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

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              <figure xlink:label="fig-053-01" xlink:href="fig-053-01a" number="59">
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            rum A B C, D E F, in pun-
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            cta A, D: </s>
            <s xml:id="echoid-s1550" xml:space="preserve">quod etiam con-
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            tingere poteſt, quando ſe-
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            gmenta A G C, D H F, ſe-
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            micirculo ſunt maiora. </s>
            <s xml:id="echoid-s1551" xml:space="preserve">Du-
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            ctis igitur rectis A B, D E,
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            erũt anguli G A B, H D E,
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            recti, ex defin. </s>
            <s xml:id="echoid-s1552" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1553" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1554" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1555" xml:space="preserve">Eu-
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            clid. </s>
            <s xml:id="echoid-s1556" xml:space="preserve">Quare, vt prius, æqua
              <lb/>
              <note position="right" xlink:label="note-053-01" xlink:href="note-053-01a" xml:space="preserve">47. primi.</note>
            lia erunt quadrata rectarũ
              <lb/>
            G A, A B, quadratis recta-
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            rum H D, D E: </s>
            <s xml:id="echoid-s1557" xml:space="preserve">Sunt autẽ
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            quadrata ex G A, H D, æ-
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            qualia, quòd & </s>
            <s xml:id="echoid-s1558" xml:space="preserve">rectæ G A,
              <lb/>
              <note position="right" xlink:label="note-053-02" xlink:href="note-053-02a" xml:space="preserve">29. tertij.</note>
            H D, æquales ſint, ob æqua
              <lb/>
            les arcus A G, D H. </s>
            <s xml:id="echoid-s1559" xml:space="preserve">Igitur
              <lb/>
            & </s>
            <s xml:id="echoid-s1560" xml:space="preserve">quadrata ex A B, D E, æ-
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            qualia erunt; </s>
            <s xml:id="echoid-s1561" xml:space="preserve">& </s>
            <s xml:id="echoid-s1562" xml:space="preserve">propterea
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            & </s>
            <s xml:id="echoid-s1563" xml:space="preserve">rectæ A B, D E, æquales.
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            </s>
            <s xml:id="echoid-s1564" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s1565" xml:space="preserve">arcus A B, D E,
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            æquales erunt. </s>
            <s xml:id="echoid-s1566" xml:space="preserve">Quod eſt {pro}-
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            poſitum. </s>
            <s xml:id="echoid-s1567" xml:space="preserve">Itaque ſi in diametris circulorum æqualium æqualia circulorum
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            ſegmenta ad angulos rectos inſiſtant, &</s>
            <s xml:id="echoid-s1568" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1569" xml:space="preserve">Quod erat demonſtrandum.</s>
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          <head xml:id="echoid-head100" xml:space="preserve">THEOR. 12. PROPOS. 12.</head>
          <note position="right" xml:space="preserve">16.</note>
          <p>
            <s xml:id="echoid-s1571" xml:space="preserve">SI in diametris circulorum æqualium, æqua-
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            lia ſegmenta circulorum erigantur, & </s>
            <s xml:id="echoid-s1572" xml:space="preserve">ab ipſis ſe-
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            gmentis æquales circunferentiæ ad extremitates
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            ſegmentorum deſumantur minores dimidijs ip-
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            ſorum partibus, ab ipſis autem circulis æquales
              <lb/>
            circunferentiæ ſumantur ad eaſdem partes, quæ
              <lb/>
            ſunt ad extremitates diametrorum, rectæ lineæ
              <lb/>
            ductæ à punctis in circunferentijs ſegmentorum
              <lb/>
            ad puncta in circunferentijs circulorum, erunt
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            æquales.</s>
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            <s xml:id="echoid-s1574" xml:space="preserve">REPETANTVR figuræ propoſition is præcedentis, cum eiſdẽ con-
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            ſtructionibus, ponanturq́; </s>
            <s xml:id="echoid-s1575" xml:space="preserve">arcus A B, D E, æquales. </s>
            <s xml:id="echoid-s1576" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s1577" xml:space="preserve">rectas G B, H E,
              <lb/>
              <note position="right" xlink:label="note-053-04" xlink:href="note-053-04a" xml:space="preserve">27. tertij.</note>
            æquales eſſe. </s>
            <s xml:id="echoid-s1578" xml:space="preserve">Quoniam enim, vt in præcedenti propoſ. </s>
            <s xml:id="echoid-s1579" xml:space="preserve">demonſtratum eſt,
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              <note position="right" xlink:label="note-053-05" xlink:href="note-053-05a" xml:space="preserve">29. tertij.</note>
              <note position="right" xlink:label="note-053-06" xlink:href="note-053-06a" xml:space="preserve">26. primi.</note>
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