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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            erit B M, circunferentia horaria. </s>
            <s xml:id="echoid-s34671" xml:space="preserve">Si denique ex puncto n, vbi diameter paralleli diametrum Ver-
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            ticalis ſecat, vt centro, interuallo verò n K, in Meridiano ſumatur beneficio circini punctum P,
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              <figure xlink:label="fig-0554-01" xlink:href="fig-0554-01a" number="340">
                <image file="0554-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0554-01"/>
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            erit A P, circunferentia
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            deſcenſiua. </s>
            <s xml:id="echoid-s34672" xml:space="preserve">Ratio hu-
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            ius rei eſt, quòd ducta
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            recta f L, perpendicula
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            ris eſt ad rectam ELY:
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            </s>
            <s xml:id="echoid-s34673" xml:space="preserve">ducta autẽ recta MLN,
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            ad B D, perpẽdicularis
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            eſt; </s>
            <s xml:id="echoid-s34674" xml:space="preserve">& </s>
            <s xml:id="echoid-s34675" xml:space="preserve">recta P L O, ad
              <lb/>
              <note position="left" xlink:label="note-0554-01" xlink:href="note-0554-01a" xml:space="preserve">10</note>
            A C, vt mox demon-
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            ſtrabimus. </s>
            <s xml:id="echoid-s34676" xml:space="preserve">Cum ergo
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            prius per has perpendi
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            culares L f, M L N,
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            P L O, inuentę ſint tres
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            dictæ circunferentię, vt
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            in ſequenti cap. </s>
            <s xml:id="echoid-s34677" xml:space="preserve">oſten-
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            demus, eædem etiam
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            inuentæ erunt per pun-
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            cta f, M, P, in Meridia
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              <note position="left" xlink:label="note-0554-02" xlink:href="note-0554-02a" xml:space="preserve">20</note>
            no accepta, vt diximus.
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            </s>
            <s xml:id="echoid-s34678" xml:space="preserve">Rectam autem f L, ad
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            E L Y, perpendicularẽ
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            eſſe, ita probabimus. </s>
            <s xml:id="echoid-s34679" xml:space="preserve">
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            Ducta recta E f, quoniã
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            duo latera K L, L E, triã
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            guli K L E, ęqualia ſunt
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            duobus lateribus f L,
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            L E, trianguli f L E, (quòd interuallum L f, interuallo L K, ſumptum eſt æquale) eſtq́ue baſis k E,
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            baſi f E, ęqualis, (quòd vtraque ſit ſphęrę ſemidiameter) erit angulus k L E, angulo f L E, ęqualis. </s>
            <s xml:id="echoid-s34680" xml:space="preserve">
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              <note position="left" xlink:label="note-0554-03" xlink:href="note-0554-03a" xml:space="preserve">8. primi.</note>
              <note position="left" xlink:label="note-0554-04" xlink:href="note-0554-04a" xml:space="preserve">30</note>
              <figure xlink:label="fig-0554-02" xlink:href="fig-0554-02a" number="341">
                <image file="0554-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0554-02"/>
              </figure>
            Cum ergo k L E, rectus ſit, vt
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            paulo ante oſtendimus, erit & </s>
            <s xml:id="echoid-s34681" xml:space="preserve">
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            f L E, rectus, ideoq́; </s>
            <s xml:id="echoid-s34682" xml:space="preserve">fL.</s>
            <s xml:id="echoid-s34683" xml:space="preserve">, ad ELY,
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            perpendicularis erit. </s>
            <s xml:id="echoid-s34684" xml:space="preserve">Viciſſim
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            etiam probabimus, ſi ex L, duca
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            tur ad E L Y, perpendicularis
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            L f, eam æqualẽ eſſe rectæ L K.
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            </s>
            <s xml:id="echoid-s34685" xml:space="preserve">Cũ enim duo quadrata ex E k,
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              <note position="left" xlink:label="note-0554-05" xlink:href="note-0554-05a" xml:space="preserve">47. primi.</note>
            E f, æqualia ſint, erunt duo qua-
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            drata ex E L, L K, duobus qua-
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              <note position="left" xlink:label="note-0554-06" xlink:href="note-0554-06a" xml:space="preserve">40</note>
            dratis ex E L, L f, æqualia Abla
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            to ergo communi quadrato re-
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            ctæ E L, reliqua erunt quadra-
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            ta rectarum L K, L f, æqualia,
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            proptereaq́ue & </s>
            <s xml:id="echoid-s34686" xml:space="preserve">rectæ L K, L f,
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            æquales erunt. </s>
            <s xml:id="echoid-s34687" xml:space="preserve">Quod etiam ita
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            confirmabimus. </s>
            <s xml:id="echoid-s34688" xml:space="preserve">Extendatur re-
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            cta Y E, vſque ad Z. </s>
            <s xml:id="echoid-s34689" xml:space="preserve">Quoniam
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            igitur K L, ad diametrum paral
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            leli a b, perpendicularis media
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              <note position="left" xlink:label="note-0554-07" xlink:href="note-0554-07a" xml:space="preserve">50</note>
            propottionalis eſt inter ſegmen
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            ta a L, Lb, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s34690" xml:space="preserve">13.
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            </s>
            <s xml:id="echoid-s34691" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34692" xml:space="preserve">6. </s>
            <s xml:id="echoid-s34693" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s34694" xml:space="preserve">erit quadratum ex
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            K L, æquale rectangulo ſub a L,
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              <note position="left" xlink:label="note-0554-08" xlink:href="note-0554-08a" xml:space="preserve">17. ſexti.</note>
            Lb, contento. </s>
            <s xml:id="echoid-s34695" xml:space="preserve">Eodem modo, erit fL, perpendicularis ducta ad Y Z, media proportionalis inter
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            ſegmenta Y L, L Z, atque adeo quadratum ex fL, rectangulo ſub γ L, L Z, æquale. </s>
            <s xml:id="echoid-s34696" xml:space="preserve">Cum ergo re-
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            ctangula ſuba L, L b, & </s>
            <s xml:id="echoid-s34697" xml:space="preserve">ſub γ L, L Z, æqualia ſint, erunt & </s>
            <s xml:id="echoid-s34698" xml:space="preserve">quadrata ex K L, f L, æqualia, ideoq́ue
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              <note position="left" xlink:label="note-0554-09" xlink:href="note-0554-09a" xml:space="preserve">35. tertij.</note>
            & </s>
            <s xml:id="echoid-s34699" xml:space="preserve">rectæ K L, f L, æquales.</s>
            <s xml:id="echoid-s34700" xml:space="preserve"/>
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            <s xml:id="echoid-s34701" xml:space="preserve">AT vero rectas M L N, P L O, ad rectas B D, A C, perpendiculares eſſe, facile comprobabi-
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            mus, ſi prius demonſtremus, ſi per L, ducantur rectæ M L N, P L O, ad B D, A C, perpendicula-
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            res, coniungaturq́ue rectæ d M, d K, & </s>
            <s xml:id="echoid-s34702" xml:space="preserve">n P, n K, rectam d M, rectæ d K, & </s>
            <s xml:id="echoid-s34703" xml:space="preserve">rectam n P, </s>
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