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-div524" type="section" level="1" n="144">
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            <s xml:id="echoid-s9462" xml:space="preserve">
              <pb o="147" file="0167" n="167" rhead="LIBER SECVNDVS."/>
            gio, quę æquinoctialem lineam ſecat, eum ſemicirculũ cœleſtem referre, cuius communis ſectio facta in cir-
              <lb/>
              <note position="right" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">Quem ſemicir-
                <lb/>
              culum cęleſtem
                <lb/>
              quælibet linea
                <lb/>
              in horologio
                <lb/>
              repræſentet.</note>
            culo, quem ex E, centro Aequatoris, atque in eius plano deſcripſimus, (ſi nimirum eius centrum E, cum
              <lb/>
            centro mundi D, coniungatur) per centrum E, tranſit, antequam æquinoctiali lineę in horologio oc-
              <lb/>
            currat: </s>
            <s xml:id="echoid-s9463" xml:space="preserve">nimirum rectam H A, eſſe horam primam à meridie, hoc eſt, referre ſemicirculum illum cœle-
              <lb/>
            ſtem, in quo Sol hora prima à meridie exiſtit; </s>
            <s xml:id="echoid-s9464" xml:space="preserve">quia in A, cadit O E, per centrum E, ducta, quæ quidẽ O E,
              <lb/>
            communis ſectio eſt ſemicirculi horæ 1. </s>
            <s xml:id="echoid-s9465" xml:space="preserve">à meridie per punctum O, ducti, tranſit{q́ue} per centrũ E, priuſquam
              <lb/>
            ęquinoctialem lineam ſecat in A; </s>
            <s xml:id="echoid-s9466" xml:space="preserve">vt conſtat, ſi circulus ex E, deſcriptus concipiatur eſſe in plano Aequa
              <lb/>
            toris, centrum{q́ue} E, cum centro mundi D, coniunctum. </s>
            <s xml:id="echoid-s9467" xml:space="preserve">Cauſa huius rei eſt, quia Sol proijcit radium ſuum
              <lb/>
            prius ad centrum mundi, ſeu verticem ſtyli, antequam vmbra ſtyli in horologij planum cadat, vt perſpi-
              <lb/>
            cuum eſt. </s>
            <s xml:id="echoid-s9468" xml:space="preserve">Hac rationc erit quoque recta H K, hora 7. </s>
            <s xml:id="echoid-s9469" xml:space="preserve">à media nocte, hoc eſt, illum ſemicirculum cœle-
              <lb/>
              <note position="left" xlink:label="note-0167-02" xlink:href="note-0167-02a" xml:space="preserve">10</note>
            ſtem repræſentabit, in quo Sol exiſtit hora 7. </s>
            <s xml:id="echoid-s9470" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s9471" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s9472" xml:space="preserve">quia in K, cadit V E, per centrum E, ducta, quæ
              <lb/>
            quidem V E, communis ſectio eſt ſemicir culi horæ 7. </s>
            <s xml:id="echoid-s9473" xml:space="preserve">à media nocte, per punctum V, ducti, tranſit{q́ue} per
              <lb/>
            centrum E, antequam lineam ęquinoctialem ſecat in k, vt perſpicuum eſt; </s>
            <s xml:id="echoid-s9474" xml:space="preserve">atque ita de cęteris.</s>
            <s xml:id="echoid-s9475" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9476" xml:space="preserve">NON eſt etiam omittendum, lineam cuiuſcunque horę à meridie vltra centrum horologij productam
              <lb/>
              <note position="right" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">Linea cuiuſuis
                <lb/>
              horę à meridie
                <lb/>
              vltra centrum
                <lb/>
              horologij pro-
                <lb/>
              ducta indicat
                <lb/>
              eiuſdem nume-
                <lb/>
              ri horã à med.
