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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            tem ipſius lineæ meridianæ eundem ſitum habent, eoſdemq́ue numeros lineæ Verticales, vt pa-
              <lb/>
            tet. </s>
            <s xml:id="echoid-s17783" xml:space="preserve">Circulos igitur Verticales in eodem horologio polari deſcripſimus. </s>
            <s xml:id="echoid-s17784" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s17785" xml:space="preserve"/>
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        <div xml:id="echoid-div906" type="section" level="1" n="219">
          <head xml:id="echoid-head225" xml:space="preserve">PROBLEMA 41. PROPOSITIO 41.</head>
          <p>
            <s xml:id="echoid-s17786" xml:space="preserve">PARALLELOS Horizontis in eodem polari horologio
              <lb/>
            deſcribere.</s>
            <s xml:id="echoid-s17787" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17788" xml:space="preserve">SIT Analemma A B C, in quo Horizon B C; </s>
            <s xml:id="echoid-s17789" xml:space="preserve">Verticalis A D; </s>
            <s xml:id="echoid-s17790" xml:space="preserve">axis mundi, vel communis ſe-
              <lb/>
              <note position="left" xlink:label="note-0278-01" xlink:href="note-0278-01a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              rallelorum Ho
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              rizontis in eodẽ
                <lb/>
              polari horolo
                <lb/>
              gio.</note>
              <note position="left" xlink:label="note-0278-02" xlink:href="note-0278-02a" xml:space="preserve">10</note>
            ctio circuli horæ 6. </s>
            <s xml:id="echoid-s17791" xml:space="preserve">& </s>
            <s xml:id="echoid-s17792" xml:space="preserve">Meridiani E F; </s>
            <s xml:id="echoid-s17793" xml:space="preserve">& </s>
            <s xml:id="echoid-s17794" xml:space="preserve">Aequator G H, Diuiſo autem ſemicirculo B A C, in 180.
              <lb/>
            </s>
            <s xml:id="echoid-s17795" xml:space="preserve">partes æquales, vt ſingulæ ſingulos contineant gradus, vel in pauciores, habita ratione magnitu-
              <lb/>
            dinis horologii, (Nos eum partiti
              <lb/>
            ſumus in partes 12. </s>
            <s xml:id="echoid-s17796" xml:space="preserve">vt quælibet
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              <figure xlink:label="fig-0278-01" xlink:href="fig-0278-01a" number="193">
                <image file="0278-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0278-01"/>
              </figure>
            grad. </s>
            <s xml:id="echoid-s17797" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17798" xml:space="preserve">comprehendat) iungantur
              <lb/>
            bina puncta à recta B C, vel à pun-
              <lb/>
            cto A, æqualiter remota, lineis re-
              <lb/>
            ctis, quæ communes erunt ſectio-
              <lb/>
            nes Meridiani, & </s>
            <s xml:id="echoid-s17799" xml:space="preserve">parallelorum Ho
              <lb/>
            rizontis, quos vocant Almucanta-
              <lb/>
              <note position="left" xlink:label="note-0278-03" xlink:href="note-0278-03a" xml:space="preserve">20</note>
            rath. </s>
            <s xml:id="echoid-s17800" xml:space="preserve">Deinde ex punctis diuiſionũ
              <lb/>
            per centrum D, rectæ ducantur li-
              <lb/>
            neæ, vt conſtituantur triangula per
              <lb/>
            axem in conis, quorum baſes ſunt
              <lb/>
            paralleli Horizontis tam infra Ho-
              <lb/>
            rizontem, quàm ſupra, vertex autẽ
              <lb/>
            communis centrum mundi D. </s>
            <s xml:id="echoid-s17801" xml:space="preserve">Me-
              <lb/>
            ridianus enim A B C, per A D, axẽ
              <lb/>
            dictorũ conorũ ductus facit trian-
              <lb/>
            gúla per axem, ex propoſ. </s>
            <s xml:id="echoid-s17802" xml:space="preserve">3. </s>
            <s xml:id="echoid-s17803" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s17804" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s17805" xml:space="preserve">
              <note position="left" xlink:label="note-0278-04" xlink:href="note-0278-04a" xml:space="preserve">30</note>
            Apóllonij. </s>
            <s xml:id="echoid-s17806" xml:space="preserve">In Aequatore quoque
              <lb/>
            G H, qui inſtar Verticalis eſt reſpe-
              <lb/>
            ctu circuli horæ 6. </s>
            <s xml:id="echoid-s17807" xml:space="preserve">E F, tanquam
              <lb/>
            Horizontis cuiuſdam, cui horolo-
              <lb/>
            gium æquidiſtat, ſumatur ex vtra-
              <lb/>
            que parte recta D I, ſtylo æqualis, & </s>
            <s xml:id="echoid-s17808" xml:space="preserve">per I, ipſi E F, parallela agatur R Q. </s>
            <s xml:id="echoid-s17809" xml:space="preserve">Erit hæc infra quidem
              <lb/>
            centrum D, communis ſectio Meridiani, & </s>
            <s xml:id="echoid-s17810" xml:space="preserve">plani horologii ſuperioris ad Zenith A, ſpectantis, il-
              <lb/>
            la verò ſupra centrum D, communis ſectio eiuſdem Meridiani, & </s>
            <s xml:id="echoid-s17811" xml:space="preserve">plani horologii inferioris ad Na
              <lb/>
            dir pertinentis. </s>
            <s xml:id="echoid-s17812" xml:space="preserve">Secabit autem recta R Q, latera triangulorum per axem in punctis K, L, M,
              <lb/>
            N, O, &</s>
            <s xml:id="echoid-s17813" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17814" xml:space="preserve">eruntq́ue diametri conicarum ſectionum K Q, L Q, M Q, N Q, O Q. </s>
            <s xml:id="echoid-s17815" xml:space="preserve">Itaque ſi pun
              <lb/>
              <note position="left" xlink:label="note-0278-05" xlink:href="note-0278-05a" xml:space="preserve">40</note>
            cta K, L, M, N, (omittimus enim hic punctum O, cum translatum cadat extra tropicos) transfe-
              <lb/>
            rantur in lineam meridianam ſuperioris horologii infra ho@izontalem lineam, initio facto in hac
              <lb/>
            figura à puncto T, Horizontis, in horologio autem à puncto D, lineæ horizontalis; </s>
            <s xml:id="echoid-s17816" xml:space="preserve">& </s>
            <s xml:id="echoid-s17817" xml:space="preserve">per propoſ.
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            </s>
            <s xml:id="echoid-s17818" xml:space="preserve">S. </s>
            <s xml:id="echoid-s17819" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17820" xml:space="preserve">circa lineam meridianam dictæ conicæ ſectiones deſcribantur tranſeuntes per
              <lb/>
            puncta K, L, M, N, (erunt autem hæ conicæ ſectiones partim hyperbolæ, partim Ellipſes, vt con-
              <lb/>
            ſtat ex propoſ. </s>
            <s xml:id="echoid-s17821" xml:space="preserve">6. </s>
            <s xml:id="echoid-s17822" xml:space="preserve">& </s>
            <s xml:id="echoid-s17823" xml:space="preserve">7. </s>
            <s xml:id="echoid-s17824" xml:space="preserve">antecedentis lib. </s>
            <s xml:id="echoid-s17825" xml:space="preserve">Parallelus autem Horizontis 42. </s>
            <s xml:id="echoid-s17826" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s17827" xml:space="preserve">erit parabola, ex
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            propoſ. </s>
            <s xml:id="echoid-s17828" xml:space="preserve">5. </s>
            <s xml:id="echoid-s17829" xml:space="preserve">eiuſdem ſuperioris lib. </s>
            <s xml:id="echoid-s17830" xml:space="preserve">cum illum circulus horæ 6. </s>
            <s xml:id="echoid-s17831" xml:space="preserve">contingat in polo E,) & </s>
            <s xml:id="echoid-s17832" xml:space="preserve">à linea hori-
              <lb/>
            zontali eò magis ſemper recedentes, quò longius fuerint ex vtraque parte lineæ meridianæ pro-
              <lb/>
            ductæ, deſcripti erunt paralleli Horizontis. </s>
            <s xml:id="echoid-s17833" xml:space="preserve">In horologio inferiori transferenda eſt recta T S, in
              <lb/>
            lineam meridianam à puncto D, infra horizontalem lineam, &</s>
            <s xml:id="echoid-s17834" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17835" xml:space="preserve">Nam S Q, diameter eſt conicæ
              <lb/>
              <note position="left" xlink:label="note-0278-06" xlink:href="note-0278-06a" xml:space="preserve">50</note>
            ſectionis paralleli Horizontis grad. </s>
            <s xml:id="echoid-s17836" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17837" xml:space="preserve">ſupra Horizontem in horologio inferiori. </s>
            <s xml:id="echoid-s17838" xml:space="preserve">Eodemq́ue mo-
              <lb/>
            do reliqua puncta infra S, verſus Q, transferenda eſſent, ſi latera triangulorum per axem rectam
              <lb/>
            T Q, ſecarent. </s>
            <s xml:id="echoid-s17839" xml:space="preserve">In figura præcedentis propoſ. </s>
            <s xml:id="echoid-s17840" xml:space="preserve">deſcripſimus parallelum Horizontis grad. </s>
            <s xml:id="echoid-s17841" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17842" xml:space="preserve">in
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            portione, quam linea horizontalis amputat, quia illa locum inferioris horologii ſupplet, vt in ea-
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            dem propoſ. </s>
            <s xml:id="echoid-s17843" xml:space="preserve">diximus. </s>
            <s xml:id="echoid-s17844" xml:space="preserve">Eſt igitur, vt pater, recta E F, veluti Horizon, & </s>
            <s xml:id="echoid-s17845" xml:space="preserve">G H, tanquam Verticalis;
              <lb/>
            </s>
            <s xml:id="echoid-s17846" xml:space="preserve">B C, quaſi Aequator quidam, paralleli verò Horizontis inſtar parallelorum Aequatoris noui B C. </s>
            <s xml:id="echoid-s17847" xml:space="preserve">
              <lb/>
            Quo poſito, erunt Verticales circuli inſtar horariorum circulorum, qui omnes meridianam lineã
              <lb/>
            horologii ſecant in puncto V, vbi eandem interſecat A D, axis Horizontis, quem nunc munere
              <lb/>
            Æquatoris cuiuſdam noui fungi diximus: </s>
            <s xml:id="echoid-s17848" xml:space="preserve">Ita vt ſi hæc permutatio circulorum bene cõſideretur,
              <lb/>
            deſcriptio hæc parallelorum Horizontis à deſcriptione parallelorum Aequatoris in horizontali
              <lb/>
            horologio non deſcrepet.</s>
            <s xml:id="echoid-s17849" xml:space="preserve"/>
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