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

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            <s xml:id="echoid-s14140" xml:space="preserve">
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            AB, ad ſinum totum anguli recti C, ita eſſe totum quadrantis A C, ad ſinum
              <lb/>
            totum anguli recti B, & </s>
            <s xml:id="echoid-s14141" xml:space="preserve">ſinum totum quadrantis B C,
              <lb/>
              <figure xlink:label="fig-421-01" xlink:href="fig-421-01a" number="270">
                <image file="421-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/421-01"/>
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            ad ſinum totum anguli recti A.</s>
            <s xml:id="echoid-s14142" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14143" xml:space="preserve">DEINDE ſint duo tantum anguli A, B, recti,
              <lb/>
            eruntq́; </s>
            <s xml:id="echoid-s14144" xml:space="preserve">idcirco arcus AC, BC, quadrantes, & </s>
            <s xml:id="echoid-s14145" xml:space="preserve">C, po-
              <lb/>
              <note position="right" xlink:label="note-421-01" xlink:href="note-421-01a" xml:space="preserve">25. huius.
                <lb/>
              Schol. 26.
                <lb/>
              huius.</note>
            lus arcus AB. </s>
            <s xml:id="echoid-s14146" xml:space="preserve">Itaque rurſus perſpicuum eſt, vt eſt ſi-
              <lb/>
            nus arcus AB, ad ſinum anguli C, hoc eſt, ad ſinum
              <lb/>
            arcus AB, (Eſt enim A B, arcus anguli C, cum C, ſit
              <lb/>
            polus arcus AB, vt oſtenſum eſt) ita eſſe ſinum totum
              <lb/>
            quadrantis AC, ad ſinum totum anguli recti B, & </s>
            <s xml:id="echoid-s14147" xml:space="preserve">ſi-
              <lb/>
            num totum quadrantis BC, ad ſinum totum anguli recti A; </s>
            <s xml:id="echoid-s14148" xml:space="preserve">cum ſemper ſit
              <lb/>
            æqualitatis proportio.</s>
            <s xml:id="echoid-s14149" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s14150" xml:space="preserve">TERTIO ſit angulus duntaxat C, rectus, & </s>
            <s xml:id="echoid-s14151" xml:space="preserve">reliquorum angulorum
              <lb/>
            A, B, vterque recto minor, vel maior; </s>
            <s xml:id="echoid-s14152" xml:space="preserve">vel alter recto maior, & </s>
            <s xml:id="echoid-s14153" xml:space="preserve">alter minor. </s>
            <s xml:id="echoid-s14154" xml:space="preserve">Si
              <lb/>
            igitur vterque recto minor eſt, erunt omnes arcus quadrante minores. </s>
            <s xml:id="echoid-s14155" xml:space="preserve">Produ-
              <lb/>
              <note position="right" xlink:label="note-421-02" xlink:href="note-421-02a" xml:space="preserve">28. huius.</note>
            cantur omnes, & </s>
            <s xml:id="echoid-s14156" xml:space="preserve">fiant quadrantes BD, AE, BF, AG,
              <lb/>
            & </s>
            <s xml:id="echoid-s14157" xml:space="preserve">per puncta D, F, arcus maximi circuli DF, & </s>
            <s xml:id="echoid-s14158" xml:space="preserve">per
              <lb/>
              <note position="right" xlink:label="note-421-03" xlink:href="note-421-03a" xml:space="preserve">20. i Theod.</note>
              <figure xlink:label="fig-421-02" xlink:href="fig-421-02a" number="271">
                <image file="421-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/421-02"/>
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            puncta E, G, arcus maximi circuli E G, ducatur; </s>
            <s xml:id="echoid-s14159" xml:space="preserve">e-
              <lb/>
            runtq́ue anguli D, F, E, G, recti, & </s>
            <s xml:id="echoid-s14160" xml:space="preserve">B, polus arcus
              <lb/>
              <note position="right" xlink:label="note-421-04" xlink:href="note-421-04a" xml:space="preserve">25. huius.
                <lb/>
              Schol. 26.
