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

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          <p>
            <s xml:id="echoid-s3440" xml:space="preserve">IN circunferentia maximi circuli AB, ſit parallelorum polus A, eumque
              <lb/>
            duo alij circuli maximi BC, DE, ad angulos rectos ſecent, quorum BC, ſit
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            maximus parallelorum, & </s>
            <s xml:id="echoid-s3441" xml:space="preserve">DE, ad parallelos obliquus tãgens parallelum DF.
              <lb/>
            </s>
            <s xml:id="echoid-s3442" xml:space="preserve">Per polum quoq; </s>
            <s xml:id="echoid-s3443" xml:space="preserve">A, alius
              <lb/>
              <figure xlink:label="fig-101-01" xlink:href="fig-101-01a" number="105">
                <image file="101-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/101-01"/>
              </figure>
            circulus maximus deſcri-
              <lb/>
            batur AE, ſecans obliquũ
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            DE, in puncto E, inter ma
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            ximũ parallelorum BC, & </s>
            <s xml:id="echoid-s3444" xml:space="preserve">
              <lb/>
            parallelum DF, quem ob-
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            liquus tangit, poſito. </s>
            <s xml:id="echoid-s3445" xml:space="preserve">Di-
              <lb/>
            co diametrum ſphæræ ad
              <lb/>
            diametrum paralleli DF,
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            maiorem habere rationé,
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            quàm circunferétiam BC,
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            ad circunferentiam DE.
              <lb/>
            </s>
            <s xml:id="echoid-s3446" xml:space="preserve">Sit AG, recta communis
              <lb/>
            ſectio circulorũ AB, AE; </s>
            <s xml:id="echoid-s3447" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s3448" xml:space="preserve">BG, communis ſectio
              <lb/>
            circulorũ AB, BC; </s>
            <s xml:id="echoid-s3449" xml:space="preserve">eruntq; </s>
            <s xml:id="echoid-s3450" xml:space="preserve">
              <lb/>
            AG, BG, ſemidiametri
              <lb/>
            ipſorum, (cum ſe mutuo
              <lb/>
            ſecent bifariã circuli ma-
              <lb/>
              <note position="right" xlink:label="note-101-01" xlink:href="note-101-01a" xml:space="preserve">11.1.huius.</note>
            ximi in ſphæra) atque adeo & </s>
            <s xml:id="echoid-s3451" xml:space="preserve">ſphæræ, ſecantes ſe ſe in G, centro ſphæræ, & </s>
            <s xml:id="echoid-s3452" xml:space="preserve">
              <lb/>
            circulorum maximorum. </s>
            <s xml:id="echoid-s3453" xml:space="preserve">Sit quoque DL, communis ſectio circulorum AB,
              <lb/>
            DE, quæ quoque diameter ſphæræ erit tranſiens per centrum G. </s>
            <s xml:id="echoid-s3454" xml:space="preserve">Rurſus
              <lb/>
            DM, ſit communis ſectio circulorum AB, DF; </s>
            <s xml:id="echoid-s3455" xml:space="preserve">eritque DM, diameter cir-
              <lb/>
            culi DF, propterea quòd circulus AB, parallelum DF, ſecet bifariam per
              <lb/>
              <note position="right" xlink:label="note-101-02" xlink:href="note-101-02a" xml:space="preserve">15. 1. huius.</note>
            polos. </s>
            <s xml:id="echoid-s3456" xml:space="preserve">Item FN, CG, ſint communes ſectiones circulorum DF, BC,
              <lb/>
            cum circulo AE. </s>
            <s xml:id="echoid-s3457" xml:space="preserve">Ex polo A, interuallo vero AE, parallelus deſcribatur
              <lb/>
            OE, fintq́ue OH, EH, communes eius ſectiones cum circulis AB, AE;
              <lb/>
            </s>
            <s xml:id="echoid-s3458" xml:space="preserve">Eruntq́ue & </s>
            <s xml:id="echoid-s3459" xml:space="preserve">FN, EH, CG, ſemidiametri circulorum DF, OE, BC, quòd
              <lb/>
            ipſos bifariam ſecet circulus maximus AE, per polos; </s>
            <s xml:id="echoid-s3460" xml:space="preserve">atque adeo communes
              <lb/>
              <note position="right" xlink:label="note-101-03" xlink:href="note-101-03a" xml:space="preserve">15. 1. huius.</note>
            ſectiones diametri ſint occurrentes diametris DM, OH, BG, in centris N,
              <lb/>
            H, G. </s>
            <s xml:id="echoid-s3461" xml:space="preserve">Eſt enim & </s>
            <s xml:id="echoid-s3462" xml:space="preserve">OH, diameter circuli OE, cum eum circulus AB, per po-
              <lb/>
              <note position="right" xlink:label="note-101-04" xlink:href="note-101-04a" xml:space="preserve">15. 1. huius.</note>
            lum A, bifariam ſecet. </s>
            <s xml:id="echoid-s3463" xml:space="preserve">Sit rurſum EG, communis ſectio circulorum maximo-
              <lb/>
            rum AE, DE, quæ etiam diameter erit tran ſiens per G, centrum ſphæræ.
