italics"/>
                  nimirum
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  H
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  I,
                    <emph.end type="italics"/>
                  & ob
                    <lb/>
                  datos omnes angulos figuræ, dabuntur rationes
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PA
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PA
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum