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-div163" type="section" level="1" n="47">
          <p>
            <s xml:id="echoid-s2936" xml:space="preserve">
              <pb o="44" file="0064" n="64" rhead="GNOMONICES"/>
              <note position="left" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve">Vmbra ſtyli, &
                <lb/>
              radiu Solari@
                <lb/>
              extra æꝗnoctia
                <lb/>
              proiicitur in ſe
                <lb/>
              ctionem conicã,
                <lb/>
              quæ commun@s
                <lb/>
              ſectio eſt plani
                <lb/>
              horologu, & co-
                <lb/>
              nicę ſuperficiei,
                <lb/>
              cuius baſis eſt
                <lb/>
              parallelus paral
                <lb/>
              lelo Solis oppo-
                <lb/>
              ſitus.</note>
            communis ſectio eſt plani horologij, & </s>
            <s xml:id="echoid-s2937" xml:space="preserve">conicæ ſuperficiei, cuius baſis
              <lb/>
            eſt parallelus parallelo Solis oppoſitus.</s>
            <s xml:id="echoid-s2938" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2939" xml:space="preserve">SOL extra Aequatorem A B, exiſtat in puncto C, quod motu diurno parallelum D C E, & </s>
            <s xml:id="echoid-s2940" xml:space="preserve">
              <lb/>
            eius punctum oppoſitum F, parallelũ
              <lb/>
              <figure xlink:label="fig-0064-01" xlink:href="fig-0064-01a" number="47">
                <image file="0064-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0064-01"/>
              </figure>
            G F H, radius verò C F, per centrum
              <lb/>
            mundi I, extenſus conicas ſuperficies
              <lb/>
            I D E, I G H, deſcribat. </s>
            <s xml:id="echoid-s2941" xml:space="preserve">Sit quoque
              <lb/>
            planum horologij K L M N, circulo
              <lb/>
            maximo O P, æquidiſtans, faciensq́ue
              <lb/>
              <note position="left" xlink:label="note-0064-02" xlink:href="note-0064-02a" xml:space="preserve">10</note>
            in conica ſuperficie vmbræ I G H, cõ-
              <lb/>
            munem ſectionem curuam lineam
              <lb/>
            Q L N, quæ vel circulus erit, vel Para-
              <lb/>
            bole, vel Hyperbole, vel Ellipſis, vt pa
              <lb/>
            tet ex propoſ. </s>
            <s xml:id="echoid-s2942" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2943" xml:space="preserve">5. </s>
            <s xml:id="echoid-s2944" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2945" xml:space="preserve">& </s>
            <s xml:id="echoid-s2946" xml:space="preserve">7. </s>
            <s xml:id="echoid-s2947" xml:space="preserve">huius lib.
              <lb/>
            </s>
            <s xml:id="echoid-s2948" xml:space="preserve">Dico radium Solarem C F, atque id-
              <lb/>
            circo vmbram I F, proiici in curuam
              <lb/>
            lineam Q L N. </s>
            <s xml:id="echoid-s2949" xml:space="preserve">Nam radius C F, cum
              <lb/>
            deſcribat motu diurno vtramque ſu-
              <lb/>
            perficiem conicam, non recedet ab
              <lb/>
              <note position="left" xlink:label="note-0064-03" xlink:href="note-0064-03a" xml:space="preserve">20</note>
            vtraque earum, Sole exiſtente in C,
              <lb/>
            (Negligimus enim etiam hic modi-
              <lb/>
            cam illam declinationem, quam Sol
              <lb/>
            motu proprio acquirit.) </s>
            <s xml:id="echoid-s2950" xml:space="preserve">ſed produ-
              <lb/>
            ctus ſecabit parallelum oppoſitum in
              <lb/>
            puncto F, quod puncto C, opponitur,
              <lb/>
            ita vt, per propoſ. </s>
            <s xml:id="echoid-s2951" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2952" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2953" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2954" xml:space="preserve">Apoll. </s>
            <s xml:id="echoid-s2955" xml:space="preserve">iaceat in ſuperficie vtraque conica. </s>
            <s xml:id="echoid-s2956" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s2957" xml:space="preserve">curua linea
              <lb/>
            Q L N, in ſuperficie conica vmbræ I G H, exiſtat, ſecabit radius C F, curuam lineam Q L N, in
              <lb/>
            puncto R; </s>
            <s xml:id="echoid-s2958" xml:space="preserve">ac propterea radius Solis C I F, & </s>
            <s xml:id="echoid-s2959" xml:space="preserve">vmbra verticis ſtyli I, proijcietur in lineam curuam
              <lb/>
            Q L N, cõmunem ſectionem conicæ ſuperficiei vmbræ I G H, & </s>
            <s xml:id="echoid-s2960" xml:space="preserve">plani horologij K L M N. </s>
            <s xml:id="echoid-s2961" xml:space="preserve">Idemq́
              <lb/>
              <note position="left" xlink:label="note-0064-04" xlink:href="note-0064-04a" xml:space="preserve">30</note>
            oſtendemus contingere, in quocunque puncto cæli Sol ponatur extra Aequatorem. </s>
            <s xml:id="echoid-s2962" xml:space="preserve">Sole igitur
              <lb/>
            in quocunque puncto extra Aequatorem exiſtente, &</s>
