Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
101
101 		102
102
103
103 		104
104
105
105 		106
106
107
107 		108
108
109
109 		110
110
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <pb xlink:href="039/01/109.jpg" pagenum="81"/>
                <p type="main">
                  <s>Dico præterea quod ſi recta aliqua tangat lineam curvam in fi­
                    <lb/>
                    <arrow.to.target n="note57"/>
                  gura prima; hæc recta eodem modo cum curva in figuram novam
                    <lb/>
                  tranſlata tanget lineam illam curvam in figura nova: & contra. </s>
                  <s>Nam
                    <lb/>
                  ſi Curvæ puncta quævis duo accedunt ad invicem & coeunt in fi­
                    <lb/>
                  gura prima, puncta eadem tranſlata accedent ad invicem & coibunt
                    <lb/>
                  in figura nova, atque adeo rectæ, quibus hæc puncta junguntur, ſi­
                    <lb/>
                  mul evadent curvarum tangentes in figura utraque. </s>
                  <s>Componi poſ­
                    <lb/>
                  ſent harum aſſertionum Demonſtrationes more magis Geometrico. </s>
                  <s>
                    <lb/>
                  Sed brevitati conſulo. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note57"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>Igitur ſi figura rectilinea in aliam tranſmutanda eſt, ſufficit rec­
                    <lb/>
                  tarum a quibus conflatur interſectiones transferre, & per eaſdem
                    <lb/>
                  in figura nova lineas rectas ducere. </s>
                  <s>Sin curvilineam tranſmutare
                    <lb/>
                  oportet, transferenda ſunt puncta, tangentes & aliæ rectæ quarum
                    <lb/>
                  ope curva linea definitur. </s>
                  <s>Inſervit autem hoc Lemma ſolutioni
                    <lb/>
                  difficiliorum Problematum, tranſmutando figuras propoſitas in ſim­
                    <lb/>
                  pliciores. </s>
                  <s>Nam rectæ quævis convergentes tranſmutantur in pa­
                    <lb/>
                  rallelas, adhibendo pro radio ordinato primo, lineam quam­
                    <lb/>
                  vis rectam quæ per concurſum convergentium tranſit: id adeo quia
                    <lb/>
                  concurſus ille hoc pacto abit in infinitum, lineæ autem parallelæ
                    <lb/>
                  ſunt quæ ad punctum infinite diſtans tendunt. </s>
                  <s>Poſtquam autem
                    <lb/>
                  Problema ſolvitur in figura nova, ſi per inverſas operationes tranſ­
                    <lb/>
                  mutetur hæc figura in figuram primam, habebitur ſolutio quæſita. </s>
                </p>
                <p type="main">
                  <s>Utile eſt etiam hoc Lemma in ſolutione Solidorum Problema­
                    <lb/>
                  tum. </s>
                  <s>Nam quoties duæ ſectiones Conicæ obvenerint, quarum in­
                    <lb/>
                  terſectione Problema ſolvi poteſt, tranſmutare licet earum alter­
                    <lb/>
                  utram, ſi Hyperbola ſit vel Parabola, in Ellipſin: deinde Ellipſis
                    <lb/>
                  facile mutatur in Circulum. </s>
                  <s>Recta item & ſectio Conica, in con­
                    <lb/>
                  ſtructione Planorum Problematum, vertuntur in Rectam & Cir­
                    <lb/>
                  culum. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXV. PROBLEMA XVII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Trajectoriam deſcribere qua per data duo puncta tranſibit & rectas
                    <lb/>
                  tres continget poſitione datas.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Per concurſum tangentium quarumvis duarum cum ſe invicem, &
                    <lb/>
                  concurſum tangentis tertiæ cum recta illa, quæ per puncta duo data
                    <lb/>
                  tranſit, age rectam infinitam; eaque adhibita pro radio ordinato pri­
                    <lb/>
                  mo, tranſmutetur figura, per Lemma ſuperius, in figuram novam. </s>
                  <s>In </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum