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-s10599" xml:space="preserve">
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            nis minor eſt angulo D H μ, altitudinis poli, (Si enim æquales eſſent anguli A D a, D H μ, exter-
              <lb/>
            nus, & </s>
            <s xml:id="echoid-s10600" xml:space="preserve">internus, recta H B, foret radio D a, parallela; </s>
            <s xml:id="echoid-s10601" xml:space="preserve">ſi autem maior eſſet angulus A D a, angulo
              <lb/>
              <note position="left" xlink:label="note-0184-01" xlink:href="note-0184-01a" xml:space="preserve">28. primi.</note>
            D H μ, coirent inter ſe rectæ H B, & </s>
            <s xml:id="echoid-s10602" xml:space="preserve">D a, quod non ponitur) fit, vt Horizon parallelis illis oppoſi-
              <lb/>
              <note position="left" xlink:label="note-0184-02" xlink:href="note-0184-02a" xml:space="preserve">Quando alicu-
                <lb/>
              ius ſigni atcus
                <lb/>
              eſt Parabola, vel
                <lb/>
              Ellipſis, arcus ſi-
                <lb/>
              gni oppoſiti in
                <lb/>
              horologio de-
                <lb/>
              ſcribi nequit.</note>
            tis neq; </s>
            <s xml:id="echoid-s10603" xml:space="preserve">æquidiſtet, neque eos tangat, neque ſecet, vt ex coroll. </s>
            <s xml:id="echoid-s10604" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s10605" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10606" xml:space="preserve">præcedentis lib. </s>
            <s xml:id="echoid-s10607" xml:space="preserve">conſtat.
              <lb/>
            </s>
            <s xml:id="echoid-s10608" xml:space="preserve">Quamobrem arcus ſigni illius, cuius radius ſecatur, erit per eandem propoſ. </s>
            <s xml:id="echoid-s10609" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10610" xml:space="preserve">Ellipſis. </s>
            <s xml:id="echoid-s10611" xml:space="preserve">Manife-
              <lb/>
            ſtum autem eſt, quando alicuius ſigni arcus Parabola eſt, vel Ellipſis, oppoſiti ſigni arcum in horo-
              <lb/>
            logio deſcribi non poſſe; </s>
            <s xml:id="echoid-s10612" xml:space="preserve">propterea quòd rectæ ex H, emiſſę radium illius non ſecant, vt diximus.</s>
            <s xml:id="echoid-s10613" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10614" xml:space="preserve">CÆTERVM ſatis erit, ſi ex poſteriori figura huius propoſ. </s>
            <s xml:id="echoid-s10615" xml:space="preserve">portionem arcus cuiuslibet ſi-
              <lb/>
              <note position="left" xlink:label="note-0184-03" xlink:href="note-0184-03a" xml:space="preserve">Quo pacto ex
                <lb/>
              portione vnius
                <lb/>
              arcus alicuius ſi
                <lb/>
              gni uſque ad li-
                <lb/>
              neam meridia-
                <lb/>
              nam deſcripti,
                <lb/>
              deſcribatur re
                <lb/>
              liqua portio, at-
                <lb/>
              que etĩam arcus
                <lb/>
              ſigni oppoſi ti, ſi
                <lb/>
              arcus ſignorum
                <lb/>
              õ
                <unsure/>
              ppoſitorũ ſue-
                <lb/>
              @int hyperbolę.</note>
            gni vſque ad lineam meridianam ex vna duntaxat parte deſcribamus. </s>
            <s xml:id="echoid-s10616" xml:space="preserve">Ex hac enim & </s>
            <s xml:id="echoid-s10617" xml:space="preserve">reliqua por-
              <lb/>
            tio ex alia parte, (atque in ſequentibus quidem horologiis multo accuratius, quàm ſi totum arcũ
              <lb/>
              <note position="left" xlink:label="note-0184-04" xlink:href="note-0184-04a" xml:space="preserve">10</note>
            ex figura radiorum Zodiaci deſcriberemus, vt ſuo loco dicemus) immo & </s>
            <s xml:id="echoid-s10618" xml:space="preserve">totus arcus ſigni oppo
              <lb/>
            ſiti (ſi tamen diameter arcuum, nempe recta H B, in figura radiorum radios ſignorum oppoſito-
              <lb/>
            rum ſecet. </s>
            <s xml:id="echoid-s10619" xml:space="preserve">Nam tunc ſolum, vt oſtendimus, illorum ſignorum arcus hyperbolæ oppoſitæ ſunt, & </s>
            <s xml:id="echoid-s10620" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0184-01" xlink:href="fig-0184-01a" number="135">
                <image file="0184-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0184-01"/>
              </figure>
              <note position="left" xlink:label="note-0184-05" xlink:href="note-0184-05a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0184-06" xlink:href="note-0184-06a" xml:space="preserve">30</note>
            ęquales) deſcribi poterit. </s>