                <lb/>
              noc. & contra.</note>
            monſtrare eiuſdem numeri horam à media nocte, & </s>
            <s xml:id="echoid-s9477" xml:space="preserve">contra. </s>
            <s xml:id="echoid-s9478" xml:space="preserve">Quod ita demonſtrabimus. </s>
            <s xml:id="echoid-s9479" xml:space="preserve">Sumatur exem-
              <lb/>
            pli gratia, circulus horæ quintæ à mer. </s>
            <s xml:id="echoid-s9480" xml:space="preserve">& </s>
            <s xml:id="echoid-s9481" xml:space="preserve">med. </s>
            <s xml:id="echoid-s9482" xml:space="preserve">nocte faciens in horologio lineam eiuſdem horæ per centrũ
              <lb/>
            H, ductam. </s>
            <s xml:id="echoid-s9483" xml:space="preserve">Quoniam igitur, ſi Sol in polo arctico poneretur, vmbra ſtyli caderet in punctum H, cum ra-
              <lb/>
            dius Solis tunc idem eſſet, qui axis mundi, qui quidem per verticem ſtyli ductus in puncto H, occurrit pla
              <lb/>
            no horologij, efficitur, vt Sole existente in ſemicirculo dicti circuli, qui oceidentalior eſt, quàm Meridia-
              <lb/>
            nus, vmbra ſtyli cadat in partem oppoſitam, nempe in eam partem lineæ horę quintæ, quæ orientalior eſt
              <lb/>
              <note position="left" xlink:label="note-0167-04" xlink:href="note-0167-04a" xml:space="preserve">20</note>
            in horologio, quàm linea meridiana; </s>
            <s xml:id="echoid-s9484" xml:space="preserve">exiſtente autem Sole in eiuſdem circuli altero ſemicirculo, quiorien
              <lb/>
            talior eſt Meridiano, vmbra ſtyli in partem eiuſdem lineę horę quintæ, quæ occidentalior eſt, quàm linea
              <lb/>
            meridiana, cadat. </s>
            <s xml:id="echoid-s9485" xml:space="preserve">Semper enim vmbra in dictam lineam cadit, dum Sol in dicto circulo exiſtit, vt pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s9486" xml:space="preserve">11. </s>
            <s xml:id="echoid-s9487" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s9488" xml:space="preserve">oſtendimus. </s>
            <s xml:id="echoid-s9489" xml:space="preserve">Cum ergo ſemicirculus occidentalis pertineat ad horam quintam pome
              <lb/>
            ridianam, & </s>
            <s xml:id="echoid-s9490" xml:space="preserve">orientalis ad quintam poſt mediam noctem, indicabit orientalis portio illius lineæ, quæni-
              <lb/>
            mirum ex centro H, tendit ad partem orienta lem horologij, (Diuidit porrò linea meridiana horologium
              <lb/>
            totum in partem orientalem, & </s>
            <s xml:id="echoid-s9491" xml:space="preserve">occidentalem, quemadmodum & </s>
            <s xml:id="echoid-s9492" xml:space="preserve">Meridianus totam ſphęram cœleſtem
              <lb/>
            in hemiſphærium orientale, & </s>
            <s xml:id="echoid-s9493" xml:space="preserve">occidentale partitur) horam quintam à meridie, reliqua autem portio eiuſ-
              <lb/>
            dem lineæ in partem occidentalem vergens, horam quintam à media nocte. </s>
            <s xml:id="echoid-s9494" xml:space="preserve">Eadem{q́ue} ratio eſt de cęteris
              <lb/>
            lineis, in alijs etiam horologijs, quæ non ſunt horizontalia.</s>
            <s xml:id="echoid-s9495" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p style="it">
            <s xml:id="echoid-s9496" xml:space="preserve">IDEM hac etiam ratione oſtendemus, & </s>
            <s xml:id="echoid-s9497" xml:space="preserve">breuius. </s>
            <s xml:id="echoid-s9498" xml:space="preserve">Quoniam vmbra styli ante meridiem cadit in par
              <lb/>
            tem occidentalem horologij, poſt meridiem verò in orientalem, cum in contrariam ſemper partem Solis
              <lb/>
