Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres
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              <pb o="379" file="391" n="391" rhead=""/>
            latera æqualia ſint quadrantes, erunt duo anguli
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            æquales ſuper baſim recti: </s>
            <s xml:id="echoid-s12848" xml:space="preserve">ſi verò vtrumque qua-
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            drante minus ſit, acuti: </s>
            <s xml:id="echoid-s12849" xml:space="preserve">ſi denique maius quadran
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            te, obtuſi. </s>
            <s xml:id="echoid-s12850" xml:space="preserve">Et ſi duo anguli æquales ad baſim ſint
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            recti, erunt duo latera æqualia, quadrantes: </s>
            <s xml:id="echoid-s12851" xml:space="preserve">ſi ve-
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            rò acuti, vtrumque quadrante minus erit: </s>
            <s xml:id="echoid-s12852" xml:space="preserve">ſi deni-
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            que obtuſi, vtrumque quadrante maius.</s>
            <s xml:id="echoid-s12853" xml:space="preserve"/>
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            <s xml:id="echoid-s12854" xml:space="preserve">IN triangulo ſphærico Iſoſcelc ABC, ſint primum duo arcus æquales
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            AB, AC, quadrantes. </s>
            <s xml:id="echoid-s12855" xml:space="preserve">Dico æquales angulos B, C, ad baſim eſſe rectos, Cum
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            enim vterque atcus AB, AC, quadrans ſit, erunt
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              <figure xlink:label="fig-391-01" xlink:href="fig-391-01a" number="229">
                <image file="391-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/391-01"/>
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            ambo ſimul ſemicirculo æquales. </s>
            <s xml:id="echoid-s12856" xml:space="preserve">Quare producto
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            arcu BC, ad D, angulus ACD, æqualis erit an-
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              <note position="right" xlink:label="note-391-01" xlink:href="note-391-01a" xml:space="preserve">14. huius.</note>
            gulo B: </s>
            <s xml:id="echoid-s12857" xml:space="preserve">ſed angulus B, angulo ACB, æqualis eſt.
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            </s>
            <s xml:id="echoid-s12858" xml:space="preserve">
              <note position="right" xlink:label="note-391-02" xlink:href="note-391-02a" xml:space="preserve">8. huius.</note>
            Igitur & </s>
            <s xml:id="echoid-s12859" xml:space="preserve">angulus, ACD, angulo ACB, æqualis
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            erit; </s>
            <s xml:id="echoid-s12860" xml:space="preserve">atque adeò, cum duo anguli ad C, duobus re-
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              <note position="right" xlink:label="note-391-03" xlink:href="note-391-03a" xml:space="preserve">5. huius.</note>
            ctis ęquales ſint, erit vterque angulus ad C, rectus.
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            </s>
            <s xml:id="echoid-s12861" xml:space="preserve">Qnare & </s>
            <s xml:id="echoid-s12862" xml:space="preserve">angulus B, quirecto ACB, æqualis eſt,
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              <note position="right" xlink:label="note-391-04" xlink:href="note-391-04a" xml:space="preserve">8. huius.</note>
            rectus erit. </s>
            <s xml:id="echoid-s12863" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12864" xml:space="preserve"/>
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            <s xml:id="echoid-s12865" xml:space="preserve">SIT deinde vterque arcuum AB, AC, æqua-
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            lium quadrante minor. </s>
            <s xml:id="echoid-s12866" xml:space="preserve">Dico angulos B, C, æqua-
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            les eſſe acutos. </s>
            <s xml:id="echoid-s12867" xml:space="preserve">Cum enim vterque arcus AB, AC,
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            quadrante minor ſit, erunt ambo ſimul ſemicircu-
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            lo minores. </s>
            <s xml:id="echoid-s12868" xml:space="preserve">Quare angulus ACD, maior erit
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              <note position="right" xlink:label="note-391-05" xlink:href="note-391-05a" xml:space="preserve">14. huius.</note>
            angulo B, hoceſt, angulo ACB; </s>
            <s xml:id="echoid-s12869" xml:space="preserve">cum anguli B,
              <lb/>
              <note position="right" xlink:label="note-391-06" xlink:href="note-391-06a" xml:space="preserve">8. huius.</note>
