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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            <s xml:id="echoid-s2818" xml:space="preserve">
              <pb o="42" file="0062" n="62" rhead="GNOMONICES"/>
            G X, & </s>
            <s xml:id="echoid-s2819" xml:space="preserve">C G, G L, & </s>
            <s xml:id="echoid-s2820" xml:space="preserve">rectæ C T, L X, arcus{q́ue} C T, L X, æquales erunt. </s>
            <s xml:id="echoid-s2821" xml:space="preserve">Itaque quoniam arcus A S,
              <lb/>
            arcui I V, æqualis est, & </s>
            <s xml:id="echoid-s2822" xml:space="preserve">arcus B
              <unsure/>
            S, arcui K V, ſuperabit A B, arcus primæ horæ ♋, eadem quantita-
              <lb/>
            te arcum A S, horæ æquinoctialis, qua I K, arcus ab arcu I V, horæ æquinoctialis ſuperatur. </s>
            <s xml:id="echoid-s2823" xml:space="preserve">Ergo per
              <lb/>
            ea, quæ dictaſunt, erit I K, arcus primæ horæ ♑; </s>
            <s xml:id="echoid-s2824" xml:space="preserve">at que adeò circulus maximus B F K, per primam ho-
              <lb/>
            ram ♋, & </s>
            <s xml:id="echoid-s2825" xml:space="preserve">Acquatoris ductus, tran-
              <lb/>
              <figure xlink:label="fig-0062-01" xlink:href="fig-0062-01a" number="45">
                <image file="0062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0062-01"/>
              </figure>
            ſit quoque per primam horam ♑. </s>
            <s xml:id="echoid-s2826" xml:space="preserve">Eo-
              <lb/>
            dem prorſus pacto demonſtr abimus ar-
              <lb/>
            cum I K, eſſe duarum horarum ♑,
              <lb/>
            quemadmodum & </s>
            <s xml:id="echoid-s2827" xml:space="preserve">arcus A C, duas ho-
              <lb/>
            ras ♋, complectitur, & </s>
            <s xml:id="echoid-s2828" xml:space="preserve">E G, arcus
              <lb/>
              <note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">10</note>
            duas horas Aequatoris; </s>
            <s xml:id="echoid-s2829" xml:space="preserve">quoniam vide-
              <lb/>
            licet arcus T C, quo A C, arcus dua-
              <lb/>
            rum horarum ♋, ſuperat arcum A T,
              <lb/>
            duarum horarum æquinoctialium, ęqua-
              <lb/>
            lis eſt arcui L X, quo I L, arcus ab ar-
              <lb/>
            cu I X, duarum horarum æquinoctia-
              <lb/>
            lium ſuperatur. </s>
            <s xml:id="echoid-s2830" xml:space="preserve">Cum igitur I K, oſten-
              <lb/>
            ſus ſit arcus primæ horæ ♑, erit K L,
              <lb/>
            arcus ſecundæ horæ. </s>
            <s xml:id="echoid-s2831" xml:space="preserve">Eadem{q́ue}, demon-
              <lb/>
            ſtratio erit in reliquis horis inæquali-
              <lb/>
              <note position="left" xlink:label="note-0062-02" xlink:href="note-0062-02a" xml:space="preserve">20</note>
            bus ♑, & </s>
            <s xml:id="echoid-s2832" xml:space="preserve">aliorum ſignorum, ſi loco
              <lb/>
            parallelorum ♋, & </s>
            <s xml:id="echoid-s2833" xml:space="preserve">♑, aſſumantur
              <lb/>
            alij duo oppoſiti, & </s>
            <s xml:id="echoid-s2834" xml:space="preserve">æquales. </s>
            <s xml:id="echoid-s2835" xml:space="preserve">Quod est
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s2836" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2837" xml:space="preserve">OMNIA autem, quæ proximis
              <lb/>
              <note position="left" xlink:label="note-0062-03" xlink:href="note-0062-03a" xml:space="preserve">In ſphęra recta
                <lb/>
              iidẽ circuli indi
                <lb/>
              cãt horas à mer.
                <lb/>
              vel med. noc &
                <lb/>
              ab or. vel occ
                <lb/>
              Nullæ autẽ ibi
                <lb/>
              ſunt horę in-
                <lb/>
              æquales.</note>
            duabus propoſ. </s>
            <s xml:id="echoid-s2838" xml:space="preserve">demonſtr auimus, intel-
              <lb/>
            ligenda ſunt in ſphæra obliqua tantum.
              <lb/>
            </s>
            <s xml:id="echoid-s2839" xml:space="preserve">Nam in recta non eſt vllus parallelus perpetuo apparens, cum omnes paralleli ab Horizonte per il-
              <lb/>
            lorum polos ducto bifariam ſecentur, vt conſtat ex propoſ. </s>
            <s xml:id="echoid-s2840" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2841" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2842" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2843" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s2844" xml:space="preserve">Vnde in ſphæra recta
              <lb/>
            maximi circuli, inter quos eſt & </s>
            <s xml:id="echoid-s2845" xml:space="preserve">Meridianus & </s>
            <s xml:id="echoid-s2846" xml:space="preserve">Horizon, incedentes per polos mundi, ſecantes{q́ue}
              <lb/>
              <note position="left" xlink:label="note-0062-04" xlink:href="note-0062-04a" xml:space="preserve">30</note>
            Aequatorem, ac proinde, per propoſ. </s>
            <s xml:id="echoid-s2847" xml:space="preserve">10. </s>
            <s xml:id="echoid-s2848" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2849" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2850" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s2851" xml:space="preserve">& </s>
            <s xml:id="echoid-s2852" xml:space="preserve">reliquos omnes parallelos in 24.
