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-div133" type="section" level="1" n="39">
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            <s xml:id="echoid-s2575" xml:space="preserve">
              <pb o="39" file="0059" n="59" rhead="LIBER PRIMVS."/>
            horarij ſemicirculi inter duos polos à Meridiani ſemicirculo ſupra Horizontem extante per occidentem
              <lb/>
            procedendo vſq; </s>
            <s xml:id="echoid-s2576" xml:space="preserve">ad ſemicir culum Meridiani inſra Horizontẽ, parallelum ſecent, vt perſpicuũ es@: </s>
            <s xml:id="echoid-s2577" xml:space="preserve">puncta
              <lb/>
            verò in reliquo ſemicir culo C B A, ostendunt horas à media nocte; </s>
            <s xml:id="echoid-s2578" xml:space="preserve">quia in illis parallelus ſecatur à reliquis
              <lb/>
            ſemicir culis horarijs. </s>
            <s xml:id="echoid-s2579" xml:space="preserve">Pari ratione in parallelo ſemper occultorum maximo puncta ſemicirculi verſus
              <lb/>
            occidentem poſiti incipiendo ab eo puncto, vbi Horizontem tangit, dabunt horas à meridie, punct a verò
              <lb/>
            alterius ſemicir culi verſus Orientem horas à media nocte indicabunt, propter eandem rationem. </s>
            <s xml:id="echoid-s2580" xml:space="preserve">Id quod
              <lb/>
            facile intelligi poteſt, ſi duo illi paralleli, & </s>
            <s xml:id="echoid-s2581" xml:space="preserve">circuli horarij in propria poſitione cogitentur eſſe poſiti.</s>
            <s xml:id="echoid-s2582" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2583" xml:space="preserve">MALVIMVS autem proponere, circulos horarios ſecare parallelum omnium, qui ſemper appa-
              <lb/>
            rent, maximum in vigintiquatuor partes æquales, quàm Aequatorem, (quamuis & </s>
            <s xml:id="echoid-s2584" xml:space="preserve">hoc verum ſit, vt
              <lb/>
            ex demonſtratione constat) quoniam & </s>
            <s xml:id="echoid-s2585" xml:space="preserve">cognitio circulorum horariorum, qui horas ab ortu & </s>
            <s xml:id="echoid-s2586" xml:space="preserve">occaſu
              <lb/>
              <note position="left" xlink:label="note-0059-01" xlink:href="note-0059-01a" xml:space="preserve">10</note>
            monſtrant, & </s>
            <s xml:id="echoid-s2587" xml:space="preserve">plcraque alia ad horas tam à mer. </s>
            <s xml:id="echoid-s2588" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s2589" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s2590" xml:space="preserve">quàm ab Or. </s>
            <s xml:id="echoid-s2591" xml:space="preserve">vel Occ. </s>
            <s xml:id="echoid-s2592" xml:space="preserve">attinentia, ex pun-
              <lb/>
            ctis horarijs dicti paralleli pendent, vt ex ſequentibus fiet perſpicuum.</s>
            <s xml:id="echoid-s2593" xml:space="preserve"/>
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        <div xml:id="echoid-div137" type="section" level="1" n="40">
          <head xml:id="echoid-head43" xml:space="preserve">THEOREMA 8. PROPOSITIQ 10.</head>
          <note position="right" xml:space="preserve">Circuli horatũ
            <lb/>
          ab @r@u vel oc-
            <lb/>
          caſu qui ſint.</note>
          <p>
            <s xml:id="echoid-s2594" xml:space="preserve">CIRCVLI maximi in Sphæra, quorum vnus ſit Horizon, tangen-
              <lb/>
            tes eundem parallelum omnium ſemper apparentium maximum in 24.