            <s xml:id="echoid-s10621" xml:space="preserve">Ita autem propoſitum exequemur. </s>
            <s xml:id="echoid-s10622" xml:space="preserve">Sit hyperbolarum oppoſitarum, vel
              <lb/>
            Parabolæ, vel Ellipſis axis A B, qualis eſt meridiana linea in horologio horizontali, & </s>
            <s xml:id="echoid-s10623" xml:space="preserve">portio arcus
              <lb/>
              <note position="left" xlink:label="note-0184-07" xlink:href="note-0184-07a" xml:space="preserve">40</note>
            illius, vel ſectionis conicæ vſque ad axem deſcripta ſit C D: </s>
            <s xml:id="echoid-s10624" xml:space="preserve">Inuento autem in axe A B, puncto E,
              <lb/>
            per quod arcus ſigni oppofiti tranſire debet, (quod quidem habetur, ſi D E, ſumatur æqualis dia-
              <lb/>
            metro tranſuerſæ arcuum oppoſiterum in figura radiorum, nempe ſegmento rectæ H B, inter ra-
              <lb/>
            dios illorum ſignorum oppoſitorum) & </s>
            <s xml:id="echoid-s10625" xml:space="preserve">acceptis rectis D A, E B, inter ſe æqualibus cuiuſcunque
              <lb/>
            magnitudinis; </s>
            <s xml:id="echoid-s10626" xml:space="preserve">diuiſaq́; </s>
            <s xml:id="echoid-s10627" xml:space="preserve">diametro D E, bifariam in F, ponemus vnum pedem circini in F, & </s>
            <s xml:id="echoid-s10628" xml:space="preserve">alterũ
              <lb/>
            extendemus ad quodlibet punctum arcus C D, vtpote vſque ad C, & </s>
            <s xml:id="echoid-s10629" xml:space="preserve">circino non variato deſcribe-
              <lb/>
            mus ex F, ex altera parte axis arcũ occultum alicuius circuli; </s>
            <s xml:id="echoid-s10630" xml:space="preserve">Item alios duos ex vtraque parte eiuſ-
              <lb/>
            dem axis verſus partes E. </s>
            <s xml:id="echoid-s10631" xml:space="preserve">Rurſus vnum pedem circini ſtatuentes in A, extendemus alterum vſque
              <lb/>
            ad C, & </s>
            <s xml:id="echoid-s10632" xml:space="preserve">ſic manentibus circini cruribus extenſis, deſcribemus ex A, arcum circuli, qui priorem ex
              <lb/>
            F, deſcriptum ex altera parte axis ſecet in G; </s>
            <s xml:id="echoid-s10633" xml:space="preserve">Item duos alios ex B, qui priores duos ex F, ex vtraq;
              <lb/>
            </s>
            <s xml:id="echoid-s10634" xml:space="preserve">
              <note position="left" xlink:label="note-0184-08" xlink:href="note-0184-08a" xml:space="preserve">50</note>
            parte eiuſdem axis verſus partes E, deſcriptos ſecent in H, I. </s>
            <s xml:id="echoid-s10635" xml:space="preserve">Nam per punctum G, tranſibit arcus
              <lb/>
            C D, productus, & </s>
            <s xml:id="echoid-s10636" xml:space="preserve">per puncta H, I, incedet arcus oppoſitus, & </s>
            <s xml:id="echoid-s10637" xml:space="preserve">æqualis, qui per punctum E, poſi-
              <lb/>
            tus eſt tranſire. </s>
            <s xml:id="echoid-s10638" xml:space="preserve">Eodem pacto, ſi circinum extendamus ex F, in K, & </s>
            <s xml:id="echoid-s10639" xml:space="preserve">ex F, tres arcus deſcribamus ad
              <lb/>
            interuallum F K; </s>
            <s xml:id="echoid-s10640" xml:space="preserve">Item ex A, & </s>
            <s xml:id="echoid-s10641" xml:space="preserve">B, alios tres ad interuallum A K, vnum quidem ex A, & </s>
            <s xml:id="echoid-s10642" xml:space="preserve">duos ex B,
              <lb/>
            qui priores tres ſecent in L, M, N, tranſibunt ijdem arcus per puncta L, M, N; </s>
            <s xml:id="echoid-s10643" xml:space="preserve">Et ita alia atque alia
              <lb/>
            puncta, quotquot voluerimus, inueniemus. </s>
            <s xml:id="echoid-s10644" xml:space="preserve">Hortarer tamen, vt ex F, in portione arcus C D, acci
              <lb/>
            perentur puncta illa, vbi à lineis horarijs ſecatur. </s>
            <s xml:id="echoid-s10645" xml:space="preserve">Quòd ſi arcus ſignorum oppoſitorum non ſunt
              <lb/>
            hyperbolę oppoſitæ, & </s>
            <s xml:id="echoid-s10646" xml:space="preserve">æquales, vt contingit, cum diameter arcuum, vel recta H B, in figura radio-
              <lb/>
            rum Zodiaci radios oppoſitos non ſecat, ſed vnum tantum, ſatis eſt, ſi bini duntaxat arcus ex alte-
              <lb/>
            ra parte axis D E, ſeſe ſecantes deſcribantur ex F, & </s>
            <s xml:id="echoid-s10647" xml:space="preserve">A, ita vt F, ſumatur in quocunque loco diame-
              <lb/>
            tri A B, etiamſi illud non ſit centrum: </s>
            <s xml:id="echoid-s10648" xml:space="preserve">Nam tunc arcus oppoſiti ſigni deſcribi non poteſt, vt </s>
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