Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of figures

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            <s xml:id="echoid-s8268" xml:space="preserve">
              <pb o="204" file="240" n="241" rhead="Comment. in I. Cap. Sphæræ"/>
            M K. </s>
            <s xml:id="echoid-s8269" xml:space="preserve">Qu are quilibet illorum ſui circuli quadrans erit. </s>
            <s xml:id="echoid-s8270" xml:space="preserve">Ducantur denique re-
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            ctæ E D, E O, efficientes angulum D E O, non rectum. </s>
            <s xml:id="echoid-s8271" xml:space="preserve">Dico adhuc arcus
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              <figure xlink:label="fig-240-01" xlink:href="fig-240-01a" number="72">
                <image file="240-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/240-01"/>
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            D O, I P, N Q, eſſe ſimiles, hoc
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            eſt, talem partem eſſe D O, qua-
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            drantis D A, qualis pars eſt arcus
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            I P, quadrãtis I F, & </s>
            <s xml:id="echoid-s8272" xml:space="preserve">arcus N Q,
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            quadrantis N
              <emph style="sc">K</emph>
            . </s>
            <s xml:id="echoid-s8273" xml:space="preserve">Quoniam. </s>
            <s xml:id="echoid-s8274" xml:space="preserve">n. </s>
            <s xml:id="echoid-s8275" xml:space="preserve">eſt,
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            ut angulus D E O, ad angulum
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            D E A, ita arcus D O, ad arcum
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              <note position="left" xlink:label="note-240-01" xlink:href="note-240-01a" xml:space="preserve">33. ſexti.</note>
            D A, & </s>
            <s xml:id="echoid-s8276" xml:space="preserve">arcus I P, ad arcum I F, & </s>
            <s xml:id="echoid-s8277" xml:space="preserve">
              <lb/>
            arcus N K, manifeſtũ eſt, ſupradi-
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            ctos arcus inter ſe eſſe ſimiles, cũ
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            ad quadrãtes ſuorũ circulorũ ean
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            dem habeant proportionẽ. </s>
            <s xml:id="echoid-s8278" xml:space="preserve">Quod
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            ẽt hac ratione colligi põt. </s>
            <s xml:id="echoid-s8279" xml:space="preserve">Vt an-
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            gulus D E O, ad quatuor rectos,
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            quibus totæ circũferentiæ ſubtẽ
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            duntur, ita (per 2. </s>
            <s xml:id="echoid-s8280" xml:space="preserve">coroll. </s>
            <s xml:id="echoid-s8281" xml:space="preserve">vltimæ
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              <note position="left" xlink:label="note-240-02" xlink:href="note-240-02a" xml:space="preserve">Al@a demõ
                <unsure/>
                <lb/>
              @tratio.</note>
            propoſ. </s>
            <s xml:id="echoid-s8282" xml:space="preserve">li. </s>
            <s xml:id="echoid-s8283" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8284" xml:space="preserve">à nobis demõſtratũ)
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            arcus D O, ad totam circunferen
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            tiam D A C B, & </s>
            <s xml:id="echoid-s8285" xml:space="preserve">arcus I P, ad circunferentiam totam I F H G, & </s>
            <s xml:id="echoid-s8286" xml:space="preserve">arcus N Q,
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            ad totã circunferentiã N K M L. </s>
            <s xml:id="echoid-s8287" xml:space="preserve">Igitur arcus D O, I P, N Q, ſimiles ſunt,
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            cum ad circunferentias, quarum ſunt arcus, eandem habeant proportionem.</s>
            <s xml:id="echoid-s8288" xml:space="preserve"/>
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              <emph style="sc">Aliter</emph>
            idem theorema hoc modo demonſtrari poteſt, ſine proportio-
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              <note position="left" xlink:label="note-240-03" xlink:href="note-240-03a" xml:space="preserve">Alia demõ-
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              ftratio ſine
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              prop@rtioni
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              bus.</note>
            nibus. </s>
            <s xml:id="echoid-s8290" xml:space="preserve">Ex centro E, circulorum A B C D, F G H I, ducantur duæ rectæ E A,
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              <figure xlink:label="fig-240-02" xlink:href="fig-240-02a" number="73">
                <image file="240-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/240-02"/>
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            E B. </s>
            <s xml:id="echoid-s8291" xml:space="preserve">Dico arcus A B, F G,
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            inter ſe ſimiles eſſe. </s>
            <s xml:id="echoid-s8292" xml:space="preserve">Nã pro
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            ductis rectis A E, B E, vſque
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            ad C, D, ducãtur rectæ B C,
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            G H: </s>
            <s xml:id="echoid-s8293" xml:space="preserve">Sumantur quoque in
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            arcubus A B, F G, puncta,
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            K, L, vtcunque, ad q̃ ducant̃
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            rectę A K, B K, F L, G L. </s>
            <s xml:id="echoid-s8294" xml:space="preserve">Qm̃
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            igitur anguli E, G, H, trian
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            guli E G H, ęquales ſunt an
              <lb/>
            gulis E, B, C, triãguli EBC,
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              <note position="left" xlink:label="note-240-04" xlink:href="note-240-04a" xml:space="preserve">32. primi.</note>
            ꝙ tã illi, ꝗ̃ hi duobus ſint re
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            ctis æquales: </s>
            <s xml:id="echoid-s8295" xml:space="preserve">ſi dematur an-
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            gulus cõis E, erunt duo an-
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            gulis B, C, æquales: </s>
            <s xml:id="echoid-s8296" xml:space="preserve">Sed tam
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            hi duo, ꝗ̃ illi duo, inter ſe ę-
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              <note position="left" xlink:label="note-240-05" xlink:href="note-240-05a" xml:space="preserve">5. primi.</note>
            quales ſunt, quod tam rectæ
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            E G, E H, inter ſe, quàm rectæ E B, E C, inter ſe æquales ſint, ex defin. </s>
            <s xml:id="echoid-s8297" xml:space="preserve">circuli.
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            </s>
            <s xml:id="echoid-s8298" xml:space="preserve">Igitur angulus EHG, angulo ECB, æqualis erit. </s>
            <s xml:id="echoid-s8299" xml:space="preserve">Rurſus, quia in quadrilatero
              <lb/>
              <note position="left" xlink:label="note-240-06" xlink:href="note-240-06a" xml:space="preserve">22. tertij.</note>
            FLGH, duo anguli oppoſiti FHG, GLF, æquales ſunt duobus rectis: </s>
            <s xml:id="echoid-s8300" xml:space="preserve">Item duo
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            anguli oppoſiti ACB, A K B C, in quadrilatero A K B C, demptis æqualibus
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            FHG, ACB, erunt reliqui anguli BKA, GLF, æquales: </s>
            <s xml:id="echoid-s8301" xml:space="preserve">& </s>
            <s xml:id="echoid-s8302" xml:space="preserve">idcirco, per definitio-
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            nem, arcus AB, FG, ſimiles inter ſe erunt: </s>
            <s xml:id="echoid-s8303" xml:space="preserve">quod erat oſtendendum.</s>
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