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

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            <s xml:id="echoid-s14643" xml:space="preserve">
              <pb o="117" file="0295" n="310" rhead=""/>
            ADLK. </s>
            <s xml:id="echoid-s14644" xml:space="preserve">item patet _ſegmentum_ ADB unà cum _rectangulo_ ADZR
              <lb/>
            majus eſſe _figurâ circumſcriptâ_ (etenim _rectangulum_ ADZR_rectan-_
              <lb/>
            _gulis_ RH, PG, OF, NE, MZ æ quatur, proindéque majus eſt _irili-_
              <lb/>
            _neis_ AXR, XXP, XXO, XXN, XBM). </s>
            <s xml:id="echoid-s14645" xml:space="preserve">ergò _ſegmentum_ ADB
              <lb/>
              <note position="right" xlink:label="note-0295-01" xlink:href="note-0295-01a" xml:space="preserve">Fig. 176,</note>
            unà cum _rectangulo_ ADLK multo majus eſt _figurâ circumſcriptâ_;
              <lb/>
            </s>
            <s xml:id="echoid-s14646" xml:space="preserve">hoc eſt, _ſpatium_ S majus eſt _figurâ circumſcriptâ_, contra _Hypotbeſin._</s>
            <s xml:id="echoid-s14647" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14648" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s14649" xml:space="preserve">Item, ſi ponatur _figura inſcripta_ HXGXFXEXZDH minor
              <lb/>
            _ſpatio quodam_ S; </s>
            <s xml:id="echoid-s14650" xml:space="preserve">dico _ſegmentum_ ADB non eſſe majus quàm S.</s>
            <s xml:id="echoid-s14651" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14652" xml:space="preserve">Nam ſi majus eſſe velis, eſto rurſum _exceſſus par rectangulo_ ADLK;
              <lb/>
            </s>
            <s xml:id="echoid-s14653" xml:space="preserve">quod utique (ſicut prius) majus erit _rectangulo_ ADZR. </s>
            <s xml:id="echoid-s14654" xml:space="preserve">Eſt autem
              <lb/>
            _ſegmentum_ ADB, dempto _rectangulo_ ADZR, minus figurâ inſcriptâ. </s>
            <s xml:id="echoid-s14655" xml:space="preserve">
              <lb/>
            ergò ſegmentum ADB, dempro rectangulo ADLK, multo minus fit
              <lb/>
            inſcriptâ; </s>
            <s xml:id="echoid-s14656" xml:space="preserve">hoc eſt _ſpatium_ S minus eſt inſcriptâ figurâ, contra
              <lb/>
            _Hypotbeſin._</s>
            <s xml:id="echoid-s14657" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14658" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s14659" xml:space="preserve">Hinc, ſi _ſp@tium_ quodcunque fuerit, (puta S) cui circumſcripta
              <lb/>
            figura æquetur _ſigurœ_ ADBMNOPRA; </s>
            <s xml:id="echoid-s14660" xml:space="preserve">nec non cui _inſcripta figura_
              <lb/>
            _æquetur figuræ_ HGFEZDH; </s>
            <s xml:id="echoid-s14661" xml:space="preserve">palàm eſt _ſpatium_ iſtud S _ſegmento_
              <lb/>
            ADB exæquari.</s>
            <s xml:id="echoid-s14662" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14663" xml:space="preserve">Nam (utì mox oſtenſum) hoc illo majus eſſe nequit, aut mi-
              <lb/>
            nus.</s>
            <s xml:id="echoid-s14664" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14665" xml:space="preserve">Poterunt autem hæc ad _alios circumſcriptionis ac inſcriptionis modos_
              <lb/>
            accomodari. </s>
            <s xml:id="echoid-s14666" xml:space="preserve">ſuffecerit innuiſſe.</s>
            <s xml:id="echoid-s14667" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div480" type="section" level="1" n="47">
          <head xml:id="echoid-head50" style="it" xml:space="preserve">Conicorum Superſicies dimetiendi Metbodus.</head>
          <p>
            <s xml:id="echoid-s14668" xml:space="preserve">S It _curva_ quæpiam AMB, cujus _Axis_ AD, & </s>
            <s xml:id="echoid-s14669" xml:space="preserve">in hoc ſignatum
              <lb/>
              <note position="right" xlink:label="note-0295-02" xlink:href="note-0295-02a" xml:space="preserve">Fig. 177.</note>
            punctum C; </s>
            <s xml:id="echoid-s14670" xml:space="preserve">ad ipſum vero ordinata recta BD. </s>
            <s xml:id="echoid-s14671" xml:space="preserve">à puncto quo-
              <lb/>
            piam M in curva ſumpto ducatur recta ME curvam tangens, & </s>
            <s xml:id="echoid-s14672" xml:space="preserve">à C
              <lb/>
            demittatur CGad ME perpendicularis; </s>
            <s xml:id="echoid-s14673" xml:space="preserve">ſit item determinata recta
              <lb/>
            CV ad planam DAB recta, & </s>
            <s xml:id="echoid-s14674" xml:space="preserve">connectatur VG(erit VG _ipſi_ MG
              <lb/>
            perpendicularis; </s>
            <s xml:id="echoid-s14675" xml:space="preserve">nam ſi ducatur CHad GM parallela, liquet CH
              <lb/>
            plano GVG rectam eſſe, adeoque GMeidem recta erit) Porrò ſit
              <lb/>
            linea RStalis, ut ductâ rectâ MIX ad AD parallelâ (quæ ſecet </s>
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