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

Table of figures

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            <s xml:id="echoid-s12381" xml:space="preserve">POSITO eodem triangulo ſphærico, & </s>
            <s xml:id="echoid-s12382" xml:space="preserve">conſtructione figuræ eadem;
              <lb/>
            </s>
            <s xml:id="echoid-s12383" xml:space="preserve">Sint primum duo anguli B, C, duobus rectis æquales ſupra latus BC. </s>
            <s xml:id="echoid-s12384" xml:space="preserve">Dico
              <lb/>
            reliqua duo latera AB, AC, ſemicirculo æqualia eſſe, &</s>
            <s xml:id="echoid-s12385" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12386" xml:space="preserve">Cum enim & </s>
            <s xml:id="echoid-s12387" xml:space="preserve">an-
              <lb/>
              <figure xlink:label="fig-382-01" xlink:href="fig-382-01a" number="217">
                <image file="382-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/382-01"/>
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            guli duo ad C, æquales ſint duobus rectis; </s>
            <s xml:id="echoid-s12388" xml:space="preserve">dempto
              <lb/>
              <note position="left" xlink:label="note-382-01" xlink:href="note-382-01a" xml:space="preserve">5. huius.</note>
            communi angulo ACB, remanebit angulus ACD,
              <lb/>
              <note position="left" xlink:label="note-382-02" xlink:href="note-382-02a" xml:space="preserve">15. huius.</note>
            angulo B, æqualis. </s>
            <s xml:id="echoid-s12389" xml:space="preserve">Quare ſemicirculo æquales ſunt
              <lb/>
            arcus AB, AC.</s>
            <s xml:id="echoid-s12390" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12391" xml:space="preserve">SINT deinde anguli B, ACB, duobus rectis mi-
              <lb/>
              <note position="left" xlink:label="note-382-03" xlink:href="note-382-03a" xml:space="preserve">5. huius.</note>
            nores. </s>
            <s xml:id="echoid-s12392" xml:space="preserve">Cum ergo duo anguli ad C, ſint duobus rectis
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            æquales; </s>
            <s xml:id="echoid-s12393" xml:space="preserve">dempto communiangulo ACB, remane-
              <lb/>
            bit angulus ACD, maior angulo B. </s>
            <s xml:id="echoid-s12394" xml:space="preserve">Arcus ergo AB,
              <lb/>
              <note position="left" xlink:label="note-382-04" xlink:href="note-382-04a" xml:space="preserve">15. huius.</note>
            AC, ſemicirculo ſunt minores.</s>
            <s xml:id="echoid-s12395" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12396" xml:space="preserve">SINT denique anguli B, ACB, duobus rectis maiores. </s>
            <s xml:id="echoid-s12397" xml:space="preserve">Cum ergo duo
              <lb/>
              <note position="left" xlink:label="note-382-05" xlink:href="note-382-05a" xml:space="preserve">5. huius.</note>
            anguli ad C, ſint æquales duobus rectis; </s>
            <s xml:id="echoid-s12398" xml:space="preserve">ſi dematur communis angulus ACB,
              <lb/>
              <note position="left" xlink:label="note-382-06" xlink:href="note-382-06a" xml:space="preserve">15. huius.</note>
            erit reliquus ACD, reliquo B, minor; </s>
            <s xml:id="echoid-s12399" xml:space="preserve">atque adeo arcus AB, AC, ſemicir-
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            culo maiores. </s>
            <s xml:id="echoid-s12400" xml:space="preserve">Quo circa ſi cuiuſcunque trianguli ſphærici, &</s>
            <s xml:id="echoid-s12401" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12402" xml:space="preserve">Quod oſten-
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            dendum erat.</s>
            <s xml:id="echoid-s12403" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div982" type="section" level="1" n="505">
          <head xml:id="echoid-head540" xml:space="preserve">THEOR. 16. PROP. 18.</head>
          <p>
            <s xml:id="echoid-s12404" xml:space="preserve">SI duo triangula ſphærica habeant tria latera
