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

Table of handwritten notes

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            <s xml:id="echoid-s13141" xml:space="preserve">
              <pb o="385" file="397" n="397" rhead=""/>
            duos quidem maiores quadrante, & </s>
            <s xml:id="echoid-s13142" xml:space="preserve">vnum quadranti æqualem: </s>
            <s xml:id="echoid-s13143" xml:space="preserve">Sed poſſunt eſſe duo
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            quidem quadrante maiores, reliquus verò quadrante minor. </s>
            <s xml:id="echoid-s13144" xml:space="preserve">Sint enim duo ſemicir-
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            culi in ſuperficie ſphæra continentes angulos _A, C,_ obtuſos. </s>
            <s xml:id="echoid-s13145" xml:space="preserve">Si igitur accipiantur
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            duo arcus æquales _AB, AD,_ quorum vterque
              <lb/>
              <figure xlink:label="fig-397-01" xlink:href="fig-397-01a" number="238">
                <image file="397-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/397-01"/>
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            maior ſit ſesqusaltero quadrante, ita vt ambo
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            ſimul tres quadrantes ſuperent; </s>
            <s xml:id="echoid-s13146" xml:space="preserve">deſeribatur
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            autem per puncta _B, D,_ arcus circuli maximi
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              <note position="right" xlink:label="note-397-01" xlink:href="note-397-01a" xml:space="preserve">20. 1 Theod.</note>
            _BD;_ </s>
            <s xml:id="echoid-s13147" xml:space="preserve">erit hic arcus _BD,_ quadrante minor. </s>
            <s xml:id="echoid-s13148" xml:space="preserve">Cum
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            enim tres arcus _AB, AD, BD,_ integro circu-
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              <note position="right" xlink:label="note-397-02" xlink:href="note-397-02a" xml:space="preserve">4. huius.</note>
            lo minores ſint, ponatur autem duo arcus _AB,_
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            _AD,_ tribus quadrantibus maiores; </s>
            <s xml:id="echoid-s13149" xml:space="preserve">erit neceſ-
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            ſario tertius arcus _BD,_ minor quadrãte: </s>
            <s xml:id="echoid-s13150" xml:space="preserve">Alias,
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            ſi quadrans eſſet, aut maior quadrante, ſupe-
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            rarent tres arcus trianguli _ABC,_ integrum
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            circulum. </s>
            <s xml:id="echoid-s13151" xml:space="preserve">Quoniam igitur duo anguli _B,_ & </s>
            <s xml:id="echoid-s13152" xml:space="preserve">_D,_ in triangulo _ABD,_ obtuſi ſunt,
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              <note position="right" xlink:label="note-397-03" xlink:href="note-397-03a" xml:space="preserve">25. huius.</note>
            necnon & </s>
            <s xml:id="echoid-s13153" xml:space="preserve">tertius angulus _A,_ obtuſus quoque, ex bypotheſi; </s>
            <s xml:id="echoid-s13154" xml:space="preserve">erunt omnes tres anguli
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            _A, B, D,_ obtuſi; </s>
            <s xml:id="echoid-s13155" xml:space="preserve">& </s>
            <s xml:id="echoid-s13156" xml:space="preserve">tamen neque omnes arcus ſunt quadrante maiores; </s>
            <s xml:id="echoid-s13157" xml:space="preserve">neque duo
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            tantum, & </s>
            <s xml:id="echoid-s13158" xml:space="preserve">tertius quadrans; </s>
            <s xml:id="echoid-s13159" xml:space="preserve">ſed duo quidem _AB, AD,_ quadrante maiores ſunt,
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            at tertius arcus _BD,_ quadrante minor, vt oſtendimus.</s>
            <s xml:id="echoid-s13160" xml:space="preserve"/>
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        <div xml:id="echoid-div1040" type="section" level="1" n="523">
          <head xml:id="echoid-head558" xml:space="preserve">THEOR. 26. PROPOS. 28.</head>
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            <s xml:id="echoid-s13161" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cuius
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            omnes arcus ſint quadrante minores, reliqui duo
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            anguli acuti ſunt. </s>
            <s xml:id="echoid-s13162" xml:space="preserve">Et ſi reliqui duo anguli ſint acu-
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            ti, erunt ſinguli arcus quadrante minores.</s>
            <s xml:id="echoid-s13163" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13164" xml:space="preserve">IN triangulo ſphærico ABC, ſit angulus B, rectus, & </s>
            <s xml:id="echoid-s13165" xml:space="preserve">ſinguli arcus qua-
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            drante minores. </s>
            <s xml:id="echoid-s13166" xml:space="preserve">Dico reliquos angulos A, C, eſſe acutos. </s>
            <s xml:id="echoid-s13167" xml:space="preserve">Producantur enim
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            arcus BA, BC, vt ſint quadrantes BD, BE; </s>
            <s xml:id="echoid-s13168" xml:space="preserve">& </s>
            <s xml:id="echoid-s13169" xml:space="preserve">per puncta C, D, arcus maxi-
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            mi circuli ducatur CD, necnon per puncta A, E, ar-
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              <note position="right" xlink:label="note-397-04" xlink:href="note-397-04a" xml:space="preserve">20. 1 Theod.</note>
              <figure xlink:label="fig-397-02" xlink:href="fig-397-02a" number="239">
                <image file="397-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/397-02"/>
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            cus circuli maximi AE. </s>
            <s xml:id="echoid-s13170" xml:space="preserve">Et quoniam quadrans BD,
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            ob angulum rectum B, per polos arcus BC, tranſit,
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              <note position="right" xlink:label="note-397-05" xlink:href="note-397-05a" xml:space="preserve">13. 1. Theod.
