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-div632" type="section" level="1" n="164">
          <p>
            <s xml:id="echoid-s11733" xml:space="preserve">
              <pb o="180" file="0200" n="200" rhead="GNOMONIGES"/>
            Min. </s>
            <s xml:id="echoid-s11734" xml:space="preserve">28. </s>
            <s xml:id="echoid-s11735" xml:space="preserve">à metidie, in eodem puncto occaſus Horizontem; </s>
            <s xml:id="echoid-s11736" xml:space="preserve">atque adeo eandem habebunt ſectio-
              <lb/>
            nem communem Ecliptica, circulus ille horarius, & </s>
            <s xml:id="echoid-s11737" xml:space="preserve">Horizon. </s>
            <s xml:id="echoid-s11738" xml:space="preserve">Quare cum planum horologii Ho-
              <lb/>
            rizonti, atque idcirco communi illi ſectioni æquidiſtet, parallelæ erunt, per propoſ. </s>
            <s xml:id="echoid-s11739" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11740" xml:space="preserve">præceden-
              <lb/>
            tis libri, linea hor. </s>
            <s xml:id="echoid-s11741" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11742" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11743" xml:space="preserve">28. </s>
            <s xml:id="echoid-s11744" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s11745" xml:space="preserve">communis ſectio Eclipticæ tunc temporis, ac pla-
              <lb/>
            ni horologii. </s>
            <s xml:id="echoid-s11746" xml:space="preserve">Si igitur ducatur linea hor. </s>
            <s xml:id="echoid-s11747" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11748" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11749" xml:space="preserve">28. </s>
            <s xml:id="echoid-s11750" xml:space="preserve">à meridie, cui per punctum in linea
              <lb/>
            æquinoctiali inuentum, per quod ſcilicet duci debet linea ♋, parallela agatur, dabit hæc ſi-
              <lb/>
            gnum ♋, aſcendens. </s>
            <s xml:id="echoid-s11751" xml:space="preserve">Eodemq́ue modo lineam ♑, aſcendentis ducemus. </s>
            <s xml:id="echoid-s11752" xml:space="preserve">Immo eadem hac
              <lb/>
            demonſtratione concludemus, lineam cuiuſque ſigni aſcendentis in horologio horizontali
              <lb/>
            æquidiſtare illi lineæ horariæ à meridie, vel media nocte, quæ indicat tempus occaſus ſigni op-
              <lb/>
            poſiti, nempe lineam ♏, æquidiſtare lineæ hor. </s>
            <s xml:id="echoid-s11753" xml:space="preserve">6. </s>
            <s xml:id="echoid-s11754" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11755" xml:space="preserve">42. </s>
            <s xml:id="echoid-s11756" xml:space="preserve">à meridie, vel media nocte, qua
              <lb/>
              <note position="left" xlink:label="note-0200-01" xlink:href="note-0200-01a" xml:space="preserve">10</note>
            videlicet hora principium ♉, ſigni oppoſiti occidit. </s>
            <s xml:id="echoid-s11757" xml:space="preserve">Tot enim horas arcus ſemidiurnus ♉,
              <lb/>
            continet. </s>
            <s xml:id="echoid-s11758" xml:space="preserve">Ratio verò eſt, quia Ecliptica illo tempore, & </s>
            <s xml:id="echoid-s11759" xml:space="preserve">circulus horæ illius, & </s>
            <s xml:id="echoid-s11760" xml:space="preserve">Horizon, eandem
              <lb/>
            communem habent ſectionem, vt patet, &</s>
            <s xml:id="echoid-s11761" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11762" xml:space="preserve">Itaque ſi ſumantur arcus ſemidiurni omniũ ſigno-
              <lb/>
            rum, vt in hac tabella, facile cognoſcemus, quibusnam lineis horariis à meridie, vel media nocte</s>
