Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

Table of figures

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          <p>
            <s xml:id="echoid-s12100" xml:space="preserve">
              <pb o="363" file="375" n="375" rhead=""/>
            tur æquales AB, AC, erunt & </s>
            <s xml:id="echoid-s12101" xml:space="preserve">BD, CF, æquales. </s>
            <s xml:id="echoid-s12102" xml:space="preserve">Quare duo latera DB,
              <lb/>
            DC, trianguli DBC, æqualia ſunt duobus
              <lb/>
              <figure xlink:label="fig-375-01" xlink:href="fig-375-01a" number="204">
                <image file="375-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/375-01"/>
              </figure>
            lateribus FC, FB, trianguli FCB: </s>
            <s xml:id="echoid-s12103" xml:space="preserve">quæ cum
              <lb/>
            contineant angulos æquales D, F, vt oſten-
              <lb/>
            dimus, erunt & </s>
            <s xml:id="echoid-s12104" xml:space="preserve">anguli DBC, DCB, angu-
              <lb/>
              <note position="right" xlink:label="note-375-01" xlink:href="note-375-01a" xml:space="preserve">7. huius.</note>
            lis FCB, FBC, æquales. </s>
            <s xml:id="echoid-s12105" xml:space="preserve">Quòd ſi ex angu-
              <lb/>
            lis ABF, ACD, quos oſtendimus æquales
              <lb/>
            eſſe, auferantur anguli FBC, DCB, quos
              <lb/>
            etiam æquales eſſe demonſtrauimus, rema-
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            nebunt anguli ABC, ACB, ſupra baſim
              <lb/>
            BC, æquales: </s>
            <s xml:id="echoid-s12106" xml:space="preserve">Oſtenſum eſt autem & </s>
            <s xml:id="echoid-s12107" xml:space="preserve">angu-
              <lb/>
            los DBC, FCB, infra eandem baſim BC,
              <lb/>
            eſſe æquales. </s>
            <s xml:id="echoid-s12108" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s12109" xml:space="preserve">anguli ſupra baſim in-
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            ter ſe, & </s>
            <s xml:id="echoid-s12110" xml:space="preserve">anguli infra eandem inter ſe æquales ſunt. </s>
            <s xml:id="echoid-s12111" xml:space="preserve">Quam ob rem Iſoſcelium
              <lb/>
            triangulorum ſphæricorum, &</s>
            <s xml:id="echoid-s12112" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12113" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s12114" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div950" type="section" level="1" n="494">
          <head xml:id="echoid-head529" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s12115" xml:space="preserve">HING manifeſtum eſt, omne triangulum ſphæricum æquilaterum, eſſe quoque
              <gap/>
              <lb/>
            @uiangulum.</s>
            <s xml:id="echoid-s12116" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div951" type="section" level="1" n="495">
          <head xml:id="echoid-head530" xml:space="preserve">THEOR. 8. PROPOS. 9.</head>
          <p>
            <s xml:id="echoid-s12117" xml:space="preserve">SI trianguli ſphærici duo anguli æquales inter
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            ſe fuerint: </s>
            <s xml:id="echoid-s12118" xml:space="preserve">Et ſub æqualibus angulis ſubtenſa late-
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            ra æqualia inter ſe erunt.</s>
            <s xml:id="echoid-s12119" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12120" xml:space="preserve">IN triangulo ABC, ſint duo anguli B, C, ſupra latus BC, æquales. </s>
            <s xml:id="echoid-s12121" xml:space="preserve">Di-
              <lb/>
            co latera quoque AB, AC, illis ſubtenſa eſſe æqualia. </s>
            <s xml:id="echoid-s12122" xml:space="preserve">Si enim non ſunt æ-
              <lb/>
            qualia, ſit, ſi fieri poteſt AB, maius. </s>
            <s xml:id="echoid-s12123" xml:space="preserve">Et quo-
              <lb/>
              <figure xlink:label="fig-375-02" xlink:href="fig-375-02a" number="205">
                <image file="375-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/375-02"/>
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            niam arcus AC, minor eſt ſemicirculo, abſcin-
              <lb/>
              <note position="right" xlink:label="note-375-02" xlink:href="note-375-02a" xml:space="preserve">2. huius.</note>
            datur ex arcu maiore AB, arcus BD, arcui mi-
              <lb/>
              <note position="right" xlink:label="note-375-03" xlink:href="note-375-03a" xml:space="preserve">1. huius.</note>
            nori AC, æqualis; </s>
            <s xml:id="echoid-s12124" xml:space="preserve">& </s>
            <s xml:id="echoid-s12125" xml:space="preserve">per puncta C, D, arcus cir
              <lb/>
              <note position="right" xlink:label="note-375-04" xlink:href="note-375-04a" xml:space="preserve">20 1. Theo.</note>
            culi maximi ducatur CD. </s>
            <s xml:id="echoid-s12126" xml:space="preserve">Quoniam ergo duo
              <lb/>
            latera AC, CB, trianguli ACB, æqualia ſunt
              <lb/>
            duobus lateribus DB, BC, trianguli DBC,
              <lb/>
            continentq́; </s>
            <s xml:id="echoid-s12127" xml:space="preserve">angulos æquales ACB, DBC;
              <lb/>
            </s>
            <s xml:id="echoid-s12128" xml:space="preserve">erunt triangula ACB, DBC, æqualia, totum
              <lb/>
              <note position="right" xlink:label="note-375-05" xlink:href="note-375-05a" xml:space="preserve">7. huius.</note>
            & </s>
            <s xml:id="echoid-s12129" xml:space="preserve">pars. </s>
            <s xml:id="echoid-s12130" xml:space="preserve">Quod fieri non poteſt. </s>
            <s xml:id="echoid-s12131" xml:space="preserve">Non ergo inæ-
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            qualia ſunt latera AB, AC, ſed æqualia. </s>
            <s xml:id="echoid-s12132" xml:space="preserve">Si trian
              <lb/>
            guli igitur ſphærici duo anguli, &</s>
            <s xml:id="echoid-s12133" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12134" xml:space="preserve">Quod erat
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            oſtendendum.</s>
            <s xml:id="echoid-s12135" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div953" type="section" level="1" n="496">
          <head xml:id="echoid-head531" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s12136" xml:space="preserve">SEQVITVR hinc, omne triangulum ſphætricum æquiangulum, eſſe quoque æqui-
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            laterum.</s>
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