                <lb/>
              huius.</note>
            DF, & </s>
            <s xml:id="echoid-s14161" xml:space="preserve">A, polus arcus EG; </s>
            <s xml:id="echoid-s14162" xml:space="preserve">ac proinde arcus DF,
              <lb/>
            EG, arcus erunt angulorum B, A. </s>
            <s xml:id="echoid-s14163" xml:space="preserve">Tam verò qua-
              <lb/>
            drans BD, quam AE, arcus eſt anguli recti C, vt ex
              <lb/>
            defin. </s>
            <s xml:id="echoid-s14164" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14165" xml:space="preserve">perſpicuum eſt. </s>
            <s xml:id="echoid-s14166" xml:space="preserve">Quoniam igitur duo circu-
              <lb/>
            li maximi BD, BF, ſe mutuo ſecant in ſphæra in pun
              <lb/>
            cto B, & </s>
            <s xml:id="echoid-s14167" xml:space="preserve">in arcu BD, ſumpta ſunt duo puncta A, D,
              <lb/>
            à quibus ad arcum BF, ducti ſunt arcus perpendiculares AC, DF; </s>
            <s xml:id="echoid-s14168" xml:space="preserve">erit vt ſi-
              <lb/>
            nus arcus AB, ad ſinum arcus AC, ita ſinus arcus BD, ad ſinum arcus DF:
              <lb/>
            </s>
            <s xml:id="echoid-s14169" xml:space="preserve">
              <note position="right" xlink:label="note-421-05" xlink:href="note-421-05a" xml:space="preserve">40. huius.</note>
            & </s>
            <s xml:id="echoid-s14170" xml:space="preserve">permutando, vt ſinus arcus AB, trianguli ABC, ad ſinum quadrantis BD,
              <lb/>
            hoc eſt, ad ſinum totum anguli recti C, in eodem triangulo ABC, ita ſinus
              <lb/>
            arcus AC, trianguli eiuſdem ABC, ad ſinum arcus DF, hoc eſt, ad ſinum an-
              <lb/>
            guli B, eiuſdem trianguli ABC. </s>
            <s xml:id="echoid-s14171" xml:space="preserve">Eodem modo erit, vt ſinus arcus AB, in
              <lb/>
            triangulo ABC, ad ſinum quadrantis AE, hoc eſt, ad ſinum totum anguli
              <lb/>
            recti C, eiuſdem trianguli ABC, ita ſinus arcus BC, eiuſdem trianguli ABC,
              <lb/>
            ad ſinum arcus EG, hoc eſt, ad ſinum anguli A, in eodem triangulo ABC.
              <lb/>
            </s>
            <s xml:id="echoid-s14172" xml:space="preserve">Patet ergo propoſitum.</s>
            <s xml:id="echoid-s14173" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s14174" xml:space="preserve">SI verò vterque angulorum A, B, eſt re-
              <lb/>
              <figure xlink:label="fig-421-03" xlink:href="fig-421-03a" number="272">
                <image file="421-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/421-03"/>
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            cto maior, erit arcus AB, quadrante minor:
              <lb/>
            </s>
            <s xml:id="echoid-s14175" xml:space="preserve">
              <note position="right" xlink:label="note-421-06" xlink:href="note-421-06a" xml:space="preserve">37. huius.</note>
            & </s>
            <s xml:id="echoid-s14176" xml:space="preserve">tam arcus AC, quam BC, quadrante ma-
              <lb/>
              <note position="right" xlink:label="note-421-07" xlink:href="note-421-07a" xml:space="preserve">34. huius.</note>
            ior. </s>
            <s xml:id="echoid-s14177" xml:space="preserve">Producto igitur arcu AB, in vtramque
              <lb/>
            partem, vt ſint quadrantes AE, BD, abſciſ-
              <lb/>
            ſisq́ue quadrantibus AG, BF, ducatur per
              <lb/>
            puncta D, F, arcus maximi circuli DF, & </s>
            <s xml:id="echoid-s14178" xml:space="preserve">per
              <lb/>
              <note position="right" xlink:label="note-421-08" xlink:href="note-421-08a" xml:space="preserve">20. 1 Theod.</note>
            E, G, maximi circuli arcus EG; </s>
            <s xml:id="echoid-s14179" xml:space="preserve">eritq́ue rur-
              <lb/>
              <note position="right" xlink:label="note-421-09" xlink:href="note-421-09a" xml:space="preserve">26. huius.</note>
            ſum B, polus arcus DF, & </s>
            <s xml:id="echoid-s14180" xml:space="preserve">A, polus arcus EG.
              <lb/>
            </s>
            <s xml:id="echoid-s14181" xml:space="preserve">Igitur DF, EG, arcus erunt angulorum B,
              <lb/>
            A; </s>
            <s xml:id="echoid-s14182" xml:space="preserve">necnon tam quadrans BD, quam AE, ar-
              <lb/>
            cus anguli recti C, ex defin. </s>
            <s xml:id="echoid-s14183" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14184" xml:space="preserve">Item propter
              <lb/>
            quadrantes BD, BF, vterque angulus D, F; </s>
            <s xml:id="echoid-s14185" xml:space="preserve">& </s>
            <s xml:id="echoid-s14186" xml:space="preserve">propter quadrantes AE, AG,
              <lb/>
              <note position="right" xlink:label="note-421-10" xlink:href="note-421-10a" xml:space="preserve">25. huius.</note>
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