Newton, Isaac, Philosophia naturalis principia mathematica, 1713
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/126.jpg" pagenum="98"/>
                    <arrow.to.target n="note74"/>
                  in vertice
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  ut 3 ad 8; adeoQ.E.I. ea etiam ratione eſt linea
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                    <lb/>
                  ad lineam rectam quam corpus tempore motus ſui ab
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  ea
                    <lb/>
                  cum velocitate quam habuit in vertice
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  deſcribere poſſet. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note74"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Hinc etiam vice verſa inveniri poteſt tempus quo cor­
                    <lb/>
                  pus deſcripſit arcum quemvis aſſignatum
                    <emph type="italics"/>
                  AP.
                    <emph.end type="italics"/>
                  Junge
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                  & ad
                    <lb/>
                  medium ejus punctum erige perpendiculum rectæ
                    <emph type="italics"/>
                  GH
                    <emph.end type="italics"/>
                  occur­
                    <lb/>
                  rens in
                    <emph type="italics"/>
                  H.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XXVIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Nulla extat Figura Ovalis cujus area, rectis pro lubitu abſciſſa, poſſit
                    <lb/>
                  per æquationes numero terminorum ac dimenſionum finitas genera­
                    <lb/>
                  liter inveniri.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Intra Ovalem detur punctum quodvis, circa quod ceu polum re­
                    <lb/>
                  volvatur perpetuo linea recta, uniformi cum motu, & interea in rec­
                    <lb/>
                  ta illa exeat punctum mobile de polo, pergatque ſemper ea cum
                    <lb/>
                  velocitate, quæ ſit ut rectæ illius intra Ovalem quadratum. </s>
                  <s>Hoc
                    <lb/>
                  motu punctum illud deſcribet Spiralem gyris infinitis. </s>
                  <s>Jam ſi areæ
                    <lb/>
                  Ovalis a recta illa abſciſſæ incrementum per finitam æquationem
                    <lb/>
                  inveniri poteſt, invenietur etiam per eandem æquationem diſtantia
                    <lb/>
                  puncti a polo, quæ huic areæ proportionalis eſt, adeoque om­
                    <lb/>
                  nia Spiralis puncta per æquationem finitam inveniri poſſunt: &
                    <lb/>
                  propterea rectæ cujuſvis poſitione datæ interſectio cum Spirali in­
                    <lb/>
                  veniri etiam poteſt per æquationem finitam. </s>
                  <s>Atqui recta omnis
                    <lb/>
                  infinite producta Spiralem ſecat in punctis numero infinitis, & æqua­
                    <lb/>
                  tio, qua interſectio aliqua duarum linearum invenitur, exhibet ea­
                    <lb/>
                  rum interſectiones omnes radicibus totidem, adeoque aſcendit ad
                    <lb/>
                  rot dimenſiones quot ſunt interſectiones. </s>
                  <s>Quoniam Circuli duo ſe
                    <lb/>
                  mutuo ſecant in punctis duobus, interſectio una non invenietur
                    <lb/>
                  niſi per æquationem duarum dimenſionum, qua interſectio altera
                    <lb/>
                  etiam inveniatur. </s>
                  <s>Quoniam duarum ſectionum Conicarum quatuor
                    <lb/>
                  eſſe poſſunt interſectiones, non poteſt aliqua earum generaliter in­
                    <lb/>
                  veniri niſi per æquationem quatuor dimenſionum, qua omnes ſi­
                    <lb/>
                  mul inveniantur. </s>
                  <s>Nam ſi interſectiones illæ ſeorſim quærantur, quo­
                    <lb/>
                  niam eadem eſt omnium lex & conditio, idem erit calculus in caſu
                    <lb/>
                  unoquoque & propterea eadem ſemper concluſio, quæ igitur de­
                    <lb/>
                  bet omnes interſectiones ſimul complecti & indifferenter exhibere. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum