Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div962" type="section" level="1" n="341">
          <p>
            <s xml:id="echoid-s15707" xml:space="preserve">
              <pb o="336" file="366" n="366" rhead="GEOMETR. PRACT."/>
            LM, ſimiles ſint, quorum chordæ IK, LM, bifariam ſectæ ſint à ſemidiametris in
              <lb/>
            N, O. </s>
            <s xml:id="echoid-s15708" xml:space="preserve">Dico eandem eſſe proportionem arcus IBK, ad arcum L F M, quæ eſt
              <lb/>
            chordæ IK, ad chordam LM, &</s>
            <s xml:id="echoid-s15709" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15710" xml:space="preserve"> Quoniam enim eſt circumferentia ABD,
              <note symbol="a" position="left" xlink:label="note-366-01" xlink:href="note-366-01a" xml:space="preserve">2. hui{us}.</note>
            circumferentiam EFH, hoc eſt, quadrans AB, ad quadrantem EF, vt
              <note symbol="b" position="left" xlink:label="note-366-02" xlink:href="note-366-02a" xml:space="preserve">15. quinti.</note>
            ter AC, ad diametrum EG; </s>
            <s xml:id="echoid-s15711" xml:space="preserve">hoc eſt, vt ſemidiame-
              <lb/>
              <figure xlink:label="fig-366-01" xlink:href="fig-366-01a" number="256">
                <image file="366-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/366-01"/>
              </figure>
            ter PB, ad ſemidiametrum QF. </s>
            <s xml:id="echoid-s15712" xml:space="preserve"> Eſt autem, vt
              <note symbol="c" position="left" xlink:label="note-366-03" xlink:href="note-366-03a" xml:space="preserve">15. quinti.</note>
            drans AB, ad quadrantem EF, ita arcus IB, ad arcum
              <lb/>
            LF, cum ſimiles ponantur. </s>
            <s xml:id="echoid-s15713" xml:space="preserve">Igitur erit quoque ar-
              <lb/>
            cus IB, ad arcum L F, vt ſemidiameter P B, ad ſemi-
              <lb/>
            diametrum QF. </s>
            <s xml:id="echoid-s15714" xml:space="preserve">Cum ergo ex Lemmate propoſ. </s>
            <s xml:id="echoid-s15715" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s15716" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15717" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15718" xml:space="preserve">noſtræ Gnomonicæ, vel ex Lemmate 5. </s>
            <s xml:id="echoid-s15719" xml:space="preserve">libr. </s>
            <s xml:id="echoid-s15720" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15721" xml:space="preserve">
              <lb/>
            noſtri Aſtrolabilij, ita ſe habeat P B, ſinus totus ad
              <lb/>
            QF, ſinum totum, quemadmo dum ſinus IN, ad ſinum L O. </s>
            <s xml:id="echoid-s15722" xml:space="preserve">erit quo que arcus
              <lb/>
            IB, ad arcum LF, vt ſinus IN, ad ſinum LO, id eſt, duplus arcus IK, ad
              <note symbol="d" position="left" xlink:label="note-366-04" xlink:href="note-366-04a" xml:space="preserve">15. quinti.</note>
            arcum LM, vt chorda IK, ipſius IN, dupla, ad chordam LM, ipſius LO, duplam.
              <lb/>
            </s>
            <s xml:id="echoid-s15723" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s15724" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15725" xml:space="preserve">
              <emph style="sc">Vervm</emph>
            ſit iamarcus IK, ad arcum LM, vt chorda IK, ad chordam LM. </s>
            <s xml:id="echoid-s15726" xml:space="preserve">Di-
              <lb/>
            co arcus ſimiles eſſe. </s>
            <s xml:id="echoid-s15727" xml:space="preserve">Facta enim eadem conſtructione, e erit quoque arcus IB, ad
              <lb/>
              <note symbol="e" position="left" xlink:label="note-366-05" xlink:href="note-366-05a" xml:space="preserve">15. quinti.</note>
            arcum LF, ſemiſsis ad ſemiſſem, vt IN, ad LO, ſemiſsis ad ſemiſſem. </s>
            <s xml:id="echoid-s15728" xml:space="preserve"> Vt
              <note symbol="f" position="left" xlink:label="note-366-06" xlink:href="note-366-06a" xml:space="preserve">ſchol. 33.
                <lb/>
              ſexti.</note>
            IB, ad LF, ita eſt quadrans AB, ad quadrantem EF; </s>
            <s xml:id="echoid-s15729" xml:space="preserve"> Et vt quadrans ad quadran- tem, ita eſt ſemidiameter PB, ad ſemidiametrũ. </s>
            <s xml:id="echoid-s15730" xml:space="preserve">QF. </s>
            <s xml:id="echoid-s15731" xml:space="preserve">Igitur eri@ quo que ſinus IN,
              <lb/>
              <note symbol="g" position="left" xlink:label="note-366-07" xlink:href="note-366-07a" xml:space="preserve">2. hui{us}.</note>
            ad ſinum LO, vt ſinus totus PB, ad ſinum totum QF: </s>
            <s xml:id="echoid-s15732" xml:space="preserve">Atque idcirco ex Lem-
              <lb/>
            mate propoſ. </s>
            <s xml:id="echoid-s15733" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15734" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15735" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15736" xml:space="preserve">noſtræ Gnomonicæ, vel ex Lemmate 5. </s>
            <s xml:id="echoid-s15737" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15738" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15739" xml:space="preserve">noſtri Aſtro-
              <lb/>
            labij, arcus IB, LF, ſimiles erunt; </s>
            <s xml:id="echoid-s15740" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s15741" xml:space="preserve">eorum dupli IBK, LFM, ſimiles
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s15742" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s15743" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div965" type="section" level="1" n="342">
          <head xml:id="echoid-head369" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s15744" xml:space="preserve">
              <emph style="sc">Seqvitvr</emph>
            hinc, ſi arcus IBK, LFM, non ſint ſimiles, eos non habere ean-
              <lb/>
            dem cum chordis proportionem, Sinamque eandem haberent, ipſi ſimiles eſ-
              <lb/>
            ſent, vt in ſecunda parte huius propoſ. </s>
            <s xml:id="echoid-s15745" xml:space="preserve">fuit oſtenſum, quod eſt abſurdum, cum
              <lb/>
            ponantur non ſimiles.</s>
            <s xml:id="echoid-s15746" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div966" type="section" level="1" n="343">
          <head xml:id="echoid-head370" xml:space="preserve">PROBL. 1. PROPOS. 4.</head>
          <p>
            <s xml:id="echoid-s15747" xml:space="preserve">DATO quadrilatero æquale parallelogrammum in dato angulo faci-
              <lb/>
            lius, quam per propoſ. </s>
            <s xml:id="echoid-s15748" xml:space="preserve">45. </s>
            <s xml:id="echoid-s15749" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15750" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15751" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s15752" xml:space="preserve">conſtituere.</s>
            <s xml:id="echoid-s15753" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15754" xml:space="preserve">
              <emph style="sc">Sit</emph>
            quadrilaterum quodcunque ABCD, & </s>
            <s xml:id="echoid-s15755" xml:space="preserve">datus angulus K. </s>
            <s xml:id="echoid-s15756" xml:space="preserve">Ducta dia-
              <lb/>
            metro BD, eaque diuiſa bifariam in E, ducatur per E,
              <lb/>
              <figure xlink:label="fig-366-02" xlink:href="fig-366-02a" number="257">
                <image file="366-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/366-02"/>
              </figure>
            recta FG, faciens in E, angulum FED, dato angulo K,
              <lb/>
            æqualem. </s>
            <s xml:id="echoid-s15757" xml:space="preserve">Deinde ducta per D, ipſi FG, parallela HI,
              <lb/>
            & </s>
            <s xml:id="echoid-s15758" xml:space="preserve">per A, C, duabus AH, CI, ipſi BD, parallelis ſecanti-
              <lb/>
            bus FG, HI, in F, H, G, I, conſtitutum erit parallelo-
              <lb/>
              <note symbol="h" position="left" xlink:label="note-366-08" xlink:href="note-366-08a" xml:space="preserve">29. primi.</note>
            grammum FI, in dato angulo G, qui æqualis eſt an- gulo, FED, internus externo, hoc eſt, angulo K. </s>
            <s xml:id="echoid-s15759" xml:space="preserve"/>
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