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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        <div xml:id="echoid-div144" type="section" level="1" n="42">
          <p style="it">
            <s xml:id="echoid-s2720" xml:space="preserve">
              <pb o="41" file="0061" n="61" rhead="LIBER PRIMVS."/>
            grediendo ſemper ab ortu in occaſum, ſiue contra ſucceſſionem ſignorum, donec rurſus ad ſemicirculum
              <lb/>
            Horizontis orient alem perueniamus.</s>
            <s xml:id="echoid-s2721" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2722" xml:space="preserve">FORTASSE planius, & </s>
            <s xml:id="echoid-s2723" xml:space="preserve">apertius intelligemus, quinam ſemicir culi ad horas ab occaſu, vel ortu
              <lb/>
            Solis pertineant, hoc modo. </s>
            <s xml:id="echoid-s2724" xml:space="preserve">Cogitemus nos extra cælum poſitos prope parallelum ſemper apparentium
              <lb/>
            maximum, ita vt pedes habeamus in hora 12. </s>
            <s xml:id="echoid-s2725" xml:space="preserve">mediæ noctis, vel 24. </s>
            <s xml:id="echoid-s2726" xml:space="preserve">ab ortu, vel occaſu, caput autem
              <lb/>
            uerſus polum arcticum. </s>
            <s xml:id="echoid-s2727" xml:space="preserve">Hoc poſito, ſemicir culus Horizontis, ſeu horæ 24. </s>
            <s xml:id="echoid-s2728" xml:space="preserve">qui nobis eſt ad dexteram, in-
              <lb/>
            dicabit horam 24. </s>
            <s xml:id="echoid-s2729" xml:space="preserve">ab occaſu; </s>
            <s xml:id="echoid-s2730" xml:space="preserve">alter verò ad ſiniſtram, horam 24. </s>
            <s xml:id="echoid-s2731" xml:space="preserve">ab ortu. </s>
            <s xml:id="echoid-s2732" xml:space="preserve">Similiter ſi pedes ſtatuamus in
              <lb/>
            alijs horis dicti paralleli, & </s>
            <s xml:id="echoid-s2733" xml:space="preserve">caput verſus polum, pertinebunt ſemicir culi horarum ab ortu, vel occaſu,
              <lb/>
            qui nobis ad dexteram ponuntur, ad horas ab occaſu; </s>
            <s xml:id="echoid-s2734" xml:space="preserve">qui verò ſunt ad ſiniſtram, ad horas ab ortu Solis.
              <lb/>
            </s>
            <s xml:id="echoid-s2735" xml:space="preserve">Quæ omnia perſpicua erunt ei, qui diligenter percipiat parallelum ſemper apparentium maximum, quem
              <lb/>
              <note position="left" xlink:label="note-0061-01" xlink:href="note-0061-01a" xml:space="preserve">10</note>
            circulus in propoſ. </s>
            <s xml:id="echoid-s2736" xml:space="preserve">9. </s>
            <s xml:id="echoid-s2737" xml:space="preserve">nobis reſert, & </s>
            <s xml:id="echoid-s2738" xml:space="preserve">circulos horarum ab ortu, vel occaſu dictũ parallelum tangentes in
              <lb/>
            proprio ſitu poſitos.</s>
            <s xml:id="echoid-s2739" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2740" xml:space="preserve">QVOD verò attinet ad circulos horarum inæqualium, manifestum est, illos tranſire debere per duo-
              <lb/>
              <note position="right" xlink:label="note-0061-02" xlink:href="note-0061-02a" xml:space="preserve">Circuli horarũ
                <lb/>
              inæqualiũ qui
                <lb/>
              ſint.</note>
            decimas partes omnium arcuum diurnorum, & </s>
            <s xml:id="echoid-s2741" xml:space="preserve">nocturnorum, cum huiuſmodi partes duodecimæ appellen-
              <lb/>
            tur horæ inæquales. </s>
            <s xml:id="echoid-s2742" xml:space="preserve">Quod autem circuli maximi per horas inæquales Aequatoris, (quæ quidem eædem
              <lb/>
              <note position="right" xlink:label="note-0061-03" xlink:href="note-0061-03a" xml:space="preserve">Circuli maximi
                <lb/>
              ſecantes arcus
                <lb/>
              diurnos Ae-
                <lb/>
              quatoris, & pa-
                <lb/>
              rallclorum bo-
                <lb/>
              realium in 12.
                <lb/>
              partes æquales,
                <lb/>
              diuidunt quo-
                <lb/>
              que arcus diur-
                <lb/>
              nos auſtralium
                <lb/>
              parallelorũ ĩ 12.