          </p>
        </div>
        <div xml:id="echoid-div637" type="section" level="1" n="165">
          <head xml:id="echoid-head168" xml:space="preserve">Arcus ſemidiurni in initijs ſignorum, ad latitudinem grad. 42.</head>
          <note position="right" xml:space="preserve">
            <lb/>
          ♈ # ♉ # ♊ # ♋ # ♌ # ♍ # ♎ # ♏ # ♐ # ♑ # ♒ # ♓ H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. 6. 0. # 6. 42. # 7. 17. # 7. 32. # 7. 17. # 6. 42. # 6. 0. # 5. 18. # 4. 43. # 4. 28. # 4. 43. # 5. </note>
          <p>
            <s xml:id="echoid-s11763" xml:space="preserve">in horologio horizontali æquidiſtent lineæ ſignorum aſcendentium, ob rationem dictam. </s>
            <s xml:id="echoid-s11764" xml:space="preserve">Nam
              <lb/>
            lineæ ♈, & </s>
            <s xml:id="echoid-s11765" xml:space="preserve">♎, æquidiſtant lineæ hor. </s>
            <s xml:id="echoid-s11766" xml:space="preserve">6.</s>
            <s xml:id="echoid-s11767" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11768" xml:space="preserve">o. </s>
            <s xml:id="echoid-s11769" xml:space="preserve">à meridie vel media nocte. </s>
            <s xml:id="echoid-s11770" xml:space="preserve">Lineæ ♉, & </s>
            <s xml:id="echoid-s11771" xml:space="preserve">♍, æqui-
              <lb/>
            diſtant lineæ horæ 5. </s>
            <s xml:id="echoid-s11772" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11773" xml:space="preserve">18. </s>
            <s xml:id="echoid-s11774" xml:space="preserve">Lineæ ♊, & </s>
            <s xml:id="echoid-s11775" xml:space="preserve">♌, æquidiſtant lineæ hor. </s>
            <s xml:id="echoid-s11776" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11777" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11778" xml:space="preserve">43. </s>
            <s xml:id="echoid-s11779" xml:space="preserve">Vnde & </s>
            <s xml:id="echoid-s11780" xml:space="preserve">bi-
              <lb/>
            næ inter ſe æquidiſtantes erunt. </s>
            <s xml:id="echoid-s11781" xml:space="preserve">At vero linea ♋, æquidiſtat lineæ hor.</s>
            <s xml:id="echoid-s11782" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11783" xml:space="preserve">min.</s>
            <s xml:id="echoid-s11784" xml:space="preserve">28. </s>
            <s xml:id="echoid-s11785" xml:space="preserve">Linea denique
              <lb/>
              <note position="left" xlink:label="note-0200-04" xlink:href="note-0200-04a" xml:space="preserve">30. primi.</note>
            ♑, æquidiſtat lineæ hor.</s>
            <s xml:id="echoid-s11786" xml:space="preserve">7.</s>
            <s xml:id="echoid-s11787" xml:space="preserve">min.</s>
            <s xml:id="echoid-s11788" xml:space="preserve">32.</s>
            <s xml:id="echoid-s11789" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11790" xml:space="preserve">EST autem hic, & </s>
            <s xml:id="echoid-s11791" xml:space="preserve">in ſequentibus horologijs diligenter notandum, nullam lineam aſcenden-
              <lb/>
              <note position="left" xlink:label="note-0200-05" xlink:href="note-0200-05a" xml:space="preserve">Lineę aſcenden
                <lb/>
              tiu m ſignorum
                <lb/>
              tangunt tropi-
                <lb/>
              cos in horolo-
                <lb/>
              gio quocunq;.</note>
              <note position="left" xlink:label="note-0200-06" xlink:href="note-0200-06a" xml:space="preserve">30</note>
            tium ſignorum poſſe tropicos ſecare, ſed omnes contingere eos tantummodo in punctis illis, per
              <lb/>
            quæ ducendæ ſunt, ita vt omnes lineæ ſignorum aſcendentium intra limites tropicorum conti-
              <lb/>
            neantur. </s>
            <s xml:id="echoid-s11792" xml:space="preserve">Nam quemadmodum lineæ horarum ab ortu, vel occaſu tangunt ſectiones conicas pa-
              <lb/>
            rallelorum duorum, quorum vnus eſt ſemper apparentium, & </s>
            <s xml:id="echoid-s11793" xml:space="preserve">alter ſemper latentium maximus,
              <lb/>
            in illis punctis, in quibus lineæ horarum à meridie, vel media nocte eaſdem conicas ſectiones in-
              <lb/>
            terſecant, vt propoſ. </s>
            <s xml:id="echoid-s11794" xml:space="preserve">14. </s>
            <s xml:id="echoid-s11795" xml:space="preserve">præcedentis libri demonſtrauimus: </s>
            <s xml:id="echoid-s11796" xml:space="preserve">ita etiam communes ſectiones Ecli-
              <lb/>
            pticæ, & </s>
            <s xml:id="echoid-s11797" xml:space="preserve">plani horologii, quæ ex variis poſitionibus, quas Ecliptica ad motum diurnum obtinet,
              <lb/>
            efficiuntur, tangent conicas ſectiones tropicorumin illis punctis, in quibus eædem ſectiones co-
              <lb/>
            nicæ ſecantur à lineis illarum horarum à meridie, vel media nocte, in quibus illas poſitiones ha-
              <lb/>
            bet Ecliptica. </s>
            <s xml:id="echoid-s11798" xml:space="preserve">Eadem enim eſt demonſtratio hic & </s>
            <s xml:id="echoid-s11799" xml:space="preserve">ibi. </s>
            <s xml:id="echoid-s11800" xml:space="preserve">Quod ita perſpicuum faciemus. </s>
            <s xml:id="echoid-s11801" xml:space="preserve">Aſcen-
              <lb/>
              <note position="left" xlink:label="note-0200-07" xlink:href="note-0200-07a" xml:space="preserve">40</note>
            dente v.</s>
            <s xml:id="echoid-s11802" xml:space="preserve">g. </s>
            <s xml:id="echoid-s11803" xml:space="preserve">ſigno ♉, cum Sol eſt in principio ♑, linea hor.</s>
            <s xml:id="echoid-s11804" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11805" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11806" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11807" xml:space="preserve">poſt meridiem ſecat in horo
              <lb/>
            logio tropicum ♑, in K. </s>
            <s xml:id="echoid-s11808" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s11809" xml:space="preserve">circulus dictæ horæ per polos mũdi ductus circulum ♑, in cœ-
              <lb/>
            lo ſecabit in eo puncto, in quo exiſtens Sol radium emittit per verticem ſtyli ad punctum K. </s>
            <s xml:id="echoid-s11810" xml:space="preserve">Cum
              <lb/>
            ergo Ecliptica tangat in cœlo circulum ♑, in principio ♑, in quo Sol ponitur, neceſſe eſt, eam
              <lb/>
            tunc temporis tangere dictum circulum ♑, in eodem illo puncto, in quo à prædicto circulo ho-
              <lb/>
            rario ſecatur, quandoquidẽ radius Solis tunc in punctum K, cadit. </s>
            <s xml:id="echoid-s11811" xml:space="preserve">Quare in quo puncto tropicus
              <lb/>
            ♑, ſecatur tunc in horologio à linea hor. </s>
            <s xml:id="echoid-s11812" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11813" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11814" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11815" xml:space="preserve">poft meridiem, in eodem, nempe in K, tanget
              <lb/>
            eundem tropicum ♑, communis ſectio Eclipticæ, & </s>
            <s xml:id="echoid-s11816" xml:space="preserve">plani horologii, vt ex propoſ. </s>
            <s xml:id="echoid-s11817" xml:space="preserve">13. </s>
            <s xml:id="echoid-s11818" xml:space="preserve">& </s>
            <s xml:id="echoid-s11819" xml:space="preserve">14. </s>
