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

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        <div xml:id="echoid-div516" type="section" level="1" n="66">
          <p>
            <s xml:id="echoid-s15070" xml:space="preserve">
              <pb o="127" file="0305" n="320" rhead=""/>
            rallelâ, ſit rectangulum ex PM, PZ æquale quadrato ex CL (vel
              <lb/>
            PZ = {CL q/PM}). </s>
            <s xml:id="echoid-s15071" xml:space="preserve">Sit tum arc. </s>
            <s xml:id="echoid-s15072" xml:space="preserve">LX = {ſpat. </s>
            <s xml:id="echoid-s15073" xml:space="preserve">DKZP/CL} (vel ſector
              <lb/>
            LCX ſubduplw
              <unsure/>
            s ſpatii DKZP) & </s>
            <s xml:id="echoid-s15074" xml:space="preserve">in CX capiatur C μ = PM;
              <lb/>
            </s>
            <s xml:id="echoid-s15075" xml:space="preserve">erit linea βμμ ipſius BMA involuta; </s>
            <s xml:id="echoid-s15076" xml:space="preserve">vel ſpatium Cμβ ſpatii
              <lb/>
            ADB.)</s>
            <s xml:id="echoid-s15077" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15078" xml:space="preserve">_Exemp_. </s>
            <s xml:id="echoid-s15079" xml:space="preserve">Sit ADB circuli quadrans; </s>
            <s xml:id="echoid-s15080" xml:space="preserve">erit ergò (quod è præmonſtra-
              <lb/>
            tis conſtat) ſpat. </s>
            <s xml:id="echoid-s15081" xml:space="preserve">DKZP (2 ſector LCX). </s>
            <s xml:id="echoid-s15082" xml:space="preserve">ſect. </s>
            <s xml:id="echoid-s15083" xml:space="preserve">BDM
              <lb/>
            :</s>
            <s xml:id="echoid-s15084" xml:space="preserve">: CLq. </s>
            <s xml:id="echoid-s15085" xml:space="preserve">DBq. </s>
            <s xml:id="echoid-s15086" xml:space="preserve">unde arc. </s>
            <s xml:id="echoid-s15087" xml:space="preserve">LX. </s>
            <s xml:id="echoid-s15088" xml:space="preserve">arc. </s>
            <s xml:id="echoid-s15089" xml:space="preserve">BM:</s>
            <s xml:id="echoid-s15090" xml:space="preserve">: CL. </s>
            <s xml:id="echoid-s15091" xml:space="preserve">DB.
              <lb/>
            </s>
            <s xml:id="echoid-s15092" xml:space="preserve">quare ang. </s>
            <s xml:id="echoid-s15093" xml:space="preserve">LCX = ang. </s>
            <s xml:id="echoid-s15094" xml:space="preserve">BDM = ang. </s>
            <s xml:id="echoid-s15095" xml:space="preserve">DMP. </s>
            <s xml:id="echoid-s15096" xml:space="preserve">unde ang. </s>
            <s xml:id="echoid-s15097" xml:space="preserve">
              <lb/>
            C μβ eſt rectus, adeóque linea βμ C eſt _ſemicirculus_.</s>
            <s xml:id="echoid-s15098" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15099" xml:space="preserve">_Coroll_. </s>
            <s xml:id="echoid-s15100" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15101" xml:space="preserve">Subnotari poteſt, ſi duæ ſiguræ ADB, ADG analogæ fu-
              <lb/>
              <note position="right" xlink:label="note-0305-01" xlink:href="note-0305-01a" xml:space="preserve">Fig. 193.</note>
            erint; </s>
            <s xml:id="echoid-s15102" xml:space="preserve">& </s>
            <s xml:id="echoid-s15103" xml:space="preserve">harum _involu
              <unsure/>
            tæ_ ſint _Cμβ Cνγ_; </s>
            <s xml:id="echoid-s15104" xml:space="preserve">& </s>
            <s xml:id="echoid-s15105" xml:space="preserve">fuerit _Cμ. </s>
            <s xml:id="echoid-s15106" xml:space="preserve">Cν_
              <lb/>
            :</s>
            <s xml:id="echoid-s15107" xml:space="preserve">: DB. </s>
            <s xml:id="echoid-s15108" xml:space="preserve">DG; </s>
            <s xml:id="echoid-s15109" xml:space="preserve">erit reciprocè ang. </s>
            <s xml:id="echoid-s15110" xml:space="preserve">_βCμ. </s>
            <s xml:id="echoid-s15111" xml:space="preserve">β Cν:</s>
            <s xml:id="echoid-s15112" xml:space="preserve">: DG_.
