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-div916" type="section" level="1" n="222">
          <p>
            <s xml:id="echoid-s17996" xml:space="preserve">
              <pb o="266" file="0282" n="282" rhead="GNOMONICES"/>
            & </s>
            <s xml:id="echoid-s17997" xml:space="preserve">hic communis ſectio omnium circulorum cœleſtium domorum, hoc eſt, axis Verticalis circu-
              <lb/>
            li, ſeu communis ſectio Meridiani circuli, & </s>
            <s xml:id="echoid-s17998" xml:space="preserve">Horizontis, plano horologij in puncto D, occurrit, vt
              <lb/>
            patet ex figura propoſ. </s>
            <s xml:id="echoid-s17999" xml:space="preserve">38. </s>
            <s xml:id="echoid-s18000" xml:space="preserve">huius libri, in qua hæc communis ſectio eſt recta B D, ſi triangulum
              <lb/>
            A B D, intelligatur rectum ad planum horologii.</s>
            <s xml:id="echoid-s18001" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18002" xml:space="preserve">SED ex Campani ſententia ita eaſdem domos cęleſtes delineabimus. </s>
            <s xml:id="echoid-s18003" xml:space="preserve">Ex figura propoſ. </s>
            <s xml:id="echoid-s18004" xml:space="preserve">40.
              <lb/>
            </s>
            <s xml:id="echoid-s18005" xml:space="preserve">
              <note position="left" xlink:label="note-0282-01" xlink:href="note-0282-01a" xml:space="preserve">Deſcriptio do-
                <lb/>
              morum cœle-
                <lb/>
              ſtium in eodẽ
                <lb/>
              horologio pola
                <lb/>
              ri, ſecundum
                <lb/>
              Campanum.</note>
            huius libri accipiemus rectam B C, per quam Zenith C, inueſtigauimus, eamq́ue in lineam meri
              <lb/>
            dianam à puncto C, ſiue ſurſum, ſiue deorſum verſus transferemus vſque ad F. </s>
            <s xml:id="echoid-s18006" xml:space="preserve">Deinde deſcripto
              <lb/>
            circulo ex F, eoq́ue in 12. </s>
            <s xml:id="echoid-s18007" xml:space="preserve">partes æquales diſtributo, facto initio à linea meridiana, ducemus per
              <lb/>
            puncta diuiſionum, & </s>
            <s xml:id="echoid-s18008" xml:space="preserve">per centrum F, rectas occultas ſecantes lineam Verticalem in punctis, quæ
              <lb/>
            lineis rectis iuncta cum D, exhibebunt domos cęleſtes, vt vult Campanus. </s>
            <s xml:id="echoid-s18009" xml:space="preserve">Nam ſi hic circulus cir
              <lb/>
              <note position="left" xlink:label="note-0282-02" xlink:href="note-0282-02a" xml:space="preserve">10</note>
            ca linea in Verticalem vertatur, donec cum Verticali propriè dicto, eiusq́; </s>
            <s xml:id="echoid-s18010" xml:space="preserve">centrum F, cum centro
              <lb/>
            mundi B, coniungatur; </s>
            <s xml:id="echoid-s18011" xml:space="preserve">erunt occultæ illæ rectæ per F, ductæ, communes ſectiones circulorum
              <lb/>
            cœleſtium domorum, & </s>
            <s xml:id="echoid-s18012" xml:space="preserve">Verticali, ac proin de circuli domorum cęleſtium plano horologii occur-
              <lb/>
            rent in prædictis punctis lineæ Verticalis. </s>
            <s xml:id="echoid-s18013" xml:space="preserve">Quare lineæ domorum cœleſtium per eadem puncta
              <lb/>
            tranſibunt, atque idcirco, cum tranſeant quoque per punctum D, vt dictum eſt, erunt prędictæ re-
              <lb/>
            ctæ puncta Verticalis lineæ cum D, connectentes, lineæ domorum cœleſtium. </s>
            <s xml:id="echoid-s18014" xml:space="preserve">Quam obrem do-
              <lb/>
            mos cœleſtes in eodem horologio polari deſcripſimus. </s>
            <s xml:id="echoid-s18015" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s18016" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div919" type="section" level="1" n="223">
          <head xml:id="echoid-head229" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s18017" xml:space="preserve">LINEAE domorum cęleſtium vltra horizontalem lineã productæ dabunt eaſdem domos cœleſtes
              <lb/>
              <note position="left" xlink:label="note-0282-04" xlink:href="note-0282-04a" xml:space="preserve">Domus cęleſtes
                <lb/>