              <lb/>
            </s>
            <s xml:id="echoid-s3464" xml:space="preserve">Denique EI, communis ſit ſectio circulorum DE, OE. </s>
            <s xml:id="echoid-s3465" xml:space="preserve">Et quoniam re-
              <lb/>
            cta AG, ducta per polos paralleli OE, recta eſt ad planum paralleli, ca-
              <lb/>
              <note position="right" xlink:label="note-101-05" xlink:href="note-101-05a" xml:space="preserve">10. 1. huius.</note>
            ditq́ue in eius centrum H; </s>
            <s xml:id="echoid-s3466" xml:space="preserve">erit angulus OHG, ex defin. </s>
            <s xml:id="echoid-s3467" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3468" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3469" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3470" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s3471" xml:space="preserve">in
              <lb/>
            triangulo GHI, rectus; </s>
            <s xml:id="echoid-s3472" xml:space="preserve">atque adeo angulus HGI, acutus. </s>
            <s xml:id="echoid-s3473" xml:space="preserve">Latus igitur GI,
              <lb/>
            maius erit latere HI. </s>
            <s xml:id="echoid-s3474" xml:space="preserve">Auferatur recta IK, rectæ IH, æqualis, iungaturq́ue
              <lb/>
              <note position="right" xlink:label="note-101-06" xlink:href="note-101-06a" xml:space="preserve">19. primi.</note>
            recta EK. </s>
            <s xml:id="echoid-s3475" xml:space="preserve">Rurſus quia vterq; </s>
            <s xml:id="echoid-s3476" xml:space="preserve">circulus DE, OE, rectus eſt ad circulum AB;
              <lb/>
            </s>
            <s xml:id="echoid-s3477" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s3478" xml:space="preserve">EI, communis eorum ſectio ad eundem perpendicularis: </s>
            <s xml:id="echoid-s3479" xml:space="preserve">ac proinde,
              <lb/>
              <note position="right" xlink:label="note-101-07" xlink:href="note-101-07a" xml:space="preserve">19. vndec.</note>
            ex defin. </s>
            <s xml:id="echoid-s3480" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3481" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3482" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3483" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s3484" xml:space="preserve">vterque angulus EIH, EIK, rectus. </s>
            <s xml:id="echoid-s3485" xml:space="preserve">Quoniam igi-
              <lb/>
            tur duo latera EI, IH, trianguli EIH, duobus lateribus EI, IK, trianguli
              <lb/>
            EIK, ęqualia ſunt, angulosq́; </s>
            <s xml:id="echoid-s3486" xml:space="preserve">continent æquales, népe rectos, vt oſtendimus,
              <lb/>
            crunt anguli quoq; </s>
            <s xml:id="echoid-s3487" xml:space="preserve">IHE, IKE, æquales. </s>
            <s xml:id="echoid-s3488" xml:space="preserve">Quia verò maior eſt proportio re-
              <lb/>
              <note position="right" xlink:label="note-101-08" xlink:href="note-101-08a" xml:space="preserve">4. primi.</note>
            ctæ GI, ad rectam I k, quàm anguli I k E, hoc eſt anguli OHE, ſibi </s>
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