            proijciatur, pertinebunt omnes lineæ horariæ in parte occidentali (quam quidem linea meridiana ab
              <lb/>
            orientali dirimit in omni horologio) in centro H, terminatæ, ad horas antemeridianas, ſiue poſt mediam
              <lb/>
            noctem, reliquæ verò in orientali parte ad pomeridianas. </s>
            <s xml:id="echoid-s9499" xml:space="preserve">Cum ergo horariæ lineæ in parte orientali horo-
              <lb/>
            logij productæ vltra centrum exhibeant lineas earundem horarum in parte occidentali, & </s>
            <s xml:id="echoid-s9500" xml:space="preserve">econtrario,
              <lb/>
            perſpicuum eſt, quod proponitur.</s>
            <s xml:id="echoid-s9501" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9502" xml:space="preserve">HINC colligitur quemcunque circulum maximum per polos mundi tranſeuntem facere in horologio
              <lb/>
              <note position="right" xlink:label="note-0167-06" xlink:href="note-0167-06a" xml:space="preserve">Quilibet circu-
                <lb/>
              lus maximus P
                <lb/>
              polos mũdi du-
                <lb/>
              ctus facit in ho
                <lb/>
              rologio rectam
                <lb/>
              lineã, cuius una
                <lb/>
              portio in cen-
                <lb/>
              tro terminata
                <lb/>
              pertinet ad vnũ
                <lb/>
              ſemicirculũ, &
                <lb/>
              altera ad alterũ.</note>
            ſectionem, lineam rectam, cuius vna portio in centro terminata pertinet ad vnum ſemicirculum, & </s>
            <s xml:id="echoid-s9503" xml:space="preserve">al-
              <lb/>
            tera ad alterum. </s>
            <s xml:id="echoid-s9504" xml:space="preserve">Hoc enim demonſtratum eſt in circulis horarum à meridie & </s>
            <s xml:id="echoid-s9505" xml:space="preserve">media nocte. </s>
            <s xml:id="echoid-s9506" xml:space="preserve">Idem{q́ue} ve-
              <lb/>
              <note position="left" xlink:label="note-0167-07" xlink:href="note-0167-07a" xml:space="preserve">40</note>
            rum eſt de circulis Meridianis, de quibus agemus propoſ. </s>
            <s xml:id="echoid-s9507" xml:space="preserve">6. </s>
            <s xml:id="echoid-s9508" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s9509" xml:space="preserve">Item de Verticalibus circulis, de
              <lb/>
            quibus propoſ. </s>
            <s xml:id="echoid-s9510" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9511" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s9512" xml:space="preserve">diſputabimus, dummodo loco poli mundi accipiamus verticem capitis, ſeu Ze-
              <lb/>
            nith, hoc eſt, polum Horizontis, & </s>
            <s xml:id="echoid-s9513" xml:space="preserve">in horologio loco centri horologij ſumamus punctũ verticale, in quod
              <lb/>
            cadit axis Horizontis, cuiuſmodi eſt in horizontali horologio, quod deſcripſimus, punctum G.</s>
            <s xml:id="echoid-s9514" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9515" xml:space="preserve">EX his perfacile iudicare poterimus, quęnam lineæ horarię ad horas à meridie pertineant, & </s>
            <s xml:id="echoid-s9516" xml:space="preserve">quæ
              <lb/>
            ad horas à media nocte. </s>
            <s xml:id="echoid-s9517" xml:space="preserve">Quoniam enim, ſi circulus ex E, deſcriptus in proprio ſitu collocetur, punctum
              <lb/>
              <note position="right" xlink:label="note-0167-08" xlink:href="note-0167-08a" xml:space="preserve">Qua ratione iu
                <lb/>
              dicandum ſit,
                <lb/>
              quæ lineæ hora
                <lb/>
              riæ pertineant
                <lb/>
              ad horas à mer.