            <s xml:id="echoid-s2963" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2964" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s2965" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div166" type="section" level="1" n="48">
          <head xml:id="echoid-head51" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s2966" xml:space="preserve">EX his conſtat, Sole exiſtente extra æquinoctialem circulum, vt in quocunque puncto Zodiaci, præ-
              <lb/>
              <note position="left" xlink:label="note-0064-05" xlink:href="note-0064-05a" xml:space="preserve">Vmbra ſtyli
                <lb/>
              extra æꝗnoctia
                <lb/>
              deſcribit coni-
                <lb/>
              cam ſectionem
                <lb/>
              in horologio.</note>
            terquam in principio ♈, & </s>
            <s xml:id="echoid-s2967" xml:space="preserve">♎, radium ſolarem, & </s>
            <s xml:id="echoid-s2968" xml:space="preserve">extremitatem vmbræ ſtyli deſcribere motu diurno
              <lb/>
            lineam curuam, communem nimirum ſectionem conicæ ſuperficiei, quam vmbra deſcribit, & </s>
            <s xml:id="echoid-s2969" xml:space="preserve">plani ho-
              <lb/>
            rologij: </s>
            <s xml:id="echoid-s2970" xml:space="preserve">quia eo tempore radius Solis per centrum mundi incedens, atque adeò vmbræ extremitas, à ſu-
              <lb/>
            perficie conica vmbræ non recedit, ſed ſemper proijcitur in communem ſectionem ſuperficiei vmbræ, & </s>
            <s xml:id="echoid-s2971" xml:space="preserve">
              <lb/>
            plani horologij, id eſt, in curuam lineam, nempe circulum, vel Parabolen, vel Hyperbolen, vel Ellipſim,
              <lb/>
              <note position="left" xlink:label="note-0064-06" xlink:href="note-0064-06a" xml:space="preserve">40</note>
            vt demonſtratum eſt. </s>
            <s xml:id="echoid-s2972" xml:space="preserve">Quare ipſam deſcribet ad motum diurnum.</s>
            <s xml:id="echoid-s2973" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2974" xml:space="preserve">DENOMINATVR tamen eiuſmodi ſectio conica à parallelo, in quo Sol moratur. </s>
            <s xml:id="echoid-s2975" xml:space="preserve">Vt Sole exi-
              <lb/>
            ſtente in principio ♋, appellatur ſectio conica, quam vmbra percurrit, circulus, vel Parabole, vel Hyper-
              <lb/>
            bole, vel Ellipſis cancri, & </s>
            <s xml:id="echoid-s2976" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s2977" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div168" type="section" level="1" n="49">
          <head xml:id="echoid-head52" xml:space="preserve">THEOREMA 11. PROPOSITIO 13.</head>
          <p>
            <s xml:id="echoid-s2978" xml:space="preserve">CIRCVLI horarum à meridie, vel media nocte, ſecant ſuperficies
              <lb/>
              <note position="left" xlink:label="note-0064-07" xlink:href="note-0064-07a" xml:space="preserve">Circuli horarũ
                <lb/>
              à mer. vel med.
                <lb/>
              noc. ſecant ſu-
                <lb/>
              perficies coni-
                <lb/>
              cis, quarum ba-
                <lb/>
              ſes ſunt maxi-
                <lb/>
              mus parallelo-
                <lb/>
              rum ſemper ap
                <lb/>
              parentium, &
                <lb/>
              maximus ſem-
                <lb/>
              per occultorũ,
                <lb/>
              p lineas rectas,
                <lb/>
              in quibus eaſdẽ
                <lb/>
              tangunt circuli
                <lb/>
              horarum ab or.
                <lb/>
              vel occaſu.</note>
            duas conicas, quarum vertex eſt centrum mundi, baſes autem duo pa-
              <lb/>
              <note position="left" xlink:label="note-0064-08" xlink:href="note-0064-08a" xml:space="preserve">50</note>
            ralleli tangentes Hoiizontem, quorum vnus eſt maximus ſemper appa-
              <lb/>
            rentium, alter verò maximus ſemper deliteſcentium, lineis rectis ſe mu-
              <lb/>
            tuo ſecantibus in centro mundi: </s>
            <s xml:id="echoid-s2979" xml:space="preserve">In ijſdem autem lineis circuli horarũ
              <lb/>
            ab ortu, vel occaſu, eaſdem ſuperficies conicas tangunt.</s>
            <s xml:id="echoid-s2980" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2981" xml:space="preserve">IN Sphæra ABCD, cuius centrum E, & </s>
            <s xml:id="echoid-s2982" xml:space="preserve">axis A C, ſint duæ conicæ ſuperficies E F G, E H I,
              <lb/>
            quarum vertex communis E, centrum mundi, & </s>
            <s xml:id="echoid-s2983" xml:space="preserve">baſes paraileli F G, H I, maximi eorum, qui ſem
              <lb/>
            per apparent, & </s>
            <s xml:id="echoid-s2984" xml:space="preserve">ſub terra occultantur, axis quoque communis recta A C. </s>
            <s xml:id="echoid-s2985" xml:space="preserve">Sit quoque circulus
              <lb/>
            horarius à meridie, vel media nocte quicunque A N C k, qui per polos mundi A, C, tranſibit, per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s2986" xml:space="preserve">9. </s>
            <s xml:id="echoid-s2987" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s2988" xml:space="preserve">ſecans parallelos rectis K L, M N; </s>
            <s xml:id="echoid-s2989" xml:space="preserve">conicas autem ſuperficies lineis k N, L M.</s>
            <s xml:id="echoid-s2990" xml:space="preserve"/>
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