            <s xml:id="echoid-s11820" xml:space="preserve">ſu-
              <lb/>
            perioris lib. </s>
            <s xml:id="echoid-s11821" xml:space="preserve">manifeſtum eſt. </s>
            <s xml:id="echoid-s11822" xml:space="preserve">Ita enim tunc ſe habent circulus dictæ horæ 1. </s>
            <s xml:id="echoid-s11823" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11824" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11825" xml:space="preserve">poſt meridiẽ,
              <lb/>
            & </s>
            <s xml:id="echoid-s11826" xml:space="preserve">Ecliptica, (cum ille ſuperficiem conicam ♑, ſecet per lineam rectam, hæc autem eandem ſu-
              <lb/>
              <note position="left" xlink:label="note-0200-08" xlink:href="note-0200-08a" xml:space="preserve">50</note>
            perficiem in eadem linea tangat) quemadmodum ſe habent circulus quilibet horarius à meridie,
              <lb/>
            vel media nocte ſecans conicam ſuperficiem paralleli ſemper apparentium maximi per lineam re-
              <lb/>
            ctam, & </s>
            <s xml:id="echoid-s11827" xml:space="preserve">circulus horarius ab ortu, vel occaſu in eadem linea recta tangens eandem ſuperficiẽ co-
              <lb/>
            nicam; </s>
            <s xml:id="echoid-s11828" xml:space="preserve">vt perſpicuum eſt, ſi rectè conſideretur poſitio Eclipticæ, & </s>
            <s xml:id="echoid-s11829" xml:space="preserve">dicti circuli hor. </s>
            <s xml:id="echoid-s11830" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11831" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11832" xml:space="preserve">10.
              <lb/>
            </s>
            <s xml:id="echoid-s11833" xml:space="preserve">dum principium ♉, aſcendit, & </s>
            <s xml:id="echoid-s11834" xml:space="preserve">Sol in principio ♑, exiſtit. </s>
            <s xml:id="echoid-s11835" xml:space="preserve">Colurus enim Solſtitiorum fungitur
              <lb/>
            tunc officio illius circuli horarij ſecans tropicum ♑, in puncto, in quo eundem tropicum Eclipti
              <lb/>
            ca contingit, nempe in principio ♑. </s>
            <s xml:id="echoid-s11836" xml:space="preserve">Id quod luce clarius ex ſphæra materiali intelligi poteſt. </s>
            <s xml:id="echoid-s11837" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0200-09" xlink:href="note-0200-09a" xml:space="preserve">Qua ratione
                <lb/>
              ſigna aſcendẽ-
                <lb/>
              tia per doctri-
                <lb/>
              nam conicorũ
                <lb/>
              Apollonii de-
                <lb/>
              ſeribãtur in ho
                <lb/>
              rologio.</note>
            Eademq́ue ratio eſt de cæteris ſignis aſcendentibus, Sole exiſtente in principio ♑, vel ♋.</s>
            <s xml:id="echoid-s11838" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11839" xml:space="preserve">EX his colligitur alius modus deſcribendorum ſignorum aſcendentium. </s>
            <s xml:id="echoid-s11840" xml:space="preserve">Si enim ex punctis
              <lb/>
            tropicorum inuentis per tabellam tertiam, & </s>
            <s xml:id="echoid-s11841" xml:space="preserve">quartam ducantur rectæ tangentes ipſos tropicos,
              <lb/>
            per ea, quæ in coroll. </s>
            <s xml:id="echoid-s11842" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s11843" xml:space="preserve">37. </s>
            <s xml:id="echoid-s11844" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11845" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11846" xml:space="preserve">Apollonii ſcripſimus, (quod quidem hic perfacile eſt, </s>
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