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

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          <pb o="388" file="400" n="400" rhead=""/>
        </div>
        <div xml:id="echoid-div1049" type="section" level="1" n="526">
          <head xml:id="echoid-head561" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s13286" xml:space="preserve">_PORRO_ neque hæc propoſitio conuerti poteſt. </s>
            <s xml:id="echoid-s13287" xml:space="preserve">Non enim omne triangulum ſphæ-
              <lb/>
            ric@m, cuius ſinguli arcus quadrante ſunt minores, neceſſario habet omnes angulos
              <lb/>
            acutos. </s>
            <s xml:id="echoid-s13288" xml:space="preserve">Nam vnus angulus poteſt eſſe rectus, & </s>
            <s xml:id="echoid-s13289" xml:space="preserve">reliqui duo acuti, vt ex propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s13290" xml:space="preserve">præcedenti conſtat. </s>
            <s xml:id="echoid-s13291" xml:space="preserve">Immo & </s>
            <s xml:id="echoid-s13292" xml:space="preserve">vnus poteſt eſſe obtuſus, & </s>
            <s xml:id="echoid-s13293" xml:space="preserve">reliqui acuti. </s>
            <s xml:id="echoid-s13294" xml:space="preserve">Sint enim
              <lb/>
              <figure xlink:label="fig-400-01" xlink:href="fig-400-01a" number="245">
                <image file="400-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/400-01"/>
              </figure>
            duo ſemicirculi _ABC, ADC,_ continentes angulos _A,_
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            C, obtuſos, accipianturq́; </s>
            <s xml:id="echoid-s13295" xml:space="preserve">duo arcus æquales _AB, AD,_
              <lb/>
            quorum vterque ſesquialterum quadrantem ſuperet, & </s>
            <s xml:id="echoid-s13296" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-400-01" xlink:href="note-400-01a" xml:space="preserve">20. i Theod.</note>
            per puncta _B, D,_ arcus circuli maximi deſcribatur _BD,_
              <lb/>
            qui minor erit quadrante, vt in ſcbolio propoſ. </s>
            <s xml:id="echoid-s13297" xml:space="preserve">27. </s>
            <s xml:id="echoid-s13298" xml:space="preserve">oſten-
              <lb/>
            dimus. </s>
            <s xml:id="echoid-s13299" xml:space="preserve">Erunt igitur in triangulo _BCD,_ tres arcus _BC,_
              <lb/>
            _CD, BD,_ ſinguli quadrante minores, & </s>
            <s xml:id="echoid-s13300" xml:space="preserve">tamen non om-
              <lb/>
              <note position="left" xlink:label="note-400-02" xlink:href="note-400-02a" xml:space="preserve">25. huius.</note>
            nes anguli in triangulo _BCD,_ acuti ſunt, ſed _C,_ qui-
              <lb/>
            dem obtuſus, ex bypotbeſi, at verò _B, D,_ acuti, propterea quòd duo latera _CB,_
              <lb/>
            CD, æqualia ſunt, & </s>
            <s xml:id="echoid-s13301" xml:space="preserve">quadrante minora.</s>
            <s xml:id="echoid-s13302" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1051" type="section" level="1" n="527">
          <head xml:id="echoid-head562" xml:space="preserve">THEOR. 28. PROPOS. 30.</head>
          <p>
            <s xml:id="echoid-s13303" xml:space="preserve">IN quolibet triangulo ſphærico, cuius vnus
              <lb/>
            quidem arcus quadrante maior ſit, reliquorum
              <lb/>
            verò vterque quadrante minor, nullus anguloium
              <lb/>
            rectus erit.</s>
            <s xml:id="echoid-s13304" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13305" xml:space="preserve">IN triangulo ſphærico ABC, ſit quidem arcus AC, quadrante maior, at
              <lb/>
            tam AB, quam BC, minor quadrante. </s>
            <s xml:id="echoid-s13306" xml:space="preserve">Dico nullum angulorum eſſe rectum.
              <lb/>
            </s>
            <s xml:id="echoid-s13307" xml:space="preserve">Sit enim ſi fieri poteſt, angulus B, qui arcui AC, quadrante maiori opponi-
              <lb/>
            tur, rcctus. </s>
            <s xml:id="echoid-s13308" xml:space="preserve">Abſciſlo igitur AD, quadrante, & </s>
            <s xml:id="echoid-s13309" xml:space="preserve">producto arcu AB, ad E, vt
              <lb/>
              <figure xlink:label="fig-400-02" xlink:href="fig-400-02a" number="246">
                <image file="400-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/400-02"/>
              </figure>
            AE, ſit etiam quadrans, & </s>
            <s xml:id="echoid-s13310" xml:space="preserve">per puncta D, E, arcu D E,
              <lb/>
            circuli maximi deſcripto, qui arcum BC, ſecet in
              <lb/>
              <note position="left" xlink:label="note-400-03" xlink:href="note-400-03a" xml:space="preserve">20. 1 Theod.</note>
            F; </s>
            <s xml:id="echoid-s13311" xml:space="preserve">erit vterque angulus D, E, rectus: </s>
            <s xml:id="echoid-s13312" xml:space="preserve">Ponitur autem
              <lb/>
              <note position="left" xlink:label="note-400-04" xlink:href="note-400-04a" xml:space="preserve">25. huius.</note>
            & </s>
            <s xml:id="echoid-s13313" xml:space="preserve">angulus ABC, rectus, hoc eſt, EBC; </s>
            <s xml:id="echoid-s13314" xml:space="preserve">ſunt enim
              <lb/>
            duo anguli ad B, duobus rectis æquales. </s>
            <s xml:id="echoid-s13315" xml:space="preserve">Vterque igi-
              <lb/>
              <note position="left" xlink:label="note-400-05" xlink:href="note-400-05a" xml:space="preserve">5. huius.</note>
            tur arcus EF, BF, quadrans erit, atque adeo arcus
              <lb/>
              <note position="left" xlink:label="note-400-06" xlink:href="note-400-06a" xml:space="preserve">25. huius.</note>
            BC, maior quadrante, quod eſf abſurdum, cum po-
              <lb/>
            natur quadrante minor. </s>
            <s xml:id="echoid-s13316" xml:space="preserve">Non ergo angulus B, rectus
              <lb/>
            eſſe poteſt.</s>
            <s xml:id="echoid-s13317" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13318" xml:space="preserve">QVOD ſi angulus C, rectus eſſe dicatur, erit, ſi
              <lb/>
            eadem fiat conſtructio, eodem modo vterque arcus
              <lb/>
            DF, CF, quadrans: </s>
            <s xml:id="echoid-s13319" xml:space="preserve">(Nam & </s>
            <s xml:id="echoid-s13320" xml:space="preserve">angulus CDF, rectus eſt, cum vterque D, E,
              <lb/>
              <note position="left" xlink:label="note-400-07" xlink:href="note-400-07a" xml:space="preserve">25. huius.</note>
            rectus ſit, ob quadrantes AD, AE.) </s>
            <s xml:id="echoid-s13321" xml:space="preserve">atque adeo arcus BC, quadrante maior.
              <lb/>
            </s>
            <s xml:id="echoid-s13322" xml:space="preserve">
              <note position="left" xlink:label="note-400-08" xlink:href="note-400-08a" xml:space="preserve">25. huius.</note>
            quod eſt contra hypotheſim.</s>
            <s xml:id="echoid-s13323" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13324" xml:space="preserve">SI denique angulus A, rectus concedatur, ſi ex arcu CA, </s>
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