              vltra lineam ho
                <lb/>
              rizontalem pro
                <lb/>
              ductę dant eaſ-
                <lb/>
              dem domos in
                <lb/>
              Inferiori horo-
                <lb/>
              logio, ſi portio
                <lb/>
              illa horologii à
                <lb/>
              linea horizon-
                <lb/>
              tali abſciſta in-
                <lb/>
              uertatur ſecun -
                <lb/>
              dum omnes ſui
                <lb/>
              partes.</note>
            in horologio inferiori, ſi inuertatur horologium, vt ſæpe dictum eſt, at que in ſcholio propoſ. </s>
            <s xml:id="echoid-s18018" xml:space="preserve">14. </s>
            <s xml:id="echoid-s18019" xml:space="preserve">huius li-
              <lb/>
            bri demonſtratum. </s>
            <s xml:id="echoid-s18020" xml:space="preserve">Verum domus cœleſtes in inferiori horologio nullum vſum habent, præter illas, quæ
              <lb/>
            ultra horizontalem lineam tropicum ♋, ſecant, quod eò commodius fit, quò polus maiorem eleuationem
              <lb/>
            habet ſupra Horizontem, vt perſpicuum eſt. </s>
            <s xml:id="echoid-s18021" xml:space="preserve">In noſtro exemplo, quod ad latitudinem grad. </s>
            <s xml:id="echoid-s18022" xml:space="preserve">42. </s>
            <s xml:id="echoid-s18023" xml:space="preserve">fabrica-
              <lb/>
            tum eſt, nulla domus cœleſtis in inferiori horologio integra deſcribi poteſt, cum nulla tropicum ultra li-
              <lb/>
            neam horizontalem ſecet. </s>
            <s xml:id="echoid-s18024" xml:space="preserve">Solum partes domus 12. </s>
            <s xml:id="echoid-s18025" xml:space="preserve">& </s>
            <s xml:id="echoid-s18026" xml:space="preserve">7. </s>
            <s xml:id="echoid-s18027" xml:space="preserve">hoc eſt, lineæ ductæ per gradus intermedios
              <lb/>
            dictarum domorum in horologio inferiori deſcribi poſſunt, pręſcrtim per illos, qui ab Horizonte non
              <lb/>
            longè abſunt.</s>
            <s xml:id="echoid-s18028" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
        </div>
        <div xml:id="echoid-div921" type="section" level="1" n="224">
          <head xml:id="echoid-head230" xml:space="preserve">PROBLEMA. 45. PROPOSITIO 45.</head>
          <p>
            <s xml:id="echoid-s18029" xml:space="preserve">SIGNA Zodiaci aſcendentia in eodem horologio polari de-
              <lb/>
            ſcribere.</s>
            <s xml:id="echoid-s18030" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18031" xml:space="preserve">EX primis duabus tabellis propoſ. </s>
            <s xml:id="echoid-s18032" xml:space="preserve">9. </s>
            <s xml:id="echoid-s18033" xml:space="preserve">huius libri ſumantur horæ, quibus 12. </s>
            <s xml:id="echoid-s18034" xml:space="preserve">ſigna Zodiaci
              <lb/>
              <note position="left" xlink:label="note-0282-06" xlink:href="note-0282-06a" xml:space="preserve">Aſcendentium
                <lb/>
              ſignorum in eo
                <lb/>
              dem polari ho-
                <lb/>
              rologio deſcri-
                <lb/>
              ptio.</note>
            oriuntur, Sole exiſtente in principio ♈, & </s>
            <s xml:id="echoid-s18035" xml:space="preserve">♎, quæ in circulo F G H I, ex E, deſcripto, per quem vi-
              <lb/>
            delicet horæ ſunt deſignatæ, numerentur à puncto F, vel verſus ortum, vel verſus occaſum, prout
              <lb/>
            tabulæ offerunt horas ante, vel poſt meridiem. </s>
            <s xml:id="echoid-s18036" xml:space="preserve">Semper autem horæ ante meridiem numerandæ
              <lb/>
              <note position="left" xlink:label="note-0282-07" xlink:href="note-0282-07a" xml:space="preserve">40</note>
            ſunt ab F, verſus I, horæ verò poſt meridiem ab F, verſus G, in horologio ſuperiori: </s>
            <s xml:id="echoid-s18037" xml:space="preserve">in inferiori au
              <lb/>
            tem horæ antemeridianæ ab H, verſus I, pomeridianæ ab H, verſus G, vt liquido conſtat, ſi in vtro-
              <lb/>
            que horologio circulus F G H I, in propria poſitione intelligatur conſtitutus. </s>