                <lb/>
              & quæ ad horas
                <lb/>
              à med. noc. in
                <lb/>
              horologio de-
                <lb/>
              ſcripto.</note>
            N, Meridianum ſecat ſupra Horizontem, pertinebit illud ad horam 12. </s>
            <s xml:id="echoid-s9518" xml:space="preserve">meridiei, ita vt recta NE, ſit
              <lb/>
            communis ſectio Meridiani, ſeu circuli horæ 12. </s>
            <s xml:id="echoid-s9519" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s9520" xml:space="preserve">Cum ergo NE, per centrum E, tranſeat, at-
              <lb/>
            que æquinoctialem lineam ſecet in I, indicabit recta H I E, horam 12. </s>
            <s xml:id="echoid-s9521" xml:space="preserve">meridiei, & </s>
            <s xml:id="echoid-s9522" xml:space="preserve">reliqua eius portio
              <lb/>
            vltra centrum horologij H, horam 12. </s>
            <s xml:id="echoid-s9523" xml:space="preserve">mediæ noctis. </s>
            <s xml:id="echoid-s9524" xml:space="preserve">Eadem ratione pertinebunt rectę H A, H B, & </s>
            <s xml:id="echoid-s9525" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0167-09" xlink:href="note-0167-09a" xml:space="preserve">50</note>
            cæteræ in parte orientali horologij poſitæ, ad horas poſt meridiem: </s>
            <s xml:id="echoid-s9526" xml:space="preserve">quia referunt ſemicirculos horarios
              <lb/>
            ſectionum O E, Q E, & </s>
            <s xml:id="echoid-s9527" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9528" xml:space="preserve">qui quidem horas à meridie indicant in circulo ex E, deſcripto. </s>
            <s xml:id="echoid-s9529" xml:space="preserve">Denique li-
              <lb/>
            neę in parte occidentali horologij poſitæ, id eſt, ad dextram lineæ ipſius meridianæ, horas à media nocte ſi-
              <lb/>
            gnificabunt: </s>
            <s xml:id="echoid-s9530" xml:space="preserve">quoniam referunt ſemicirculos horarios, quorum ſectiones in circulo ex E, deſcripto rece-
              <lb/>
            dunt à recta N E, verſus orientalem plagam, monſtrant{q́ue} horas ante meridiem, vel à@media nocte.</s>
            <s xml:id="echoid-s9531" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9532" xml:space="preserve">HOC ſi attentè conſideretur, cognoſcemus facillimè etiam in omnibus alijs horologijs, de quibus in
              <lb/>
              <note position="right" xlink:label="note-0167-10" xlink:href="note-0167-10a" xml:space="preserve">Quomodo indi
                <lb/>
              candum ſit in
                <lb/>
              omni horolo-
                <lb/>
              gio, quæ lineæ
                <lb/>
              horariæ ad ho-
                <lb/>
              ras à mer. & quę
                <lb/>
              ad horas à med.
                <lb/>
              noc. pertinean@.</note>
            ſequentibus agemus, quęnam horæ ſint à meridie numerandæ, & </s>
            <s xml:id="echoid-s9533" xml:space="preserve">quæ à media nocte.</s>
            <s xml:id="echoid-s9534" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9535" xml:space="preserve">MONENDVS quoque lector eſt, nos hactenus horologium horizontale conſtruxiſſe in plana qua-
              <lb/>
            cunque ſuperficie, vt illud poſtea in proprio ſitu collocetur, vel in planum aliquod ſtabile, quod Horizonti
              <lb/>
            ſit parallelum, transferatur, ita vt recta H E, ſit linea meridiana, & </s>
            <s xml:id="echoid-s9536" xml:space="preserve">punctum H, ad auſtrum, punctum
              <lb/>
            verò E, ad boream vergat, velut in hoc ſcholio tradidimus. </s>
            <s xml:id="echoid-s9537" xml:space="preserve">Quòd ſiplanum aliquod ſtabile, quod </s>
          </p>
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