            & </s>
            <s xml:id="echoid-s12870" xml:space="preserve">ACB, æquales ſint. </s>
            <s xml:id="echoid-s12871" xml:space="preserve">Cum ergo duo anguli ad C, æquales ſint duobus
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              <note position="right" xlink:label="note-391-07" xlink:href="note-391-07a" xml:space="preserve">5. huius.</note>
            rectis, erit angulus ACB, recto minor; </s>
            <s xml:id="echoid-s12872" xml:space="preserve">atque adeo angulus B, qui ei æqua-
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              <note position="right" xlink:label="note-391-08" xlink:href="note-391-08a" xml:space="preserve">8. huius.</note>
            lis eſt, recto quoq; </s>
            <s xml:id="echoid-s12873" xml:space="preserve">minor erit. </s>
            <s xml:id="echoid-s12874" xml:space="preserve">Sunt ergo duo anguli B, & </s>
            <s xml:id="echoid-s12875" xml:space="preserve">ACB, acuti. </s>
            <s xml:id="echoid-s12876" xml:space="preserve">Quod
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            eſt propoſitum.</s>
            <s xml:id="echoid-s12877" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12878" xml:space="preserve">SIT poſtremo vterque arcuum AB, AC, quadrante maior. </s>
            <s xml:id="echoid-s12879" xml:space="preserve">Dico angu-
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            los æquales, B, C, eſſe obtuſos. </s>
            <s xml:id="echoid-s12880" xml:space="preserve">Cum enim vterque arcus AB, AC, maior ſit
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            quadrante, eruntambo maiores ſemicirculo. </s>
            <s xml:id="echoid-s12881" xml:space="preserve">Quare angulus ACD, minor
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              <note position="right" xlink:label="note-391-09" xlink:href="note-391-09a" xml:space="preserve">14. huius.</note>
            erit angulo B, hoc eſt, angulo ACB, qui angulo B, æqualis eſt. </s>
            <s xml:id="echoid-s12882" xml:space="preserve">Cum ergo
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              <note position="right" xlink:label="note-391-10" xlink:href="note-391-10a" xml:space="preserve">8. huius.</note>
            duo anguliad C, duobus rectis ſint æquales, erit angulus ACB, recto ma-
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              <note position="right" xlink:label="note-391-11" xlink:href="note-391-11a" xml:space="preserve">5. huius.</note>
            ior, hoc eſt, obtuſus; </s>
            <s xml:id="echoid-s12883" xml:space="preserve">atque idcirco & </s>
            <s xml:id="echoid-s12884" xml:space="preserve">angulus B, qui ei æqualis eſt, obtuſus
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              <note position="right" xlink:label="note-391-12" xlink:href="note-391-12a" xml:space="preserve">8. huius.</note>
            erit. </s>
            <s xml:id="echoid-s12885" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12886" xml:space="preserve"/>
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            <s xml:id="echoid-s12887" xml:space="preserve">SED iam vterque angulorum æqualium B, C, ſit rectus. </s>
            <s xml:id="echoid-s12888" xml:space="preserve">Dico vtrumque
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            arcum AB, AC, quadrantem eſſe. </s>
            <s xml:id="echoid-s12889" xml:space="preserve">Cum enim ACB, rectus ſit, & </s>
            <s xml:id="echoid-s12890" xml:space="preserve">duo angu-
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            li ad C, æquales duobus rectis, erit quoque ACD, rectus, ac proinde recto
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              <note position="right" xlink:label="note-391-13" xlink:href="note-391-13a" xml:space="preserve">5. huius.</note>
            B, æqualis. </s>
            <s xml:id="echoid-s12891" xml:space="preserve">Suntergo duo arcus AB, AC, ſimul ſemicirculo æquales, ac pro-
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              <note position="right" xlink:label="note-391-14" xlink:href="note-391-14a" xml:space="preserve">15 huius.</note>
            pterea cum ipſi æquales ponantur, vterq; </s>
            <s xml:id="echoid-s12892" xml:space="preserve">quadrans erit. </s>
            <s xml:id="echoid-s12893" xml:space="preserve">Quod eſt propoſitũ.</s>
            <s xml:id="echoid-s12894" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12895" xml:space="preserve">DEINDE vterque angulorum B, C, ſit acutus. </s>
            <s xml:id="echoid-s12896" xml:space="preserve">Dico vtrumque arcum
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            AB, AC, quadrante minorem eſſe. </s>
            <s xml:id="echoid-s12897" xml:space="preserve">Cum enim duo anguliad C, æquales duo-
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              <note position="right" xlink:label="note-391-15" xlink:href="note-391-15a" xml:space="preserve">5. huius.</note>
            </s>
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