                <lb/>
              partes æquales.</note>
            ſunt, quæ æquales) & </s>
            <s xml:id="echoid-s2743" xml:space="preserve">arcuum diurnorum Borealium deſcripti tranſeant quoque per eaſdem horas arcuũ
              <lb/>
            diurnorum Auſtralium, hac ratione cum Federico Commandino demonſtr abimus. </s>
            <s xml:id="echoid-s2744" xml:space="preserve">Quoniam in Horizon-
              <lb/>
            te quolibet obliquo, duobus parallelis æqualiter diſtantibus ab Aequatore, arcus diurnus vnius æqualis
              <lb/>
            eſt arcui nocturno alterius, & </s>
            <s xml:id="echoid-s2745" xml:space="preserve">cõtra, vt manifeſtè apparet ex 19. </s>
            <s xml:id="echoid-s2746" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s2747" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2748" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2749" xml:space="preserve">Theodoſii; </s>
            <s xml:id="echoid-s2750" xml:space="preserve">Et ideo, quãto
              <lb/>
            dies augentur, Sole ab æquinoctio verno ad ♋, tendente, tanto minuuntur, eodem ab æquinoctio autum-
              <lb/>
              <note position="left" xlink:label="note-0061-04" xlink:href="note-0061-04a" xml:space="preserve">20</note>
            nali ad ♑, tendente: </s>
            <s xml:id="echoid-s2751" xml:space="preserve">ſequitur vt dies ♋, tanto maior ſit æquinoctij die, quanto dies ♑, minor eſt eodẽ
              <lb/>
            die æquinoctij. </s>
            <s xml:id="echoid-s2752" xml:space="preserve">Cum igitur arcus diurnus cuiuslibet paralleli in 12. </s>
            <s xml:id="echoid-s2753" xml:space="preserve">partes æquales diuidatur, eadem{q́ue} ſit
              <lb/>
            proportio partis ad partem, quæ totius ad totum; </s>
            <s xml:id="echoid-s2754" xml:space="preserve">fit, vt arcus quoque vnius horæ ♋, eadem quantitate
              <lb/>
              <note position="right" xlink:label="note-0061-05" xlink:href="note-0061-05a" xml:space="preserve">15. quinti.</note>
            ſuperet arcum vnius horæ æquinoctialis, qua arcus vnius horæ ♑, ab eodem ſuperatur. </s>
            <s xml:id="echoid-s2755" xml:space="preserve">Quod etiam hinc
              <lb/>
            patere potest; </s>
            <s xml:id="echoid-s2756" xml:space="preserve">quia hoc modo omnes illi 12. </s>
            <s xml:id="echoid-s2757" xml:space="preserve">exceſſus duodecim horarum ♋, ſimul ſumpti æquales erunt
              <lb/>
            duodecim his defectibus duodecim horarum ♑, ſimul ſumptis. </s>
            <s xml:id="echoid-s2758" xml:space="preserve">Quod non contingeret, ſi vna hora ♋, nõ
              <lb/>
            ſuperaret vnam horam æquinoctialem eadem quantitate, qua vna hora ♑, ab hora æquinoctiali ſupera-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s2759" xml:space="preserve">Eademq́, eſt ratio arcuum durarum horarum, trium, vel quatuor, & </s>
            <s xml:id="echoid-s2760" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2761" xml:space="preserve">Et ita in alijs parallelis, qui
              <lb/>
            ab Aequatore pari diſtant interuallo, vt in parallelis ♊, & </s>
            <s xml:id="echoid-s2762" xml:space="preserve">♐. </s>
            <s xml:id="echoid-s2763" xml:space="preserve">Item in parallelis ♉, & </s>
            <s xml:id="echoid-s2764" xml:space="preserve">♏, & </s>
            <s xml:id="echoid-s2765" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2766" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2767" xml:space="preserve">SIT iam in ſphæra parallelus ♋,
              <lb/>
              <note position="left" xlink:label="note-0061-06" xlink:href="note-0061-06a" xml:space="preserve">30</note>
              <figure xlink:label="fig-0061-01" xlink:href="fig-0061-01a" number="44">
                <image file="0061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0061-01"/>
              </figure>
            A B C D; </s>
            <s xml:id="echoid-s2768" xml:space="preserve">Aequator E F G H; </s>
            <s xml:id="echoid-s2769" xml:space="preserve">paral-
              <lb/>
            lelus ♑, I K L M; </s>
            <s xml:id="echoid-s2770" xml:space="preserve">circulus parallelo-
              <lb/>
            rum ſemper apparentiũ maximus N O-
              <lb/>
            P Q, & </s>
            <s xml:id="echoid-s2771" xml:space="preserve">horum omnium polus R; </s>
            <s xml:id="echoid-s2772" xml:space="preserve">Hori
              <lb/>
            zon obliquus I E A N D H M, tangens
              <lb/>
            parallelum N O P Q, in N. </s>
            <s xml:id="echoid-s2773" xml:space="preserve">Deinde
              <lb/>
            arcus Aequatoris, & </s>
            <s xml:id="echoid-s2774" xml:space="preserve">paralleli ♋, qui
              <lb/>
            ſunt ſupra Horizontem, diuidantur in
              <lb/>
            duodecim partes æquales, vt ſit pri-
              <lb/>
            mahora paralleli ♋, punctum B, ſe-
              <lb/>
              <note position="left" xlink:label="note-0061-07" xlink:href="note-0061-07a" xml:space="preserve">40</note>
            cunda hora eiuſdem paralleli punctum
              <lb/>
            C: </s>
            <s xml:id="echoid-s2775" xml:space="preserve">Aequatoris autem prima hora F,
              <lb/>
            ſecunda G. </s>
            <s xml:id="echoid-s2776" xml:space="preserve">Et per puncta B, F; </s>
            <s xml:id="echoid-s2777" xml:space="preserve">Item
              <lb/>
            per puncta C, G, deſcribantur per 20.