              <lb/>
            </s>
            <s xml:id="echoid-s2595" xml:space="preserve">punctis, quibus diuiditur à circulis horarum à meridie, vel media nocte,
              <lb/>
              <note position="left" xlink:label="note-0059-03" xlink:href="note-0059-03a" xml:space="preserve">20</note>
            monſtrant horas æquales ab ortu, vel occaſu Solis inchoatas: </s>
            <s xml:id="echoid-s2596" xml:space="preserve">Eorum au-
              <lb/>
            tem poli ſunt puncta paralleli per verticem loci, ſeu polum Horizontis
              <lb/>
            deſcripti, quibus à circulis horarum à meridie, vel media nocte ſecatur.</s>
            <s xml:id="echoid-s2597" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2598" xml:space="preserve">TANGANT eundem parallelum A B C D, in 24. </s>
            <s xml:id="echoid-s2599" xml:space="preserve">punctis horarum à meridie, vel media
              <lb/>
            nocte circuli maximi, quorum vnus ſit Horizon. </s>
            <s xml:id="echoid-s2600" xml:space="preserve">Dico hos circulos maximos monſtrare horas
              <lb/>
            æquales ab ortu, vel occaſu Solis inchoatas, &</s>
            <s xml:id="echoid-s2601" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2602" xml:space="preserve">Cum enim tangant parallelum A B C D, & </s>
            <s xml:id="echoid-s2603" xml:space="preserve">pro-
              <lb/>
            pterea, per propoſitionem 6. </s>
            <s xml:id="echoid-s2604" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2605" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2606" xml:space="preserve">Theodoſii, parallelum quoque ei æqualem, nempe omnium,
              <lb/>
              <note position="left" xlink:label="note-0059-04" xlink:href="note-0059-04a" xml:space="preserve">30</note>
            qui ſemper ſub terra occultantur, maximum; </s>
            <s xml:id="echoid-s2607" xml:space="preserve">ſecabunt omnes parallelos intermedios, per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s2608" xml:space="preserve">13. </s>
            <s xml:id="echoid-s2609" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2610" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2611" xml:space="preserve">Theodoſii, in partes (quæ ſcilicet intercipiuntur inter quoſuis duos proximos ſe-
              <lb/>
            micirculos non concurrentes) ſimiles partibus paralleli A B C D: </s>
            <s xml:id="echoid-s2612" xml:space="preserve">Ac propterea, cum partes paral-
              <lb/>
            leli A B C D, ponantur æquales, erunt & </s>
            <s xml:id="echoid-s2613" xml:space="preserve">partes paralleli cuiuslibet intermedij inter ſeæquales.
              <lb/>
            </s>
            <s xml:id="echoid-s2614" xml:space="preserve">Quare illas ſol motu diurno æqualibus 24. </s>
            <s xml:id="echoid-s2615" xml:space="preserve">temporibus percurret, initio facto ab Horizonte, hoc
              <lb/>
            eſt, ab ortu, vel occaſu Solis: </s>
            <s xml:id="echoid-s2616" xml:space="preserve">Sed hæc 24. </s>
            <s xml:id="echoid-s2617" xml:space="preserve">tempora æqualia, horæ ſunt 24. </s>
            <s xml:id="echoid-s2618" xml:space="preserve">æquales ab ortu, vel
              <lb/>
            occaſu inchoatæ. </s>
            <s xml:id="echoid-s2619" xml:space="preserve">Circuli igitur illi maximi monſtrant horas 24. </s>
            <s xml:id="echoid-s2620" xml:space="preserve">æquales ab ortu, vel occaſu in-
              <lb/>
            choatas. </s>
            <s xml:id="echoid-s2621" xml:space="preserve">quod eſt primum.</s>
            <s xml:id="echoid-s2622" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2623" xml:space="preserve">NEQVE vero vlli alij circuli, præter dictos, in cælo excogitari poſſunt, qui horas ab ortu, vel
              <lb/>
            occaſu indicent. </s>
            <s xml:id="echoid-s2624" xml:space="preserve">Cum enim huiuſmodi horæ ab Horizonte incipiant, diuidantq́; </s>
            <s xml:id="echoid-s2625" xml:space="preserve">ſingulos paralle-
              <lb/>
            los, quos ſecant, in partes 24. </s>
            <s xml:id="echoid-s2626" xml:space="preserve">æquales, ſequitur ex propoſ. </s>
            <s xml:id="echoid-s2627" xml:space="preserve">16. </s>
            <s xml:id="echoid-s2628" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2629" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2630" xml:space="preserve">Theodoſii, circulos maximos
              <lb/>
              <note position="left" xlink:label="note-0059-05" xlink:href="note-0059-05a" xml:space="preserve">40</note>