            <s xml:id="echoid-s18038" xml:space="preserve">Nam ſi circulus
              <lb/>
            F G H I, in plano Aequatoris intelligatur, & </s>
            <s xml:id="echoid-s18039" xml:space="preserve">centrum E, in centro mundi, & </s>
            <s xml:id="echoid-s18040" xml:space="preserve">in vertice ſtyli, erit in
              <lb/>
            ſuperiori quidem horologio F, in meridie, & </s>
            <s xml:id="echoid-s18041" xml:space="preserve">H, in media nocte; </s>
            <s xml:id="echoid-s18042" xml:space="preserve">in inferiori verò H, exiſtet in me-
              <lb/>
            ridie, & </s>
            <s xml:id="echoid-s18043" xml:space="preserve">F, in media nocte. </s>
            <s xml:id="echoid-s18044" xml:space="preserve">Deinde per fines num erationum, & </s>
            <s xml:id="echoid-s18045" xml:space="preserve">centrum E, ducantur occultæ li-
              <lb/>
            neæ rectæ ſecantes æquinoctialem lineam in punctis illarum horarum, per quæ lineæ ſignorum
              <lb/>
            aſcendentium ſunt ducendæ. </s>
            <s xml:id="echoid-s18046" xml:space="preserve">Cauendum eſt autem, ne ex dictis tabellis ſumantur horæ illorum
              <lb/>
            ſignorum, quæ ſex horis, vel pluribus ante, vel poſt meridiem oriuntur. </s>
            <s xml:id="echoid-s18047" xml:space="preserve">Hæ enim in horologium
              <lb/>
            ſuperius polare non cadunt. </s>
            <s xml:id="echoid-s18048" xml:space="preserve">Quòd ſi ſigna aſcendentia deſcribenda ſint in inferiori horologio,
              <lb/>
              <note position="left" xlink:label="note-0282-08" xlink:href="note-0282-08a" xml:space="preserve">50</note>
            accipiendæ ſunt hæ horæ, non autem illorum ſignorum, quę ſex horis, ante aut poſt meridiem, vel
              <lb/>
            paucioribus oriuntur. </s>
            <s xml:id="echoid-s18049" xml:space="preserve">Poſt hæc in linea horizontali notentur puncta, per quæ arcus ſignorum du
              <lb/>
            cuntur. </s>
            <s xml:id="echoid-s18050" xml:space="preserve">In illa enim, quæ in parte antemeridiana continentur, (nempe in ſiniſtra ſuperioris horo-
              <lb/>
            logii, vel in dextra inferioris) proiiciuntur vmbræ, cum illa ſigna oriuntur, nempe ♑, in ſuperiori
              <lb/>
            horologio & </s>
            <s xml:id="echoid-s18051" xml:space="preserve">♐, ♒, & </s>
            <s xml:id="echoid-s18052" xml:space="preserve">♏, ♓. </s>
            <s xml:id="echoid-s18053" xml:space="preserve">in inferiori verò ♋, & </s>
            <s xml:id="echoid-s18054" xml:space="preserve">♊, ♌, & </s>
            <s xml:id="echoid-s18055" xml:space="preserve">♉, ♍. </s>
            <s xml:id="echoid-s18056" xml:space="preserve">In ea autem puncta, quæ
              <lb/>
            in pomeridiana parte ſunt ſignata, (hoc eſt, in dextra horologii ſuperioris, vel in ſiniſtra inferio-
              <lb/>
            ris) proiiciuntur vmbræ illorum ſignorum occidentium, quorum oppoſita tunc oriuntur, qua-
              <lb/>
            lia ſunt in ſuperiori horologio ♑, & </s>
            <s xml:id="echoid-s18057" xml:space="preserve">♐, ♒, & </s>
            <s xml:id="echoid-s18058" xml:space="preserve">♏, ♓. </s>
            <s xml:id="echoid-s18059" xml:space="preserve">horum enim vmbræ in illa puncta cadunt, cũ
              <lb/>
            occidunt. </s>
            <s xml:id="echoid-s18060" xml:space="preserve">oppoſita verò ſigna vt ♋, & </s>
            <s xml:id="echoid-s18061" xml:space="preserve">♊, ♌, & </s>
            <s xml:id="echoid-s18062" xml:space="preserve">♉, ♍, tunc oriuntur. </s>
            <s xml:id="echoid-s18063" xml:space="preserve">In inferiori autem horolo-
              <lb/>
            gio vmbræ horum ſignorum ♋, & </s>
            <s xml:id="echoid-s18064" xml:space="preserve">♊, ♌, & </s>
            <s xml:id="echoid-s18065" xml:space="preserve">♉, ♍, in illa puncta cadunt, cum occidunt: </s>
            <s xml:id="echoid-s18066" xml:space="preserve">oppoſi-
              <lb/>
            ta verò ſigna, nempe ♑, & </s>
            <s xml:id="echoid-s18067" xml:space="preserve">♐, ♒, & </s>
            <s xml:id="echoid-s18068" xml:space="preserve">♏, ♓, tunc ſupra Horizontem aſcendunt. </s>
            <s xml:id="echoid-s18069" xml:space="preserve">Itaque ſi puncta </s>
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