Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

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          <p>
            <s xml:id="echoid-s34627" xml:space="preserve">
              <pb o="537" file="0553" n="553" rhead="LIBER SEXTVS."/>
            a d a b, diametrum paralle
              <unsure/>
            li propoſiti perpendicularis; </s>
            <s xml:id="echoid-s34628" xml:space="preserve">& </s>
            <s xml:id="echoid-s34629" xml:space="preserve">per L, excitentur ad B E, A E, duæ per-
              <lb/>
            p
              <unsure/>
            endiculares N L M, O L P. </s>
            <s xml:id="echoid-s34630" xml:space="preserve">Ex quibus, quoniam maiores ſunt recta K L, (Nam ſi concipiatur ſe-
              <lb/>
            inicirculus paralleli conuerſus ad propriam poſitionem, vt ad Meridianum ſit rectus, erit K L, per
              <lb/>
              <figure xlink:label="fig-0553-01" xlink:href="fig-0553-01a" number="338">
                <image file="0553-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0553-01"/>
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            defin. </s>
            <s xml:id="echoid-s34631" xml:space="preserve">4. </s>
            <s xml:id="echoid-s34632" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34633" xml:space="preserve">11. </s>
            <s xml:id="echoid-s34634" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s34635" xml:space="preserve">ad eundem
              <lb/>
            recta, atque adeo, per defin. </s>
            <s xml:id="echoid-s34636" xml:space="preserve">3. </s>
            <s xml:id="echoid-s34637" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s34638" xml:space="preserve">11. </s>
            <s xml:id="echoid-s34639" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s34640" xml:space="preserve">perpendicularis ad om
              <lb/>
            nes in eo lineas per L, ductas. </s>
            <s xml:id="echoid-s34641" xml:space="preserve">
              <lb/>
            Ducta igitur recta E L Y, erit an-
              <lb/>
            gulus k L E, rectus. </s>
            <s xml:id="echoid-s34642" xml:space="preserve">Cum igitur
              <lb/>
            & </s>
            <s xml:id="echoid-s34643" xml:space="preserve">anguli M N E, P O E, recti ſint; </s>
            <s xml:id="echoid-s34644" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0553-01" xlink:href="note-0553-01a" xml:space="preserve">10</note>
            ſi ducantur tres ſemidiametri
              <lb/>
            ſphęrę E k, E M, E P, quarū qua-
              <lb/>
            drata æqualia ſunt, erũt tam duo
              <lb/>
            quadrata rectarũ MN, NE, quàm
              <lb/>
              <note position="right" xlink:label="note-0553-02" xlink:href="note-0553-02a" xml:space="preserve">47. primi.</note>
            duo quadrata rectarum P O, OE,
              <lb/>
            duobus quadratis rectarum K L,
              <lb/>
            L E, æqualia. </s>
            <s xml:id="echoid-s34645" xml:space="preserve">Quamobrem cum
              <lb/>
            tam quadratum ex N E, quàm ex
              <lb/>
            O E minus ſit quadrato ex L E,
              <lb/>
            quòd tam linea N E, quàm O E,
              <lb/>
              <note position="left" xlink:label="note-0553-03" xlink:href="note-0553-03a" xml:space="preserve">20</note>
            in triangulis rectangulis N E L,
              <lb/>
            O E L, minor ſit quàm L E; </s>
            <s xml:id="echoid-s34646" xml:space="preserve">erit
              <lb/>
              <note position="right" xlink:label="note-0553-04" xlink:href="note-0553-04a" xml:space="preserve">19. primi.</note>
            tam reliquum quadratum rectæ
              <lb/>
            M N, quàm reliquum quadratũ
              <lb/>
            rectæ P O, maius reliquo quadra
              <lb/>
            to rectæ K L: </s>
            <s xml:id="echoid-s34647" xml:space="preserve">atque idcirco vtra-
              <lb/>
            que recta M N, P O, maior erit
              <lb/>
            quàm K L. </s>
            <s xml:id="echoid-s34648" xml:space="preserve">Solum quando perpendicularis K L, cadit in punctum n, vbi diameter paralleli Verti
              <lb/>
            calis diametrum diuidit, vt in figura 3. </s>
            <s xml:id="echoid-s34649" xml:space="preserve">contingit, recta k L, æqualis eſt rectæ P O. </s>
            <s xml:id="echoid-s34650" xml:space="preserve">Quia enim tunc
              <lb/>
              <figure xlink:label="fig-0553-02" xlink:href="fig-0553-02a" number="339">