              <lb/>
            </s>
            <s xml:id="echoid-s2778" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s2779" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2780" xml:space="preserve">primi Theodoſii, duo circuli
              <lb/>
            maximi ſecantes parallelum ♑, in pun-
              <lb/>
            ctis K, L. </s>
            <s xml:id="echoid-s2781" xml:space="preserve">Dico circulum B F K, etiam
              <lb/>
            per primam horam ♑, tranſire, & </s>
            <s xml:id="echoid-s2782" xml:space="preserve">
              <lb/>
            C G L, per ſecundam, hoc eſt, I K,
              <lb/>
            eſſe primam horam ♑, & </s>
            <s xml:id="echoid-s2783" xml:space="preserve">K L, ſecun-
              <lb/>
              <note position="left" xlink:label="note-0061-08" xlink:href="note-0061-08a" xml:space="preserve">50</note>
            dam. </s>
            <s xml:id="echoid-s2784" xml:space="preserve">Deſcribantur enim per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s2785" xml:space="preserve">15. </s>
            <s xml:id="echoid-s2786" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2787" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2788" xml:space="preserve">Theodoſii, per puncta F, & </s>
            <s xml:id="echoid-s2789" xml:space="preserve">
              <lb/>
            G, alij duo circuli maximi tangentes parallelum N O P Q, ſecantes{q́ue}, parallelos ♋, & </s>
            <s xml:id="echoid-s2790" xml:space="preserve">♑, in S, T, V,
              <lb/>
            X. </s>
            <s xml:id="echoid-s2791" xml:space="preserve">Erunt igitur, per propoſ. </s>
            <s xml:id="echoid-s2792" xml:space="preserve">13. </s>
            <s xml:id="echoid-s2793" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2794" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2795" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s2796" xml:space="preserve">arcus A S, S T, I V, V X, arcubus E F, F G, ſimiles,
              <lb/>
            cum omnes hi arcus intercipiantur inter ſemicir culos non concurrentes, vt ex præcedenti ſcholio conſtat: </s>
            <s xml:id="echoid-s2797" xml:space="preserve">
              <lb/>
            Sunt autem E F, F G, arcus horarum æquinoctialium æquales. </s>
            <s xml:id="echoid-s2798" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s2799" xml:space="preserve">A S, S T, & </s>
            <s xml:id="echoid-s2800" xml:space="preserve">I V, V X, arcus
              <lb/>
            ſunt horarum æquinoctialiũ, & </s>
            <s xml:id="echoid-s2801" xml:space="preserve">æquales; </s>
            <s xml:id="echoid-s2802" xml:space="preserve">atque adeo, cum paralleli A C D, I X M, æquales ſint, æquales
              <lb/>
            erunt quatuor arcus A S, S T, I V, V X. </s>
            <s xml:id="echoid-s2803" xml:space="preserve">Et quoniam paralleli A C D, I X M, æquales ſunt, erunt & </s>
            <s xml:id="echoid-s2804" xml:space="preserve">
              <lb/>
            arcus S F, F V, & </s>
            <s xml:id="echoid-s2805" xml:space="preserve">B F, F K, circulorũ maximorum à parallelis abſciſſi, æquales, ex propoſ. </s>
            <s xml:id="echoid-s2806" xml:space="preserve">18. </s>
            <s xml:id="echoid-s2807" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2808" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2809" xml:space="preserve">
              <lb/>
            Theod. </s>
            <s xml:id="echoid-s2810" xml:space="preserve">Igitur ex propoſ. </s>
            <s xml:id="echoid-s2811" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2812" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2813" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2814" xml:space="preserve">Theodoſii, recta linea coniungens puncta B, S, æqualis erit rectæ con-
              <lb/>
            nectenti puncta K, V; </s>
            <s xml:id="echoid-s2815" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s2816" xml:space="preserve">arcus B S, arcui k V, æqualis erit. </s>
            <s xml:id="echoid-s2817" xml:space="preserve">Eodem{q́ue}, modo & </s>
            <s xml:id="echoid-s2818" xml:space="preserve">arcus T G,
              <lb/>
              <note position="right" xlink:label="note-0061-09" xlink:href="note-0061-09a" xml:space="preserve">28. tert@.</note>
            </s>
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