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-div820" type="section" level="1" n="197">
          <pb o="239" file="0257" n="257" rhead="LIBER SECVNDVS."/>
        </div>
        <div xml:id="echoid-div823" type="section" level="1" n="198">
          <head xml:id="echoid-head201" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="right" xml:space="preserve">Segmenta lineę
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          ęqu
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          i
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          noctialis in
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          utrouis horolo-
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          gi
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          o Meridi
            <unsure/>
          ano
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          inter lineã ho-
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          ræ 6. & b@nas ho
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          ras u@rinque à
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          linea ho@æ 6.
            <lb/>
          æquali @empo-
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          ris @patio re
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          m
            <unsure/>
          o
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          tas, ſ
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          untæqua-
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          lia.</note>
          <p style="it">
            <s xml:id="echoid-s16212" xml:space="preserve">IN quocunq; </s>
            <s xml:id="echoid-s16213" xml:space="preserve">horologio Meridiano binæ lineæ quæunq; </s>
            <s xml:id="echoid-s16214" xml:space="preserve">horariæ hinc inde à linea horæ ſextæ D E,
              <lb/>
            æquali ſpatio temporis remotæ auferunt ex linea æquinoctiali A C, lineas inter ipſas, & </s>
            <s xml:id="echoid-s16215" xml:space="preserve">lineã horæ ſex-
              <lb/>
            tæ interiectas æquales, ita vt in linea æquinoctiali ſpatia horaria ante ſextam horam æqualia ſint hora-
              <lb/>
            rijs ſpatijs poſt ſextam horam, ſingula ſingulis. </s>
            <s xml:id="echoid-s16216" xml:space="preserve">Vt lineæ A M, A N, in occident ali horologio, quarum
              <lb/>
            quælibet quatuor horas complectitur, æquales ſunt. </s>
            <s xml:id="echoid-s16217" xml:space="preserve">Cũ enim anguli M E A, N E A, in centro E, æqua-
              <lb/>
            libus arcubus ſubtenſi æquales ſint, & </s>
            <s xml:id="echoid-s16218" xml:space="preserve">anguli ad A, recti, latus{q́ue} A E, commune; </s>
            <s xml:id="echoid-s16219" xml:space="preserve">erunt quoque rectæ
              <lb/>
            A M, A N, æquales, ſimiliter & </s>
            <s xml:id="echoid-s16220" xml:space="preserve">E M, E N. </s>
            <s xml:id="echoid-s16221" xml:space="preserve">Eademq́, de cæteris ratio eſt habenda. </s>
            <s xml:id="echoid-s16222" xml:space="preserve">Ex quo fit, ſatis eſſe
              <lb/>
              <note position="right" xlink:label="note-0257-02" xlink:href="note-0257-02a" xml:space="preserve">27. tertij.</note>
              <note position="right" xlink:label="note-0257-03" xlink:href="note-0257-03a" xml:space="preserve">26. primi.</note>
            ad deſcriptionem horologij Meridiani, ſi per centrum E, & </s>
            <s xml:id="echoid-s16223" xml:space="preserve">puncta diuiſionum vnius quadrantis, nem-
              <lb/>
              <note position="left" xlink:label="note-0257-04" xlink:href="note-0257-04a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0257-05" xlink:href="note-0257-05a" xml:space="preserve">Saus e@tad de-
                <lb/>
              ſcriptionẽ horo
                <lb/>
              logii Meridia-
                <lb/>
              ni, ſi vnus dun-
                <lb/>
              taxat quadrans
                <lb/>
              circuli ex E, de-
                <lb/>
              ſcripu in 6. par
                <lb/>
              tes æquales di
                <unsure/>
              -
                <lb/>
              ſtribuatur.</note>
            pe H I, rectæ ducantur ſecantes æquinoctialem lineam in punctis S, N, Q, & </s>
            <s xml:id="echoid-s16224" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16225" xml:space="preserve">Nam ſi hæc puncta ex
              <lb/>
            A, in alteram partem eiuſdem lineæ æquinoctialis beneficio circini trans ferantur, habebuntur omnia pũ
              <lb/>
            cta, per quæ ducendæ ſunt lineæ horariæ.</s>
            <s xml:id="echoid-s16226" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16227" xml:space="preserve">IAM vero ſi horologium in plano, quod Meridiano æquidiſtet, collocetur, it a vt A B, recta Hori-
              <lb/>
            zonti ſit æquidiſtans, & </s>
            <s xml:id="echoid-s16228" xml:space="preserve">punctum A, Boream, punctum vero B, Auſtrum reſpiciat, adeo vt angulus com-
              <lb/>
            plementi altitudinis poli B A C, qui ſupra a lineam horizontalem A B, exiſtit, in auſtrum vergat in vtro-
              <lb/>
              <note position="right" xlink:label="note-0257-06" xlink:href="note-0257-06a" xml:space="preserve">Quon odovtrũ
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              que horologiũ
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              Meridianu
                <unsure/>
              @@
                <lb/>
              collecandum,
                <lb/>
              vnà cum ſtylo,
                <lb/>
              vt horas demon
                <lb/>
              ſtret.</note>
            que horologio, qui vero infra eandem lineam horizontalem huic oppoſitus eſt, in Boream, indicabuntur ho
              <lb/>
            ræ à gnomone A E, ad angulos rectos inſiſtente plano horologij in puncto A, ita vt ſtylus ipſe communis
              <lb/>
            ſectio ſit Horizontis, & </s>
            <s xml:id="echoid-s16229" xml:space="preserve">Aequatoris, ſeu circuli horæſextæ, Verticaliſue. </s>
