Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

< >
[Figure 81]
[Figure 82]
[Figure 83]
[Figure 84]
[Figure 85]
[Figure 86]
[Figure 87]
[Figure 88]
[Figure 89]
[Figure 90]
[Figure 91]
[Figure 92]
[Figure 93]
[Figure 94]
[Figure 95]
[Figure 96]
[Figure 97]
[Figure 98]
[Figure 99]
[Figure 100]
[Figure 101]
[Figure 102]
[Figure 103]
[Figure 104]
[Figure 105]
[Figure 106]
[Figure 107]
[Figure 108]
[Figure 109]
[Figure 110]
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/185.jpg" pagenum="157"/>
                  eædem a viribus acceleratricibus ad alia corpora tendentibus, aut
                    <lb/>
                    <arrow.to.target n="note133"/>
                  non urgentur niſi leviſſime, aut urgentur æqualiter & ſecundum li­
                    <lb/>
                  neas parallelas quamproxime. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note133"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXVI. THEOREMA XXVI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Corpora tria, quorum Vires decreſcunt in duplicata ratione di­
                    <lb/>
                  ſtantiarum, ſe mutuo trahant, & attractiones acceleratrices bi­
                    <lb/>
                  norum quorumcunQ.E.I. tertium ſint inter ſe reciproce ut qua­
                    <lb/>
                  drata diſtantiarum; minora autem circa maximum revolvan­
                    <lb/>
                  tur: Dico quod interius circa intimum & maximum, radiis
                    <lb/>
                  ad ipſum ductis, deſcribet areas temporibus magis proportio­
                    <lb/>
                  nales, & Figuram ad formam Ellipſeos umbilicum in concur­
                    <lb/>
                  ſu radiorum habentis magis accedentem, ſi corpus maximum
                    <lb/>
                  his attractionibus agitetur, quam ſi maximum illud vel a mi­
                    <lb/>
                  noribus non attractum quieſcat, vel multo minus vel multo ma­
                    <lb/>
                  gis attractum aut multo minus aut multo magis agitetur.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Liquet fere ex demonſtratione Corollarii ſecundi Propoſitionis
                    <lb/>
                  præcedentis; ſed argumento magis diſtincto & latius cogente ſic
                    <lb/>
                  evincitur. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  1. Revolvantur
                    <lb/>
                    <figure id="id.039.01.185.1.jpg" xlink:href="039/01/185/1.jpg" number="107"/>
                    <lb/>
                  corpora minora
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <lb/>
                  in eodem plano circa
                    <lb/>
                  maximum
                    <emph type="italics"/>
                  T,
                    <emph.end type="italics"/>
                  quorum
                    <lb/>
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  deſcribat Orbem in­
                    <lb/>
                  teriorem
                    <emph type="italics"/>
                  PAB,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                    <lb/>
                  exteriorem
                    <emph type="italics"/>
                  SE.
                    <emph.end type="italics"/>
                  Sit
                    <lb/>
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                  mediocris diſtan­
                    <lb/>
                  tia corporum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  & corporis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  verſus
                    <lb/>
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  attractio acceleratrix in mediocri illa diſtantia exponatur per e­
                    <lb/>
                  andem. </s>
                  <s>In duplicata ratione
                    <emph type="italics"/>
                  SK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  capiatur
                    <emph type="italics"/>
                  SL
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SK,
                    <emph.end type="italics"/>
                  & e­
                    <lb/>
                  rit
                    <emph type="italics"/>
                  SL
                    <emph.end type="italics"/>
                  attractio acceleratrix corporis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  verſus
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  in diſtantia quavis
                    <lb/>
                    <emph type="italics"/>
                  SP.
                    <emph.end type="italics"/>
                  Junge
                    <emph type="italics"/>
                  PT,
                    <emph.end type="italics"/>
                  eique parallelam age
                    <emph type="italics"/>
                  LM
                    <emph.end type="italics"/>
                  occurrentem
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  M,
                    <emph.end type="italics"/>
                    <lb/>
                  & attractio
                    <emph type="italics"/>
                  SL
                    <emph.end type="italics"/>
                  reſolvetur (per Legum Corol 2.) in attractiones
                    <lb/>
                    <emph type="italics"/>
                  SM, LM.
                    <emph.end type="italics"/>
                  Et ſic urgebitur corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  vi acceleratrice triplici: </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>