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

Table of contents

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[61.] _Probl_. IV.
[62.] _Probl_. V.
[63.] _Probl_. VI.
[64.] _Probl_. VII
[65.] _Probl_. VIII.
[66.] _Probl_. IX.
[67.] _Probl_. X.
[68.] _Corol. Theor_. I.
[69.] _Theor_. II.
[70.] _Theor_. III.
[71.] _Theor_. IV.
[72.] _Theor_. V.
[73.] _Theor_. VI.
[74.] _Theor_. VII.
[75.] Lect. XIII.
[76.] Æquationum Series prima.
[77.] _Notetur autem_,
[78.] Series ſecunda.
[79.] Not.
[80.] Series tertia.
[81.] Not.
[82.] Not.
[83.] Series quarta.
[84.] Not.
[85.] Series quinta.
[86.] Series ſexta.
[87.] Not.
[88.] Series ſeptima.
[89.] Not.
[90.] Series octava.
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            <s xml:id="echoid-s15030" xml:space="preserve">_Aliter_. </s>
            <s xml:id="echoid-s15031" xml:space="preserve">Fiat PZ = √ 2 APM. </s>
            <s xml:id="echoid-s15032" xml:space="preserve">& </s>
            <s xml:id="echoid-s15033" xml:space="preserve">ſit ZO curvæ AZK perpendi-
              <lb/>
            cularis; </s>
            <s xml:id="echoid-s15034" xml:space="preserve">erit PM = PO.</s>
            <s xml:id="echoid-s15035" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15036" xml:space="preserve">_Exemp_. </s>
            <s xml:id="echoid-s15037" xml:space="preserve">Sit AP = x; </s>
            <s xml:id="echoid-s15038" xml:space="preserve">& </s>
            <s xml:id="echoid-s15039" xml:space="preserve">APM = {x
              <emph style="sub">3</emph>
            /r}. </s>
            <s xml:id="echoid-s15040" xml:space="preserve">quare PZ = √ {2 x
              <emph style="sub">3</emph>
            /r}
              <lb/>
            unde reperietur PO = {3 x x/r} = PM; </s>
            <s xml:id="echoid-s15041" xml:space="preserve">& </s>
            <s xml:id="echoid-s15042" xml:space="preserve">rurſus AMB
              <lb/>
            erit _Parabola_.</s>
            <s xml:id="echoid-s15043" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div514" type="section" level="1" n="65">
          <head xml:id="echoid-head68" xml:space="preserve">_Probl_. VIII.</head>
          <p>
            <s xml:id="echoid-s15044" xml:space="preserve">Sit figura quævis ADB (rectis DA, DB, & </s>
            <s xml:id="echoid-s15045" xml:space="preserve">linea AMB com-
              <lb/>
              <note position="left" xlink:label="note-0304-01" xlink:href="note-0304-01a" xml:space="preserve">Fig. 190.</note>
            prehenſa) & </s>
            <s xml:id="echoid-s15046" xml:space="preserve">à Dutcunque projectâ rectâ DM, datum ſit ſpatium
              <lb/>
            ADM; </s>
            <s xml:id="echoid-s15047" xml:space="preserve">oportet rectam DM definire.</s>
            <s xml:id="echoid-s15048" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15049" xml:space="preserve">Acceptâ quâpiam R, ſit DZ = {2 ADM/R}; </s>
            <s xml:id="echoid-s15050" xml:space="preserve">& </s>
            <s xml:id="echoid-s15051" xml:space="preserve">ZO curvæ AZK
              <lb/>
            perpendicularis; </s>
            <s xml:id="echoid-s15052" xml:space="preserve">cui occurrat DH ad DM perpendicularis;
              <lb/>
            </s>
            <s xml:id="echoid-s15053" xml:space="preserve">erit DM = √ R x DO.</s>
            <s xml:id="echoid-s15054" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15055" xml:space="preserve">_Aliter_. </s>
            <s xml:id="echoid-s15056" xml:space="preserve">Sit DZ = √ 4 ADM; </s>
            <s xml:id="echoid-s15057" xml:space="preserve">& </s>
            <s xml:id="echoid-s15058" xml:space="preserve">ZO curvæ AZK perpen-
              <lb/>
            dicularis; </s>
            <s xml:id="echoid-s15059" xml:space="preserve">cui occurrat DH ad DZ perpendicularis; </s>
            <s xml:id="echoid-s15060" xml:space="preserve">erit DM
              <lb/>
            = √ DZ x DO.</s>
            <s xml:id="echoid-s15061" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15062" xml:space="preserve">_De figuris involutis & </s>
            <s xml:id="echoid-s15063" xml:space="preserve">evolutis_ bellam σκέψιγ inſtituit _Præclarus Ge-_
              <lb/>
            _ometra D. </s>
            <s xml:id="echoid-s15064" xml:space="preserve">Gregorius Aberd._ </s>
            <s xml:id="echoid-s15065" xml:space="preserve">Alienæ meſſi nollem ego falcem meam
              <lb/>
            immittere, verùm liceat utcunque iſthuc pertinentes (aliud agenti quæ
              <lb/>
            mihi ſe ingeſſerunt) unam aut alteram obſervatiunculam his intexere.</s>
            <s xml:id="echoid-s15066" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div516" type="section" level="1" n="66">
          <head xml:id="echoid-head69" xml:space="preserve">_Probl_. IX.</head>
          <p>
            <s xml:id="echoid-s15067" xml:space="preserve">Data fit figura quæpiam ADB (cujus _axis_ AD, _baſis_ DB) oper-
              <lb/>
              <note position="left" xlink:label="note-0304-02" xlink:href="note-0304-02a" xml:space="preserve">Fig. 191.</note>
            tet ei congruentem involutam exhibere.</s>
            <s xml:id="echoid-s15068" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15069" xml:space="preserve">_Centro_ C, intervallo quopiam CL deſcribatur _Circulus_ LXX; </s>
            <s xml:id="echoid-s15070" xml:space="preserve">ſit
              <lb/>
              <note position="left" xlink:label="note-0304-03" xlink:href="note-0304-03a" xml:space="preserve">Fig. 192.</note>
            autem curva KZZ talis, ut pro lubitu ductâ rectâ MPZ ad BD </s>
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