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

Table of figures

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            <s xml:id="echoid-s12990" xml:space="preserve">
              <pb o="382" file="394" n="394" rhead=""/>
            erit vterque angulus A, B, rectus. </s>
            <s xml:id="echoid-s12991" xml:space="preserve">Rectus igitur eſt angulus. </s>
            <s xml:id="echoid-s12992" xml:space="preserve">A.</s>
            <s xml:id="echoid-s12993" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12994" xml:space="preserve">SIT deinde baſis BC, quadrante minor. </s>
            <s xml:id="echoid-s12995" xml:space="preserve">Dico angulum BAC, eſſe acu-
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            tum. </s>
            <s xml:id="echoid-s12996" xml:space="preserve">Producto enim arcu BC, ad D, vt ſit BD, quadrans, ducatur per pun-
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              <figure xlink:label="fig-394-01" xlink:href="fig-394-01a" number="233">
                <image file="394-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/394-01"/>
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            cta A, D, arcus AD, cir-
              <lb/>
              <note position="left" xlink:label="note-394-01" xlink:href="note-394-01a" xml:space="preserve">20. 1 Theod.</note>
            culi maximi. </s>
            <s xml:id="echoid-s12997" xml:space="preserve">Quoniã igi-
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            tur duo arcus BA, BD,
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            quadrãtes ſunt, erit vter-
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              <note position="left" xlink:label="note-394-02" xlink:href="note-394-02a" xml:space="preserve">25. huius.</note>
            que angulus D, & </s>
            <s xml:id="echoid-s12998" xml:space="preserve">DAB,
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            rectus. </s>
            <s xml:id="echoid-s12999" xml:space="preserve">Acutus igitur eſt
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            angulus BAC.</s>
            <s xml:id="echoid-s13000" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13001" xml:space="preserve">SIT tãdem baſis BC,
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            maior quadrante. </s>
            <s xml:id="echoid-s13002" xml:space="preserve">Dico
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            angulum BAC, obtuſum
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            eſſe. </s>
            <s xml:id="echoid-s13003" xml:space="preserve">Abſcindatur BD, ar-
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              <note position="left" xlink:label="note-394-03" xlink:href="note-394-03a" xml:space="preserve">1. huius.</note>
            cus æqualis quadrãti AB;
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            </s>
            <s xml:id="echoid-s13004" xml:space="preserve">& </s>
            <s xml:id="echoid-s13005" xml:space="preserve">per puncta A, D, arcus
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            circuli maximi deſcriba-
              <lb/>
              <note position="left" xlink:label="note-394-04" xlink:href="note-394-04a" xml:space="preserve">20. 1 Theod.</note>
            tur AD. </s>
            <s xml:id="echoid-s13006" xml:space="preserve">Et quia duo arcus BA, BD, quadrantes ſunt, erit vterque angu-
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            lus BDA, DAB, rectus. </s>
            <s xml:id="echoid-s13007" xml:space="preserve">Obtuſus igitur eſt BAC, angulus.</s>
            <s xml:id="echoid-s13008" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">25. huius.</note>
          <p>
            <s xml:id="echoid-s13009" xml:space="preserve">DICO præterea, in omnibus his punctum A, polum eſſe baſis BC. </s>
            <s xml:id="echoid-s13010" xml:space="preserve">Cum
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            enim latera AB, AC, ponantur quadrantes, erit vterque angulus ad baſim
              <lb/>
              <note position="left" xlink:label="note-394-06" xlink:href="note-394-06a" xml:space="preserve">25. huius.</note>
            BC, rectus; </s>
            <s xml:id="echoid-s13011" xml:space="preserve">ac propterea vterque arcus AB, AC, per polum arcus BC, tran-
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              <note position="left" xlink:label="note-394-07" xlink:href="note-394-07a" xml:space="preserve">23. 1 Theod.</note>
            ſibit. </s>
            <s xml:id="echoid-s13012" xml:space="preserve">Siue igitur BC, quadrans ſit, ſiue minor, ſiue maior quadrante; </s>
            <s xml:id="echoid-s13013" xml:space="preserve">Et ſi-
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            ue angulus A, ſit rectus, ſiue acutus, ſiue obtuſus, ſemper punctum A, vbi
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            coëunt arcus AB, AC, polus erit baſis BC. </s>
            <s xml:id="echoid-s13014" xml:space="preserve">In omni igitur triangulo Ifo-
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            ſcele ſphærico, cuius duo latera, &</s>
            <s xml:id="echoid-s13015" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13016" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s13017" xml:space="preserve"/>
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        <div xml:id="echoid-div1030" type="section" level="1" n="520">
          <head xml:id="echoid-head555" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s13018" xml:space="preserve">_IMMO_ in omni triangulo ſphærico babente duos angulos rectos, demonſtrabi-
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            mus eodem modo, in concurſu duorum laterum, quæ rectos ſubtendunt angulos, re-
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            liqui lateris, quod rectis angulis adiacet, polum eſſe, etiam ſinondum ſciatur, duo
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            illa latera eſſe quadrantes. </s>
            <s xml:id="echoid-s13019" xml:space="preserve">Sint enim intrangulo ſphærico _ABC,_ duo anguli recti
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            _B, C._ </s>
            <s xml:id="echoid-s13020" xml:space="preserve">Dico _A,_ polum eſſe arcus _BC;_ </s>
            <s xml:id="echoid-s13021" xml:space="preserve">Nam vterque arcus _AB, AC,_ per polum arcus
              <lb/>
              <note position="left" xlink:label="note-394-08" xlink:href="note-394-08a" xml:space="preserve">13. 1. Theod.</note>
            BC, tranſibits ac propterea A, polus erit arcus BC.</s>
            <s xml:id="echoid-s13022" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13023" xml:space="preserve">_VERVM_ eſt tamen, duos arcus AB, AC, eſſe ſemper quadrantes, propter an-
              <lb/>
              <note position="left" xlink:label="note-394-09" xlink:href="note-394-09a" xml:space="preserve">25. huius.</note>
            gulos rectos _B, C._</s>
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        <div xml:id="echoid-div1033" type="section" level="1" n="521">
          <head xml:id="echoid-head556" xml:space="preserve">THEOR. 25. PROPOS. 27.</head>
          <p>
            <s xml:id="echoid-s13025" xml:space="preserve">IN omni triangulo ſphærico, cuius omnes ar-
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            cus ſint quadrante maiores, vel vnus quadrans,
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            & </s>
            <s xml:id="echoid-s13026" xml:space="preserve">reliqui duo quadrante maiores, omnes tres an-
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            guli ſunt obtuſi.</s>
            <s xml:id="echoid-s13027" xml:space="preserve"/>
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