            ea ratione parallelos diuidentes vel tranſire per parallelorum polos, vel eundem vnũ parallelum
              <lb/>
            tangere. </s>
            <s xml:id="echoid-s2631" xml:space="preserve">Cum ergo per polos non tranſeant, quòd Horizon, qui vnus eſt ex illis, per polos mini-
              <lb/>
            mè tranſeat, niſi in ſphæra recta, tangent neceſſario eundem unum parallelum. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">Quare cum Ho-
              <lb/>
            rizon tangat parallelum ſemper apparentium maximum, tangent & </s>
            <s xml:id="echoid-s2633" xml:space="preserve">reliqui eundem. </s>
            <s xml:id="echoid-s2634" xml:space="preserve">Omnino igi-
              <lb/>
            tur circuli maximi horas ab ortu, vel occaſu monſtrantes tangunt parallelum ſemper apparen-
              <lb/>
            tium maximum.</s>
            <s xml:id="echoid-s2635" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2636" xml:space="preserve">QVONIAM verò circuli hi omnes eundem parallelum, qui ſemper apparentium maximus
              <lb/>
            eſt, tangunt, fit, vt æqualiter inclinati ſint ad Aequatorem, ex Theorem. </s>
            <s xml:id="echoid-s2637" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2638" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s2639" xml:space="preserve">21. </s>
            <s xml:id="echoid-s2640" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2641" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s2642" xml:space="preserve">Theodoſii, quod quidem eſt, ſecundum traditionem Franciſci Maurolyci, propoſitio 26. </s>
            <s xml:id="echoid-s2643" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2644" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2645" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0059-06" xlink:href="note-0059-06a" xml:space="preserve">50</note>
            Theodoſii. </s>
            <s xml:id="echoid-s2646" xml:space="preserve">Quare ex Theoremate 2. </s>
            <s xml:id="echoid-s2647" xml:space="preserve">eiuſdem ſcholij, quod eſt propoſitio 27. </s>
            <s xml:id="echoid-s2648" xml:space="preserve">ſecundum Mauro-
              <lb/>
            lycum, polos habent in circunferentia eiuſdem paralleli. </s>
            <s xml:id="echoid-s2649" xml:space="preserve">Cum ergo polus Horizontis, qui vnus eſt
              <lb/>
              <note position="right" xlink:label="note-0059-07" xlink:href="note-0059-07a" xml:space="preserve">Poli circuloru
                <lb/>
              hoias ab or. uel
                <lb/>
              occ. indicantiũ
                <lb/>
              ſunt in paralle-
                <lb/>
              lo per verticem
                <lb/>
              loci deſcripto.</note>
            ex illis circulis horarijs, ſit in parallelo per polum Horizontis, ſeu verticem loci deſcripto, neceſſa-
              <lb/>
            rio & </s>
            <s xml:id="echoid-s2650" xml:space="preserve">poli aliorum circulorum in eodem parallelo exiſtent. </s>
            <s xml:id="echoid-s2651" xml:space="preserve">Et quia circuli horarum à meridie,
              <lb/>
            vel media nocte tranſeuntes per puncta contactuum, & </s>
            <s xml:id="echoid-s2652" xml:space="preserve">per polos paralleli ſemper apparentium
              <lb/>
            maximi, tranſeunt quoque ex propoſ. </s>
            <s xml:id="echoid-s2653" xml:space="preserve">5. </s>
            <s xml:id="echoid-s2654" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2655" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2656" xml:space="preserve">Theodoſii, per polos circulorum monſtrantium ho-
              <lb/>
            ras ab ortu, vel occaſu, qui nimirum illum parallelum tangunt, erunt omnino poli horum circu-
              <lb/>
            lorum puncta paralleli per verticem loci, ſeu Horizontis polum deſcripti, per quæ circuli horarũ
              <lb/>
            à meridie, vel media nocte tranſeunt, quandoquidem in hoc parallelo omnes poli exiſtunt, vt de-
              <lb/>
            monſtratum eſt. </s>
            <s xml:id="echoid-s2657" xml:space="preserve">Conſtat ergo etiam ſecundum. </s>
            <s xml:id="echoid-s2658" xml:space="preserve">Quamobrem circuli maximi in ſphæra, quorum
              <lb/>
            vnus ſit Horizon, &</s>
            <s xml:id="echoid-s2659" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2660" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s2661" xml:space="preserve"/>
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