Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Table of contents

< >
< >
page |< < (121) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div490" type="section" level="1" n="52">
          <pb o="121" file="0299" n="314" rhead=""/>
        </div>
        <div xml:id="echoid-div492" type="section" level="1" n="53">
          <head xml:id="echoid-head56" xml:space="preserve">APPENDICULA 3.</head>
          <p>
            <s xml:id="echoid-s14791" xml:space="preserve">Præcedentia recolenti nonnulla videntur elapſa; </s>
            <s xml:id="echoid-s14792" xml:space="preserve">quæ forſan ex uſu
              <lb/>
            ſit adjicere. </s>
            <s xml:id="echoid-s14793" xml:space="preserve">_Demònſtrationes_ elicere poterit quiſpiam è præmiſſis; </s>
            <s xml:id="echoid-s14794" xml:space="preserve">& </s>
            <s xml:id="echoid-s14795" xml:space="preserve">
              <lb/>
            potior inde fructus emerget.</s>
            <s xml:id="echoid-s14796" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div493" type="section" level="1" n="54">
          <head xml:id="echoid-head57" xml:space="preserve">Problema I.</head>
          <note position="right" xml:space="preserve">Fig. 180.</note>
          <p>
            <s xml:id="echoid-s14797" xml:space="preserve">Sit _curva_ quævis KEG, cujus _axis_ AD; </s>
            <s xml:id="echoid-s14798" xml:space="preserve">& </s>
            <s xml:id="echoid-s14799" xml:space="preserve">in hoc ſignatum
              <lb/>
            punctum A; </s>
            <s xml:id="echoid-s14800" xml:space="preserve">curva reperiatur, puta LMB, talis, ut ſi ductâ utcun-
              <lb/>
            que rectâ PEM axi ADperpendicularis curvam KEG ſecet in E, & </s>
            <s xml:id="echoid-s14801" xml:space="preserve">
              <lb/>
            curvam LMB in M; </s>
            <s xml:id="echoid-s14802" xml:space="preserve">nec non connectatur AE, & </s>
            <s xml:id="echoid-s14803" xml:space="preserve">curvam LMB
              <lb/>
            tangat recta TM; </s>
            <s xml:id="echoid-s14804" xml:space="preserve">ſit TMipſi AEparallela.</s>
            <s xml:id="echoid-s14805" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14806" xml:space="preserve">Hoc ità fiet. </s>
            <s xml:id="echoid-s14807" xml:space="preserve">Per aliquodcunque punctum R, in axe AD fumptum,
              <lb/>
            protendatur recta RZad ipſam ADperpendicularis; </s>
            <s xml:id="echoid-s14808" xml:space="preserve">cui occurrat re-
              <lb/>
            cta EAproducta in S; </s>
            <s xml:id="echoid-s14809" xml:space="preserve">& </s>
            <s xml:id="echoid-s14810" xml:space="preserve">in recta EPſumatur PY = RS; </s>
            <s xml:id="echoid-s14811" xml:space="preserve">ità de-
              <lb/>
            terminetur curvæ OYY proprietas; </s>
            <s xml:id="echoid-s14812" xml:space="preserve">tum ſit rectangulum ex AR, & </s>
            <s xml:id="echoid-s14813" xml:space="preserve">
              <lb/>
            PMæquale ſpatio AYYP(ſeu PM = {ſpat AYYP/AR}) habebit
              <lb/>
            curva LMMBconditionem propoſitam.</s>
            <s xml:id="echoid-s14814" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14815" xml:space="preserve">Adnotari poteft, ſi ſtantibus reliquis, ſit curva QXX talis, ut cum
              <lb/>
            hanc ſecet recta E Pin X, ſit PX = AS; </s>
            <s xml:id="echoid-s14816" xml:space="preserve">erit ſpatium AXXP
              <lb/>
            æqualerectangulo ex AR, & </s>
            <s xml:id="echoid-s14817" xml:space="preserve">curva LM, ſeu {AXXP/AR} = LM.</s>
            <s xml:id="echoid-s14818" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div494" type="section" level="1" n="55">
          <head xml:id="echoid-head58" xml:space="preserve">Exemp. I.</head>
          <p>
            <s xml:id="echoid-s14819" xml:space="preserve">Sit ADG _circuli_ quadrans, & </s>
            <s xml:id="echoid-s14820" xml:space="preserve">ductâ EPad ADutcunque per-
              <lb/>
            pendiculari, connexâque DE; </s>
            <s xml:id="echoid-s14821" xml:space="preserve">deſignetur curva AMB talis, ut ſi
              <lb/>
              <note position="right" xlink:label="note-0299-02" xlink:href="note-0299-02a" xml:space="preserve">Fig. 181.</note>
            producta recta EPM hanc ſecet in M, ipſamque tangat recta MT,
              <lb/>
            ſit MTad DEparallela. </s>
            <s xml:id="echoid-s14822" xml:space="preserve">Hocita peragetur. </s>
            <s xml:id="echoid-s14823" xml:space="preserve">Ducatur AZad DG
              <lb/>
            parallela; </s>
            <s xml:id="echoid-s14824" xml:space="preserve">& </s>
            <s xml:id="echoid-s14825" xml:space="preserve">huic occurrat producta DEin S, & </s>
            <s xml:id="echoid-s14826" xml:space="preserve">curva AYY talis
              <lb/>
            ſit, ut ſi hanc ſecet producta PEin Y, ſit PY = AS; </s>
            <s xml:id="echoid-s14827" xml:space="preserve">tum capiatur
              <lb/>
            PM = {Spat. </s>
            <s xml:id="echoid-s14828" xml:space="preserve">AYP/AD}; </s>
            <s xml:id="echoid-s14829" xml:space="preserve">factum erit.</s>
            <s xml:id="echoid-s14830" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14831" xml:space="preserve">Not. </s>
            <s xml:id="echoid-s14832" xml:space="preserve">Quòd ſi curva QXX talis ſit, ut PX = DS (vel ſi AQ
              <lb/>
            = AD, & </s>
            <s xml:id="echoid-s14833" xml:space="preserve">QXX ſit _byperbola_ angulo ADG comprehenſa) erit
              <lb/>
            curva AM x AD = ſpat. </s>
            <s xml:id="echoid-s14834" xml:space="preserve">AQX P.</s>
            <s xml:id="echoid-s14835" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum