Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1041" type="section" level="1" n="375">
          <pb o="362" file="390" n="390" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s16991" xml:space="preserve">
              <emph style="sc">Iam</emph>
            verò ſi ſumma trium angulorum A, B, K, inuentorum, nimirum grad.
              <lb/>
            </s>
            <s xml:id="echoid-s16992" xml:space="preserve">
              <note position="right" xlink:label="note-390-01" xlink:href="note-390-01a" xml:space="preserve">
                <lb/>
              Angulus # A # Grad. # 108 # min. # 22
                <lb/>
              # B # Grad. # 108 # min. # 22
                <lb/>
              # H # Grad. # 107 # min. # 2
                <lb/>
              # I # Grad. # 107 # min. # 2
                <lb/>
              # K # Grad. # 109 # min. # 12
                <lb/>
              ## Summa # # 540 # min. # 0
                <lb/>
              </note>
            325. </s>
            <s xml:id="echoid-s16993" xml:space="preserve">min. </s>
            <s xml:id="echoid-s16994" xml:space="preserve">56. </s>
            <s xml:id="echoid-s16995" xml:space="preserve">auferatur ex grad.
              <lb/>
            </s>
            <s xml:id="echoid-s16996" xml:space="preserve">540. </s>
            <s xml:id="echoid-s16997" xml:space="preserve">ſumma omnium 5. </s>
            <s xml:id="echoid-s16998" xml:space="preserve">angu-
              <lb/>
            lorum pentagoni, reliqua fiet
              <lb/>
            ſumma angulorum H, I, grad. </s>
            <s xml:id="echoid-s16999" xml:space="preserve">
              <lb/>
            214. </s>
            <s xml:id="echoid-s17000" xml:space="preserve">min. </s>
            <s xml:id="echoid-s17001" xml:space="preserve">4. </s>
            <s xml:id="echoid-s17002" xml:space="preserve">Acproinde vterque
              <lb/>
            erit grad. </s>
            <s xml:id="echoid-s17003" xml:space="preserve">107. </s>
            <s xml:id="echoid-s17004" xml:space="preserve">min. </s>
            <s xml:id="echoid-s17005" xml:space="preserve">2. </s>
            <s xml:id="echoid-s17006" xml:space="preserve">minor ve-
              <lb/>
            rò angulo pentagoni grad. </s>
            <s xml:id="echoid-s17007" xml:space="preserve">180. </s>
            <s xml:id="echoid-s17008" xml:space="preserve">
              <lb/>
            Nonergo æquiangulum eſt Du-
              <lb/>
            reri pentagonum, ſed ſolum æ-
              <lb/>
            quilaterum. </s>
            <s xml:id="echoid-s17009" xml:space="preserve">Omnes tamen 5. </s>
            <s xml:id="echoid-s17010" xml:space="preserve">
              <lb/>
            anguli cõficiunt ſummam grad. </s>
            <s xml:id="echoid-s17011" xml:space="preserve">
              <lb/>
            540. </s>
            <s xml:id="echoid-s17012" xml:space="preserve">ſicut in pentagono æquila-
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            tero, atque æquiangulo, vt hæ
              <lb/>
            formula indicat.</s>
            <s xml:id="echoid-s17013" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1050" type="section" level="1" n="376">
          <head xml:id="echoid-head403" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s17014" xml:space="preserve">
              <emph style="sc">Svnt</emph>
            alij nonnulli, qui ad interuallum cuiuſuis rectæ AB, deſcriptis ex cẽ-
              <lb/>
            tris A, B, duobus circulis ſe interſecantibus in C, D, vt in ſuperiori figura, ducunt
              <lb/>
            rectam AD, affirmantque AD, latus eſſe pentagoni in circulo, cuius ſemidiame-
              <lb/>
            ter DM, inſcripti. </s>
            <s xml:id="echoid-s17015" xml:space="preserve">ſed toto cœlo aberrant. </s>
            <s xml:id="echoid-s17016" xml:space="preserve">Eſt enim AD, minus latere pentago-
              <lb/>
              <note symbol="a" position="left" xlink:label="note-390-02" xlink:href="note-390-02a" xml:space="preserve">10. tertijde-
                <lb/>
              cimi.</note>
            ni circuli prædicti. </s>
            <s xml:id="echoid-s17017" xml:space="preserve"> Nam quia latus pentagonipoteſt & </s>
            <s xml:id="echoid-s17018" xml:space="preserve">latus hexagoni, & </s>
            <s xml:id="echoid-s17019" xml:space="preserve">la- tus decagoni circuli eiuſdem: </s>
            <s xml:id="echoid-s17020" xml:space="preserve"> Poteſt autem AD, rectas DM, MA; </s>
            <s xml:id="echoid-s17021" xml:space="preserve"> & </s>
            <s xml:id="echoid-s17022" xml:space="preserve">DM,
              <note symbol="b" position="left" xlink:label="note-390-03" xlink:href="note-390-03a" xml:space="preserve">47. primi.</note>
            tus eſt hexagoni in circulo, cuius ſemidiameter DM, eſſet AM, latus decagoni in
              <lb/>
              <note symbol="c" position="left" xlink:label="note-390-04" xlink:href="note-390-04a" xml:space="preserve">coroll. 15.
                <lb/>
              quanti.</note>
            eodem circulo. </s>
            <s xml:id="echoid-s17023" xml:space="preserve">quod falſum eſt. </s>
            <s xml:id="echoid-s17024" xml:space="preserve">Quoniam enim latus decagoni maius eſt ſe-
              <lb/>
            miſſe lateris pentagoni, quod duo latera decagoniſupra latus Pentagoni con-
              <lb/>
              <note symbol="d" position="left" xlink:label="note-390-05" xlink:href="note-390-05a" xml:space="preserve">20. primi.</note>
            ſtituant Iſoſceles in quo duo latera maiora ſunt latere pentagoni: </s>
            <s xml:id="echoid-s17025" xml:space="preserve">Erit AM,
              <note symbol="e" position="left" xlink:label="note-390-06" xlink:href="note-390-06a" xml:space="preserve">10. tertijde-
                <lb/>
              cimi.</note>
            miſsis ipſius AB, vel AD, minor latere decagoni. </s>
            <s xml:id="echoid-s17026" xml:space="preserve">Igitur AD, minor eſt latere pẽ-
              <lb/>
            tagoni; </s>
            <s xml:id="echoid-s17027" xml:space="preserve"> quando quidem latus pentagoni poteſt & </s>
            <s xml:id="echoid-s17028" xml:space="preserve">latus hexagoni DM, &</s>
            <s xml:id="echoid-s17029" xml:space="preserve"> latus decagoni, quod maius eſt, quam AM, ſemiſsis ipſius AD, vt diximus.</s>
            <s xml:id="echoid-s17030" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1052" type="section" level="1" n="377">
          <head xml:id="echoid-head404" xml:space="preserve">THEOR. 12. PROPOS. 30.</head>
          <p>
            <s xml:id="echoid-s17031" xml:space="preserve">INVENTIONEM lateris heptagoni in dato circulo non rectè à qui-
              <lb/>
            buſdam tradi, demonſtrare.</s>
            <s xml:id="echoid-s17032" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17033" xml:space="preserve">
              <emph style="sc">Carolvs</emph>
            Marianus Cremonenſis totum vnum libellũ
              <lb/>
              <figure xlink:label="fig-390-01" xlink:href="fig-390-01a" number="282">
                <image file="390-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/390-01"/>
              </figure>
            edidit de inuentione lateris heptagoni in circulo dato, in
              <lb/>
            quo probare conatur, latus heptagoni reperiri hac ratione.
              <lb/>
            </s>
            <s xml:id="echoid-s17034" xml:space="preserve">Sit circulus ABC, cuius centrum D, diameter CA, in qua pro-
              <lb/>
            ducta capiatur AE, æqualis quartæ parti ſemidiametri AD, ita
              <lb/>
            vt AE, quinta pars ſit rectæ DE. </s>
            <s xml:id="echoid-s17035" xml:space="preserve">Deſcripto autem ex E, ad in-
              <lb/>
            teruallum ſemidiametri AD, circulo ſecante datum circulum
              <lb/>
            in B, iũgatur recta AB, quam dicit eſſe latus heptagoni, quod
              <lb/>
            falſum eſſe, ita oſtendemus. </s>
            <s xml:id="echoid-s17036" xml:space="preserve">Si AB, eſſet verum latus hepta-
              <lb/>
            goni, & </s>
            <s xml:id="echoid-s17037" xml:space="preserve">ducta BE, æquali ſemidiametro DB, (quod fiet, ſi </s>
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