                <image file="0553-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0553-02"/>
              </figure>
            duo quadrata ex K L, L E, duo-
              <lb/>
              <note position="left" xlink:label="note-0553-05" xlink:href="note-0553-05a" xml:space="preserve">30</note>
              <note position="right" xlink:label="note-0553-06" xlink:href="note-0553-06a" xml:space="preserve">47. primi.</note>
            bus quadratis ex P O, O E, æqua
              <lb/>
            lia ſunt; </s>
            <s xml:id="echoid-s34651" xml:space="preserve">ſi auferatur commune
              <lb/>
            quadratum rectæ L E, æquale
              <lb/>
            erit reliquum quadratum rectæ
              <lb/>
            K L, reliquo quadrato rectę
              <lb/>
            P O; </s>
            <s xml:id="echoid-s34652" xml:space="preserve">ac proinde rectæ K L, PO,
              <lb/>
            æquales erunt. </s>
            <s xml:id="echoid-s34653" xml:space="preserve">Nihilominus
              <lb/>
            tunc etiam recta M N, rectam
              <lb/>
            K L, ſuperabit, quòd M N, ſit
              <lb/>
            tunc ſemidiameter ſphæræ, at
              <lb/>
              <note position="left" xlink:label="note-0553-07" xlink:href="note-0553-07a" xml:space="preserve">40</note>
            K L, ſemidiametro minor) ab-
              <lb/>
            ſcindantur ipſi K L, duæ æqua-
              <lb/>
            les N Q, O R; </s>
            <s xml:id="echoid-s34654" xml:space="preserve">atque per pun-
              <lb/>
            cta Q, R, ex centro E, rectæ
              <lb/>
            emittantur E Q S, E R T, ſecan-
              <lb/>
            tes Meridiani circunferentiam
              <lb/>
            in S, T. </s>
            <s xml:id="echoid-s34655" xml:space="preserve">Poſtremo ad rectam
              <lb/>
            E Y, excitentur in E, & </s>
            <s xml:id="echoid-s34656" xml:space="preserve">L, duæ
              <lb/>
            perpendiculares E g, L f. </s>
            <s xml:id="echoid-s34657" xml:space="preserve">His
              <lb/>
            enim rite peractis, inuentæ erũt
              <lb/>
              <note position="left" xlink:label="note-0553-08" xlink:href="note-0553-08a" xml:space="preserve">50</note>
            omnes dictę ſex circunferentię
              <lb/>
            ad tempus propoſitum, cum ni-
              <lb/>
            mirum Sol in puncto K, paralleli a e b, exiſtit. </s>
            <s xml:id="echoid-s34658" xml:space="preserve">Nam, vt in ſequenti cap. </s>
            <s xml:id="echoid-s34659" xml:space="preserve">oſtendemus, g f, erit cir-
              <lb/>
            cunferentia hectemoria; </s>
            <s xml:id="echoid-s34660" xml:space="preserve">B M, horaria; </s>
            <s xml:id="echoid-s34661" xml:space="preserve">A P, deſcenſiua; </s>
            <s xml:id="echoid-s34662" xml:space="preserve">B Y, meridiana; </s>
            <s xml:id="echoid-s34663" xml:space="preserve">A T, Verticalis; </s>
            <s xml:id="echoid-s34664" xml:space="preserve">& </s>
            <s xml:id="echoid-s34665" xml:space="preserve">A S,
              <lb/>
            horizontalis.</s>
            <s xml:id="echoid-s34666" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s34667" xml:space="preserve">POSSVNT autem tres circunferentiæ mobiles, vt hectemoria, horaria, ac deſcenſiua faci-
              <lb/>
              <note position="right" xlink:label="note-0553-09" xlink:href="note-0553-09a" xml:space="preserve">Alia inuentio
                <lb/>
              circunferentiæ
                <lb/>
              hectemotiæ, ho-
                <lb/>
              rariæ, & deſcen-
                <lb/>
              ſiuæ.</note>
            lius reperiri, ſine tot lineis perpendicularibus, hac ratione. </s>
            <s xml:id="echoid-s34668" xml:space="preserve">Ducta ex K, loco Solis ad a b, diame-
              <lb/>
            trum paralleli perpendiculari K L, ducatur ex E, per L, recta E L Y, ad quam in E, excitetur per-
              <lb/>
            pendicularis E g. </s>
            <s xml:id="echoid-s34669" xml:space="preserve">Nam ſi ex L, vt centro, interuallo autem L K, ſumatur beneficio circini punctũ
              <lb/>
            f, in Meridiano, erit g f, circunferentia hectemoria. </s>
            <s xml:id="echoid-s34670" xml:space="preserve">Si vero ex puncto d, vbi paralleli diameter
              <lb/>
            ſecat diametrum Horizontis, vt cẽtro, interuallo autem d K, accipiatur in Meridiano punctũ </s>
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