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

Table of contents

< >
< >
page |< < (151) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div593" type="section" level="1" n="108">
          <pb o="151" file="0329" n="344" rhead=""/>
        </div>
        <div xml:id="echoid-div594" type="section" level="1" n="109">
          <head xml:id="echoid-head113" xml:space="preserve">_Theor_. IV.</head>
          <p>
            <s xml:id="echoid-s16546" xml:space="preserve">Quod ſi ponatur _m_ x TL = _n_ x arc BL , erit GL {_n_/} x BL {_m_/}
              <lb/>
            maximum, ſeu majus quàm γ λ {_n_/} x B λ {_m_/}.</s>
            <s xml:id="echoid-s16547" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div595" type="section" level="1" n="110">
          <head xml:id="echoid-head114" xml:space="preserve">_Theor_. V.</head>
          <p>
            <s xml:id="echoid-s16548" xml:space="preserve">Si fuerit TG x GL = DG LB, erit DG LB x GL maxi-
              <lb/>
            mum, ſeu majus quàm D γ λ B x γ λ.</s>
            <s xml:id="echoid-s16549" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div596" type="section" level="1" n="111">
          <head xml:id="echoid-head115" xml:space="preserve">_Theor_. VI.</head>
          <p>
            <s xml:id="echoid-s16550" xml:space="preserve">Sin TG x GL = 2 DG LB, erit GL x √ DG LB maxi-
              <lb/>
            mum, ſeu majus quàm γ λ x √ D γ λ B.</s>
            <s xml:id="echoid-s16551" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16552" xml:space="preserve">Haud difficili negotio, cum hæc demonſtrantur, tum ejuſmodi
              <lb/>
            complura deprehenduntur.</s>
            <s xml:id="echoid-s16553" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16554" xml:space="preserve">Ad illa verò ſuccinctius comprobanda deſervire poſſunt bujuſmodi
              <lb/>
            Tbeoremata.</s>
            <s xml:id="echoid-s16555" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16556" xml:space="preserve">Sint duæ curvæ AG B, DH C quarum communis axis AD ,
              <lb/>
              <note position="right" xlink:label="note-0329-01" xlink:href="note-0329-01a" xml:space="preserve">Fig. 225.</note>
            ſed ordinatæ inverſo ſitu increſcant ab A ad DB , decreſcant à D ad
              <lb/>
            AC ; </s>
            <s xml:id="echoid-s16557" xml:space="preserve">ad ordinatæ verò communis GE H terminos, recta GS cur-
              <lb/>
            vam AG B, & </s>
            <s xml:id="echoid-s16558" xml:space="preserve">recta HT curvam DH C contingant.</s>
            <s xml:id="echoid-s16559" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16560" xml:space="preserve">I. </s>
            <s xml:id="echoid-s16561" xml:space="preserve">Si recta HT rectæ GS parallela ſit, erit GE H maxima or-
              <lb/>
            dinatarum in continuum jacentium ſumma.</s>
            <s xml:id="echoid-s16562" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16563" xml:space="preserve">Nam utcunque ducta OK FL P ad GE H parallela (quæ Li-
              <lb/>
            neas ſecet ut cernis) erit GH = QP &</s>
            <s xml:id="echoid-s16564" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s16565" xml:space="preserve">KL .</s>
            <s xml:id="echoid-s16566" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16567" xml:space="preserve">Not. </s>
            <s xml:id="echoid-s16568" xml:space="preserve">Verum hoc, ſi curvarum partes concavæ axi obverſæ jaceant,
              <lb/>
            aliàs GE H erit minima.</s>
            <s xml:id="echoid-s16569" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16570" xml:space="preserve">II. </s>
            <s xml:id="echoid-s16571" xml:space="preserve">Si ES = ET, erit rectangulum ex EG , EH maximum:
              <lb/>
            </s>
            <s xml:id="echoid-s16572" xml:space="preserve">Nam ob SE. </s>
            <s xml:id="echoid-s16573" xml:space="preserve">SF :</s>
            <s xml:id="echoid-s16574" xml:space="preserve">: EG. </s>
            <s xml:id="echoid-s16575" xml:space="preserve">FO , & </s>
            <s xml:id="echoid-s16576" xml:space="preserve">TE. </s>
            <s xml:id="echoid-s16577" xml:space="preserve">TF :</s>
            <s xml:id="echoid-s16578" xml:space="preserve">: EH. </s>
            <s xml:id="echoid-s16579" xml:space="preserve">FP ; </s>
            <s xml:id="echoid-s16580" xml:space="preserve">erit
              <lb/>
            SE x TE. </s>
            <s xml:id="echoid-s16581" xml:space="preserve">SF x TF :</s>
            <s xml:id="echoid-s16582" xml:space="preserve">: EG x EH. </s>
            <s xml:id="echoid-s16583" xml:space="preserve">FO x FP, itaque cum ſit
              <lb/>
            SE x TE &</s>
            <s xml:id="echoid-s16584" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s16585" xml:space="preserve">SF x TF, erit EG x EH &</s>
            <s xml:id="echoid-s16586" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s16587" xml:space="preserve">FO x FP.</s>
            <s xml:id="echoid-s16588" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div598" type="section" level="1" n="112">
          <head xml:id="echoid-head116" xml:space="preserve">FINIS.</head>
        </div>
      </text>
    </echo>
Impressum