              <lb/>
            tribus lateribus æqualia, ſingula ſingulis: </s>
            <s xml:id="echoid-s12405" xml:space="preserve">habebũt
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            & </s>
            <s xml:id="echoid-s12406" xml:space="preserve">tres angulos tribus angulis æquales, ſingulos
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            ſingulis, ſub quibus æqualia latera ſubtenduntur.</s>
            <s xml:id="echoid-s12407" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12408" xml:space="preserve">SINT duo triangula ſphærica ABC, DEF, habentia tria latera AB,
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            AC, BC, tribus lateribus DE, DF, EF, ſingula ſingulis, æqualia. </s>
            <s xml:id="echoid-s12409" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s12410" xml:space="preserve">
              <lb/>
            angulostres A,B,C, tribus angulis D,E,F, ſingulos ſingulis, eſſe æquales,
              <lb/>
              <figure xlink:label="fig-382-02" xlink:href="fig-382-02a" number="218">
                <image file="382-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/382-02"/>
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            ſub quibus æqualia ſubtenduntur latera. </s>
            <s xml:id="echoid-s12411" xml:space="preserve">Si
              <lb/>
            enim angulus A, (vt ab hoc angulo incipia-
              <lb/>
            mus.) </s>
            <s xml:id="echoid-s12412" xml:space="preserve">non eſt æqualis angulo D, erit vel ma-
              <lb/>
              <note position="left" xlink:label="note-382-07" xlink:href="note-382-07a" xml:space="preserve">12. huius.</note>
            ior eo, vel minor. </s>
            <s xml:id="echoid-s12413" xml:space="preserve">Si maior, erit baſis BC, ma-
              <lb/>
            ior quoque baſi EF. </s>
            <s xml:id="echoid-s12414" xml:space="preserve">Quod eſt abſurdũ. </s>
            <s xml:id="echoid-s12415" xml:space="preserve">ponun
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            tur enim latera BC, EF, æqualia. </s>
            <s xml:id="echoid-s12416" xml:space="preserve">Si verò mi-
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            nor eſt angulus A, angulo D, erit baſis E F,
              <lb/>
              <note position="left" xlink:label="note-382-08" xlink:href="note-382-08a" xml:space="preserve">12. huius.</note>
            maior baſi BC. </s>
            <s xml:id="echoid-s12417" xml:space="preserve">Quod rurſum eſt abſurdum,
              <lb/>
            cum æquales ponantur. </s>
            <s xml:id="echoid-s12418" xml:space="preserve">Cum ergo angulus A,
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            neque maior ſit, neque minor angulo D, erit vtique illi æqualis. </s>
            <s xml:id="echoid-s12419" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s12420" xml:space="preserve">re-
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            liqui anguli B, C, angulis reliquis E, F, æquales erunt, nempe B, ipſi E, & </s>
            <s xml:id="echoid-s12421" xml:space="preserve">C,
              <lb/>
              <note position="left" xlink:label="note-382-09" xlink:href="note-382-09a" xml:space="preserve">7. huius.</note>
            ipſi F. </s>
            <s xml:id="echoid-s12422" xml:space="preserve">Si duo ergo triangula ſphærica, &</s>
            <s xml:id="echoid-s12423" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12424" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s12425" xml:space="preserve"/>
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        <div xml:id="echoid-div984" type="section" level="1" n="506">
          <head xml:id="echoid-head541" xml:space="preserve">THEOR. 17. PROPOS. 19.</head>
          <p>
            <s xml:id="echoid-s12426" xml:space="preserve">SI duo triangula ſphærica habeant tres angu-
              <lb/>
            los tribus angulis, ſingulos ſingulis, æquales: </s>
            <s xml:id="echoid-s12427" xml:space="preserve"/>
          </p>
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