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

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          <pb o="364" file="376" n="376" rhead=""/>
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        <div xml:id="echoid-div954" type="section" level="1" n="497">
          <head xml:id="echoid-head532" xml:space="preserve">PROBL. 2. PROPOS. 10.</head>
          <p>
            <s xml:id="echoid-s12138" xml:space="preserve">AD datum arcum circuli maximi in ſphæra,
              <lb/>
            datumq́; </s>
            <s xml:id="echoid-s12139" xml:space="preserve">in eo punctum, dato angulo ſphærico æ-
              <lb/>
            qualem angulum ſphæricum conſtituere.</s>
            <s xml:id="echoid-s12140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12141" xml:space="preserve">SIT datus arcus maximi circuli in ſphæra AB, datumq; </s>
            <s xml:id="echoid-s12142" xml:space="preserve">in eo punctum
              <lb/>
            C, oporteatq́; </s>
            <s xml:id="echoid-s12143" xml:space="preserve">dato angulo ſphærico D, ad punctum C, æqualem angulum
              <lb/>
            ſphæricum conſtituere. </s>
            <s xml:id="echoid-s12144" xml:space="preserve">Productis arcubus DE, DF, angulum D, continen-
              <lb/>
              <note position="right" xlink:label="note-376-01" xlink:href="note-376-01a" xml:space="preserve">20. 1. Theo.</note>
            tibus quantumlibet, ſumatur quadrans DG; </s>
            <s xml:id="echoid-s12145" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s12146" xml:space="preserve">per G, & </s>
            <s xml:id="echoid-s12147" xml:space="preserve">polum circuli
              <lb/>
              <figure xlink:label="fig-376-01" xlink:href="fig-376-01a" number="206">
                <image file="376-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/376-01"/>
              </figure>
            DE, arcus circuli ma-
              <lb/>
            ximi ducatur GH, ſe-
              <lb/>
            cans arcum DF, in H.
              <lb/>
            </s>
            <s xml:id="echoid-s12148" xml:space="preserve">Erit igitur angulus G,
              <lb/>
              <note position="left" xlink:label="note-376-02" xlink:href="note-376-02a" xml:space="preserve">25. 1. Theo.</note>
            rectus. </s>
            <s xml:id="echoid-s12149" xml:space="preserve">Deinde ſumpto
              <lb/>
            quoque quadrante CI,
              <lb/>
            ducatur per I, & </s>
            <s xml:id="echoid-s12150" xml:space="preserve">polum
              <lb/>
              <note position="left" xlink:label="note-376-03" xlink:href="note-376-03a" xml:space="preserve">20. 1. Theo.</note>
            circuli AB, arcus ma-
              <lb/>
            ximi circuli IK. </s>
            <s xml:id="echoid-s12151" xml:space="preserve">Erit
              <lb/>
            igitur & </s>
            <s xml:id="echoid-s12152" xml:space="preserve">angulus 1, re-
              <lb/>
              <note position="left" xlink:label="note-376-04" xlink:href="note-376-04a" xml:space="preserve">15. 1. Theo.</note>
            ctus. </s>
            <s xml:id="echoid-s12153" xml:space="preserve">Poſtremo, quia ar-
              <lb/>
            cus GH, ſemicirculo
              <lb/>
              <note position="left" xlink:label="note-376-05" xlink:href="note-376-05a" xml:space="preserve">2. huius.</note>
            minor eſt, abſcindatur
              <lb/>
              <note position="left" xlink:label="note-376-06" xlink:href="note-376-06a" xml:space="preserve">1. huius.</note>
            ei arcus IK, æqualis, ducaturque per C, K, arcus circuli maximi CK. </s>
            <s xml:id="echoid-s12154" xml:space="preserve">Dico
              <lb/>
              <note position="left" xlink:label="note-376-07" xlink:href="note-376-07a" xml:space="preserve">20. 1. Theo.</note>
            angulum C, æqualem eſſe angulo D. </s>
            <s xml:id="echoid-s12155" xml:space="preserve">Cum enim latera DG, GH, æqualia
              <lb/>
            ſint lateribus CI, IK, contineantq́ue angulos æquales, vt pote rectos; </s>
            <s xml:id="echoid-s12156" xml:space="preserve">æqua-
              <lb/>
            les erunt anguli D, & </s>
            <s xml:id="echoid-s12157" xml:space="preserve">C. </s>
            <s xml:id="echoid-s12158" xml:space="preserve">Ad datum ergo arcum circuli maximi, &</s>
            <s xml:id="echoid-s12159" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12160" xml:space="preserve">Quod fa-
              <lb/>
              <note position="left" xlink:label="note-376-08" xlink:href="note-376-08a" xml:space="preserve">7. huius.</note>
            ciendum erat.</s>
            <s xml:id="echoid-s12161" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div956" type="section" level="1" n="498">
          <head xml:id="echoid-head533" xml:space="preserve">THEOR. 9. PROPOS. 11.</head>
          <p>
            <s xml:id="echoid-s12162" xml:space="preserve">OMNIS trianguli ſphærici maior angulus
              <lb/>
            maiori lateriſubtenditur. </s>
            <s xml:id="echoid-s12163" xml:space="preserve">Et maius latus maiorem
              <lb/>
            angulum ſubtendit.</s>
            <s xml:id="echoid-s12164" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12165" xml:space="preserve">IN triangulo ſphærico ABC, ſit angulus ACB, angulo A, maior. </s>
            <s xml:id="echoid-s12166" xml:space="preserve">Dico
              <lb/>
              <figure xlink:label="fig-376-02" xlink:href="fig-376-02a" number="207">
                <image file="376-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/376-02"/>
              </figure>
            latus AB, maius eſſe latere BC. </s>
            <s xml:id="echoid-s12167" xml:space="preserve">Quoniam angulus
              <lb/>
              <note position="left" xlink:label="note-376-09" xlink:href="note-376-09a" xml:space="preserve">10. huius.</note>
            ACB, maior ponitur angulo A, fiat angulus ACD,
              <lb/>
            angulo A, æqualis, ſecetq́ue arcus CD, arcum AB,
              <lb/>
            in D. </s>
            <s xml:id="echoid-s12168" xml:space="preserve">Quoniam igitur in triangulo ADC, anguli
              <lb/>
            A, & </s>
            <s xml:id="echoid-s12169" xml:space="preserve">ACD, æquales ſunt; </s>
            <s xml:id="echoid-s12170" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s12171" xml:space="preserve">latera AD, CD,
              <lb/>
              <note position="left" xlink:label="note-376-10" xlink:href="note-376-10a" xml:space="preserve">9. huius.</note>
            æqualia. </s>
            <s xml:id="echoid-s12172" xml:space="preserve">Addito ergo communiarcu DB, erunt ar-
              <lb/>
            cus BD, DC, æquales arcui AB: </s>
            <s xml:id="echoid-s12173" xml:space="preserve">Sed arcus BD,
              <lb/>
            DC, ſimul maiores ſunt arcu BC. </s>
            <s xml:id="echoid-s12174" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s12175" xml:space="preserve">arcus
              <lb/>
              <note position="left" xlink:label="note-376-11" xlink:href="note-376-11a" xml:space="preserve">3. huius.</note>
            AB, eodẽ arcu BC, maior erit. </s>
            <s xml:id="echoid-s12176" xml:space="preserve">Quod eſt propoſitũ.</s>
            <s xml:id="echoid-s12177" xml:space="preserve"/>
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