              <lb/>
            </s>
            <s xml:id="echoid-s2853" xml:space="preserve">partes æquales, indicabunt & </s>
            <s xml:id="echoid-s2854" xml:space="preserve">horas à meridie vel media nocte, & </s>
            <s xml:id="echoid-s2855" xml:space="preserve">ab ortu vel occaſu Solis. </s>
            <s xml:id="echoid-s2856" xml:space="preserve">Ho-
              <lb/>
            ræ autem inæquales ibi nuliæ ſunt, cum perpetuum ſit æquinoctium, ac proinde horæ æquinoctiales ſint
              <lb/>
            partes duodecimæ cuiuslibet diei, quemadmodum & </s>
            <s xml:id="echoid-s2857" xml:space="preserve">horæ inæquales in ſphæra obliqua partes ſunt duo-
              <lb/>
            decimæ cuiuſque diei.</s>
            <s xml:id="echoid-s2858" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div152" type="section" level="1" n="43">
          <head xml:id="echoid-head46" xml:space="preserve">THEOREMA 9. PROPOSITIO 11.</head>
          <note position="left" xml:space="preserve">Vmbra ſtyli, &
            <lb/>
          radius Solis ꝓ-
            <lb/>
          iicitur in cõem
            <lb/>
          ſectionem plani
            <lb/>
          horologij, & cir
            <lb/>
          culi maximi, in
            <lb/>
          quo Sol exiſtit.</note>
          <p>
            <s xml:id="echoid-s2859" xml:space="preserve">SOLE in quocunque circulo horario, vel alio maximo exiſtente,
              <lb/>
              <note position="left" xlink:label="note-0062-06" xlink:href="note-0062-06a" xml:space="preserve">40</note>
            radius Solaris, atque adeò vmbra verticis ſtyli proijcitur in rectam li-
              <lb/>
            neam, quæ communis ſectio eſt ipſius circuli horarij vel maximi, &</s>
            <s xml:id="echoid-s2860" xml:space="preserve">
              <unsure/>
              <lb/>
            plani horologij.</s>
            <s xml:id="echoid-s2861" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2862" xml:space="preserve">SIT circulus horarius, vel quicunque alius maximus A B C D, ſecans planum horologii
              <lb/>
            E F G H, per rectam E G, ſitq́ ſtylus I K, cuius vertex I, in centro I, collocetur, per propoſ. </s>
            <s xml:id="echoid-s2863" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2864" xml:space="preserve">Di-
              <lb/>
            co Sole in quocunque puncto L, exiſtente in circulo A B C D, radium eius, & </s>
            <s xml:id="echoid-s2865" xml:space="preserve">vmbram verticis
              <lb/>
              <note position="left" xlink:label="note-0062-07" xlink:href="note-0062-07a" xml:space="preserve">50</note>
            ſtyli I, proijci in rectam E G. </s>
            <s xml:id="echoid-s2866" xml:space="preserve">Nam radius L I, pertinens ad centrum I, per quod & </s>
            <s xml:id="echoid-s2867" xml:space="preserve">planum cir-
              <lb/>
            culi A B C D, ducitur, à plano circuli A B C D, non recedet, Sole exiſtente in circunferentia
              <lb/>
            ipſius circuli, ſed productus ſecabit circunferentiam eiuſdem circuli in puncto M, quod puncto
              <lb/>
            L, opponitur, ita vt ipſe radius ſit circuli diameter. </s>
            <s xml:id="echoid-s2868" xml:space="preserve">Cum ergo recta E G, in plano eiuſdem
              <lb/>
            circuli exiſtat, ſecabit radius L I M, rectam E G, in N, puncto; </s>
            <s xml:id="echoid-s2869" xml:space="preserve">atque adeo radius Solis L M, & </s>
            <s xml:id="echoid-s2870" xml:space="preserve">
              <lb/>
            vmbra verticis ſtyli I, proiicietur in rectam E G, communem ſectionem circuli horarii A B-
              <lb/>
            C D, & </s>
            <s xml:id="echoid-s2871" xml:space="preserve">plani horologij E F G H. </s>
            <s xml:id="echoid-s2872" xml:space="preserve">Eodem modo, ſi alius quidam circulus horarius, vel alius
              <lb/>
            maximus A F C H, idem planum horologij E F G H, ſecet per rectam F H, & </s>
            <s xml:id="echoid-s2873" xml:space="preserve">Sol exiſtat in pun-
              <lb/>
            cto O, circuli horarij, vel maximi, demonſtrabimus radium O I, & </s>
            <s xml:id="echoid-s2874" xml:space="preserve">vmbram eiuſdem verticis
              <lb/>
            ſtyli I, proiici in rectam F H, propterea quod radius productus ad punctum oppoſitum P, re-
              <lb/>
            ctam FH, in eodem plano circuli A F C H, exiſtentem ſecet in Q, puncto. </s>
            <s xml:id="echoid-s2875" xml:space="preserve">Eademq́ eſt ratio </s>
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