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

Table of figures

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            ex eiſdem polis A, B, ad interualla AC, BC, delineentur circuli non maxi-
              <lb/>
            mi KCN, OCP, qui prioribus erunt paralleli. </s>
            <s xml:id="echoid-s15977" xml:space="preserve">Deſcriptis deinde in alio cir
              <lb/>
              <note position="right" xlink:label="note-463-01" xlink:href="note-463-01a" xml:space="preserve">2. 2. Theod.</note>
            culo communibus ſectionibus horum circulorum cum circulo ABGF, quæ
              <lb/>
            inter ſe parallelę erunt, ſeſeq́; </s>
            <s xml:id="echoid-s15978" xml:space="preserve">ad angulos rectos ſecabunt; </s>
            <s xml:id="echoid-s15979" xml:space="preserve">(Nam AX, ex A,
              <lb/>
              <note position="right" xlink:label="note-463-02" xlink:href="note-463-02a" xml:space="preserve">16. vndec.</note>
            polo circuli BF, in ſphæræ centrum X, cadens ad ipſum circulum recta eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s15980" xml:space="preserve">
              <note position="right" xlink:label="note-463-03" xlink:href="note-463-03a" xml:space="preserve">Schol. 10.</note>
            ac propterea, ex defin. </s>
            <s xml:id="echoid-s15981" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15982" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15983" xml:space="preserve">11. </s>
            <s xml:id="echoid-s15984" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s15985" xml:space="preserve">anguli ad X, recti erunt. </s>
            <s xml:id="echoid-s15986" xml:space="preserve">Ex quo fit, etiam
              <lb/>
              <note position="right" xlink:label="note-463-04" xlink:href="note-463-04a" xml:space="preserve">1. Theod.</note>
            angulos ad R, S, Y, rectos eſſe, ob parallelas lineas BF,
              <emph style="sc">K</emph>
            N, & </s>
            <s xml:id="echoid-s15987" xml:space="preserve">AG, OP.) </s>
            <s xml:id="echoid-s15988" xml:space="preserve">erit
              <lb/>
              <note position="right" xlink:label="note-463-05" xlink:href="note-463-05a" xml:space="preserve">29. primi.</note>
            AV, ſinus rectus quadrantis AB; </s>
            <s xml:id="echoid-s15989" xml:space="preserve">
              <emph style="sc">K</emph>
            Y, ſinus rectus arcus AC, ſiue arcus AK,
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            illi, ex defin. </s>
            <s xml:id="echoid-s15990" xml:space="preserve">poli, æqualis; </s>
            <s xml:id="echoid-s15991" xml:space="preserve">BR, ſinus verſus arcus BC, ſeu arcus BO, illi, ex
              <lb/>
            poli defin. </s>
            <s xml:id="echoid-s15992" xml:space="preserve">æqualis; </s>
            <s xml:id="echoid-s15993" xml:space="preserve">BQ, (ducta
              <emph style="sc">K</emph>
            Q, ad BF, perpendiculari) ſinus verſus ar-
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            cus
              <emph style="sc">Bk</emph>
            , quo arcus AB, AC, inter ſe differunt; </s>
            <s xml:id="echoid-s15994" xml:space="preserve">Denique
              <emph style="sc">K</emph>
            S, ſinus verſus ar-
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            cus
              <emph style="sc">K</emph>
            C. </s>
            <s xml:id="echoid-s15995" xml:space="preserve">Itaque ſi ſumatur DZ, ſinus verſus anguli A, ſiue arcus BL, qui ar-
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            cui
              <emph style="sc">K</emph>
            C, ſimilis eſt, demonſtrabimus, vt in primo caſu, ita eſſe quadratum ſi-
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            nus totius, nempe rectangulum ſub DX, XA, ad rectangulum ſub AV,
              <emph style="sc">K</emph>
            Y,
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            ſinubus rectis arcuum AB, AC, vt eſt DZ, ſinus verſus anguli A, ſiue arcus
              <lb/>
            BL, ad
              <emph style="sc">K</emph>
            T, ſiue ad QR, differentiam ſinuum verſorum BR, BQ, arcuum
              <lb/>
            BC,
              <emph style="sc">Bk</emph>
            , niſi quòd hic non inueniuntur triangula æquiangula, ſed AV, ab
              <lb/>
            XA, non differt, quemadmodum nec
              <emph style="sc">K</emph>
            S, à
              <emph style="sc">K</emph>
            T.</s>
            <s xml:id="echoid-s15996" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s15997" xml:space="preserve">11. </s>
            <s xml:id="echoid-s15998" xml:space="preserve">SIT iterum AC, quadrante maior, attam AB, quam BC, quadrans.