              <lb/>
            </s>
            <s xml:id="echoid-s15113" xml:space="preserve">DB.</s>
            <s xml:id="echoid-s15114" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15115" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15116" xml:space="preserve">Illud etiam conversè valet.</s>
            <s xml:id="echoid-s15117" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15118" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15119" xml:space="preserve">Sin curvæ Cνγ, CS β ſuo modo analogæ fuerint, hoc eſt,
              <lb/>
              <note position="right" xlink:label="note-0305-02" xlink:href="note-0305-02a" xml:space="preserve">Fig. 194.</note>
            ſi utcunque à Cprojectâ rectâ C ν S, habeant Cν, CS ean-
              <lb/>
            dem perpetuò rationem, erunt hæ ſimilium linearum _invo-_
              <lb/>
            _lutæ_.</s>
            <s xml:id="echoid-s15120" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div521" type="section" level="1" n="67">
          <head xml:id="echoid-head70" xml:space="preserve">_Probl_. X.</head>
          <p>
            <s xml:id="echoid-s15121" xml:space="preserve">Dàta figurâ quâpiam β C φ rectis C β, C φ, & </s>
            <s xml:id="echoid-s15122" xml:space="preserve">aliâ lineâ βφ
              <lb/>
              <note position="right" xlink:label="note-0305-03" xlink:href="note-0305-03a" xml:space="preserve">Fig. 195.</note>
            comprehensâ, eicompetentem _evolutam_ deſignare.</s>
            <s xml:id="echoid-s15123" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15124" xml:space="preserve">_Centro_ Cutcunque deſcribatur _circularis arcus_ LE (cum rectis Cβ,
              <lb/>
            Cφ conſtituens ſectorem LCE) tum ductâ CK ad LC perpendicu-
              <lb/>
              <note position="right" xlink:label="note-0305-04" xlink:href="note-0305-04a" xml:space="preserve">Fig. 196.</note>
            lari, ſit curva β YH ità rectam CK reſpiciens, ut liberè projectâ rectà
              <lb/>
            CμZ, ſumptâque CO = arcLZ, ductâque OY ad CK perpen-
              <lb/>
            diculari, ſitOY = Cμ; </s>
            <s xml:id="echoid-s15125" xml:space="preserve">porrò ad rectam DA ſic referatur curva
              <lb/>
            BMF, ut cùm ſit DP = {ſpat. </s>
            <s xml:id="echoid-s15126" xml:space="preserve">C β YO/CL}; </s>
            <s xml:id="echoid-s15127" xml:space="preserve">& </s>
            <s xml:id="echoid-s15128" xml:space="preserve">PM ad DA perpendi-
              <lb/>
            cularis; </s>
            <s xml:id="echoid-s15129" xml:space="preserve">ſit eti
              <unsure/>
            am PM = Cμ; </s>
            <s xml:id="echoid-s15130" xml:space="preserve">erit ſpatium DBFA ipſins Cβφ _evolutum_.</s>
            <s xml:id="echoid-s15131" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15132" xml:space="preserve">_Exemp_. </s>
            <s xml:id="echoid-s15133" xml:space="preserve">Sit LZE arcus circuli centro C deſcripti, & </s>
            <s xml:id="echoid-s15134" xml:space="preserve">βμ C ejuſmodi
              <lb/>
              <note position="right" xlink:label="note-0305-05" xlink:href="note-0305-05a" xml:space="preserve">Fig. 197.</note>
            </s>
          </p>
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