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              Coroll. 16.</note>
            abeſtq; </s>
            <s xml:id="echoid-s13171" xml:space="preserve">polus circuli maximi quadrate circuli maxi-
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            mi ab eo, erit D, polus arcus BC. </s>
            <s xml:id="echoid-s13172" xml:space="preserve">Igitur erit angu-
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              <note position="right" xlink:label="note-397-06" xlink:href="note-397-06a" xml:space="preserve">1. Theod.</note>
            lus BCD, rectus; </s>
            <s xml:id="echoid-s13173" xml:space="preserve">ac propterea angulus ACB, acu-
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              <note position="right" xlink:label="note-397-07" xlink:href="note-397-07a" xml:space="preserve">15. 1 Theod.</note>
            tus. </s>
            <s xml:id="echoid-s13174" xml:space="preserve">Eodem modo, quia quadrans BE, ob angulum
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            rectum B, per polos arcus AB, tranſit, abeſtq́; </s>
            <s xml:id="echoid-s13175" xml:space="preserve">polus
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              <note position="right" xlink:label="note-397-08" xlink:href="note-397-08a" xml:space="preserve">13. 1 Theod.</note>
            circuli maximi quadrante maximi circuli ab eo, erit
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              <note position="right" xlink:label="note-397-09" xlink:href="note-397-09a" xml:space="preserve">Coroll. 16.</note>
            E, polus arcus AB, Igitur angulus EAB, rectus erit;
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            </s>
            <s xml:id="echoid-s13176" xml:space="preserve">
              <note position="right" xlink:label="note-397-10" xlink:href="note-397-10a" xml:space="preserve">1. Theod.</note>
            ac proinde BAC, acutus.</s>
            <s xml:id="echoid-s13177" xml:space="preserve"/>
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          <note position="right" xml:space="preserve">15. 1 Theod.</note>
          <p>
            <s xml:id="echoid-s13178" xml:space="preserve">SED iam in eodem triangulo ABC, angulus B, rectus ſit, & </s>
            <s xml:id="echoid-s13179" xml:space="preserve">reliqui A,
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            C, acuti. </s>
            <s xml:id="echoid-s13180" xml:space="preserve">Dico ſingulos arcus eſſe quadrante minores. </s>
            <s xml:id="echoid-s13181" xml:space="preserve">Fiant enim recti angu-
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            li BCD, BAE. </s>
            <s xml:id="echoid-s13182" xml:space="preserve">Quia igitur vterque angulus B, BCD, rectus eſt, erit vter-
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              <note position="right" xlink:label="note-397-12" xlink:href="note-397-12a" xml:space="preserve">25. huius.</note>
            que arcus BD, CD, quadrans. </s>
            <s xml:id="echoid-s13183" xml:space="preserve">Arcus igitur BA, quadrante minor eſt. </s>
            <s xml:id="echoid-s13184" xml:space="preserve">Eo-
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            dem modo arcus BC, minor erit quadrante; </s>
            <s xml:id="echoid-s13185" xml:space="preserve">propterea quòd & </s>
            <s xml:id="echoid-s13186" xml:space="preserve">arcus BE, AE,
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              <note position="right" xlink:label="note-397-13" xlink:href="note-397-13a" xml:space="preserve">25. huius.</note>
            </s>
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