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            </s>
            <s xml:id="echoid-s15999" xml:space="preserve">
              <note position="right" xlink:label="note-463-06" xlink:href="note-463-06a" xml:space="preserve">11. caſus.</note>
            Completo circulo ABGF, & </s>
            <s xml:id="echoid-s16000" xml:space="preserve">reſecto quadrante AE, ex AC, deſcribantur
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            ex polo A, ad interualla AE,
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            AC, circuli BEF, KCN, & </s>
            <s xml:id="echoid-s16001" xml:space="preserve">ex
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              <figure xlink:label="fig-463-01" xlink:href="fig-463-01a" number="328">
                <image file="463-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/463-01"/>
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            polo B, ad interuallum BC, cir-
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            culus AEG, aliaque fiant, vt in
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            præcedenti caſu. </s>
            <s xml:id="echoid-s16002" xml:space="preserve">Oſtendemus
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            ergo, vt in primo caſu, ita eſſe
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            quadratum ſinus totius, hoc eſt,
              <lb/>
            rectangulum ſub DX, XA, ad re-
              <lb/>
            ctangulum ſub AV, KY, ſinu-
              <lb/>
            bus rectis arcuum AB, AC, vt
              <lb/>
            eſt DZ, ſinus verſus anguli A, ſi-
              <lb/>
            ue arcus BE, ad KT, ſeu QR, differentiam ſinuum verſorum BR, BQ, ar-
              <lb/>
            cuum BC, BK, niſi quod hic nulla adſint æquiangula triangula, quemadmo-
              <lb/>
            dum nec in præcedenti caſu, atque AV, ab XA, & </s>
            <s xml:id="echoid-s16003" xml:space="preserve">DZ, à BR, & </s>
            <s xml:id="echoid-s16004" xml:space="preserve">KS, à KT,
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            non differt.</s>
            <s xml:id="echoid-s16005" xml:space="preserve"/>
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            <s xml:id="echoid-s16006" xml:space="preserve">12. </s>
            <s xml:id="echoid-s16007" xml:space="preserve">SIT arcus AC, quadrante maior, & </s>
            <s xml:id="echoid-s16008" xml:space="preserve">AB, quadrans, ſed BC, maior
              <lb/>
              <note position="right" xlink:label="note-463-07" xlink:href="note-463-07a" xml:space="preserve">12. caſus.</note>
            etiam quadrante. </s>
            <s xml:id="echoid-s16009" xml:space="preserve">Completo cir-
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            culo ABGF, & </s>
            <s xml:id="echoid-s16010" xml:space="preserve">ablatis quadran
              <lb/>
              <figure xlink:label="fig-463-02" xlink:href="fig-463-02a" number="329">
                <image file="463-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/463-02"/>
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            tibus AL, BM, ex arcubus AC,
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            BC, deſcribantur circuli ex po-
              <lb/>
            lis A, B, ad interualla quadran-
              <lb/>
            tum AL, BM, & </s>
            <s xml:id="echoid-s16011" xml:space="preserve">arcuum AC,
              <lb/>
            BC, cæteraq́ue fiant, vt in præ-
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            cedentibus. </s>
            <s xml:id="echoid-s16012" xml:space="preserve">Erit ergo rurſus, vt
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            in primo caſu demonſtratum eſt,
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            ita quadratum ſinus totius, id
              <lb/>
            eſt, rectangulum ſub DX, XA,
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            ad rectangulum ſub AV, KY, ſinubus rectis arcuum AB, AC, vt eſt </s>
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