            <s xml:id="echoid-s16230" xml:space="preserve">Hæc enim cõmunis ſectio per-
              <lb/>
              <note position="left" xlink:label="note-0257-07" xlink:href="note-0257-07a" xml:space="preserve">20</note>
            pendicularis eſt ad planum horologij in puncto A, per quod dictorum circulorum plana ad planum ho-
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            rologii recta exiſtentia tranſeunt. </s>
            <s xml:id="echoid-s16231" xml:space="preserve">Quòd ſi ex duobus punctis quibuslibet rectæ D E, vt ex D, & </s>
            <s xml:id="echoid-s16232" xml:space="preserve">E, eri-
              <lb/>
              <note position="right" xlink:label="note-0257-08" xlink:href="note-0257-08a" xml:space="preserve">19. vndec.</note>
            gantur ad planum horologij duæ perpendiculares E O,
              <lb/>
              <figure xlink:label="fig-0257-01" xlink:href="fig-0257-01a" number="180">
                <image file="0257-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0257-01"/>
              </figure>
            D P, gnomoni aſſumpto A E, æquales, ipſis{q́ue} ſuperpo-
              <lb/>
            natur recta O P, fungetur hæc munere axis, cum per cen
              <lb/>
            trum mundi tranſeat; </s>
            <s xml:id="echoid-s16233" xml:space="preserve">per punctum nimirum, quod eſt
              <lb/>
            vertex styli ex A, erecti, æquidiſtet{q́ue} lineæ horæ 6. </s>
            <s xml:id="echoid-s16234" xml:space="preserve">vt
              <lb/>
            ratio poſtulat. </s>
            <s xml:id="echoid-s16235" xml:space="preserve">Nam linea horæ ſextæ, & </s>
            <s xml:id="echoid-s16236" xml:space="preserve">axis mundi
              <lb/>
              <note position="right" xlink:label="note-0257-09" xlink:href="note-0257-09a" xml:space="preserve">16. vndec.</note>
            ſunt æquidiſtantes, communes videlicet ſectiones Meri-
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            diani circuli, & </s>
            <s xml:id="echoid-s16237" xml:space="preserve">plani horology factæ à circulo horæ 6.
              <lb/>
            </s>
            <s xml:id="echoid-s16238" xml:space="preserve">Huius igitur axis O P, vmbra proiecta in lineas hora-
              <lb/>
              <note position="left" xlink:label="note-0257-10" xlink:href="note-0257-10a" xml:space="preserve">30</note>
            rias à meridie, vel media nocte, indicabit quoque horas à meridie, vel media nocte, quemadmodum de ho
              <lb/>
            rologio horizontali, Verticali{q́ue} diximus.</s>
            <s xml:id="echoid-s16239" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Cui ſegmento
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          æquinoctialis li
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          neæ in vtroque
            <lb/>
          horologio Me-
            <lb/>
          ridiano ſtylus
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          æqualis ſit.</note>
          <p style="it">
            <s xml:id="echoid-s16240" xml:space="preserve">GNOMON autem aſſumptus A E, perpetuo æqualis est parti æquinoctialis lineæ, quæ inter A,
              <lb/>
            & </s>
            <s xml:id="echoid-s16241" xml:space="preserve">horam tertiam vel nonam interijcitur, id eſt, rectæ A Q, vel A R, in occidentali horologio. </s>
            <s xml:id="echoid-s16242" xml:space="preserve">Quo-
              <lb/>
            niam enim totus quadrans G H, diuiſus eſt in 6. </s>
            <s xml:id="echoid-s16243" xml:space="preserve">æquales horas, diuidet circulus horæ nonæ tribus horis
              <lb/>
            diſtans à recta E H, horæſextæ, vel à recta E G, horæ 12. </s>
            <s xml:id="echoid-s16244" xml:space="preserve">eundem quadrantem bifariam; </s>
            <s xml:id="echoid-s16245" xml:space="preserve">ac proinde an-
              <lb/>
            gulus A E R, angulo G E R, æqualis erit. </s>
            <s xml:id="echoid-s16246" xml:space="preserve">Cum ergo totus A E G, rectus ſit, erit vterq; </s>
            <s xml:id="echoid-s16247" xml:space="preserve">angulorũ G E R,
              <lb/>
              <note position="right" xlink:label="note-0257-12" xlink:href="note-0257-12a" xml:space="preserve">27. tertij.</note>
            A E R, ſemirectus. </s>
            <s xml:id="echoid-s16248" xml:space="preserve">Quare cum angulus E A R, rectus ſit, erit & </s>
            <s xml:id="echoid-s16249" xml:space="preserve">reliquus angulus E R A, ſemirectus;
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            </s>
            <s xml:id="echoid-s16250" xml:space="preserve">
              <note position="right" xlink:label="note-0257-13" xlink:href="note-0257-13a" xml:space="preserve">32. primi.</note>
              <note position="right" xlink:label="note-0257-14" xlink:href="note-0257-14a" xml:space="preserve">O@entale horo
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              logium, ſi ita
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              inuertatur, vt
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              ſuperiota in in
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              feriora, & quæ
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              in hoc ſi@u dex-
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              rra ſunt, fiant ſi
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              niſtra, & cõtra,
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              exhibet horolo
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              gium occiden-
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              tale. Eodemq́;
                <lb/>
              modo occiden-
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              tale dabi
                <unsure/>
              orien
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              tale.</note>
            ac propterea exiſtentibus angulis E R A, A E R, æqualibus, æquales quoque erunt rectæ A E, A R; </s>
            <s xml:id="echoid-s16251" xml:space="preserve">Ea-
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            dem{q́ue} ratio eſt de A E, A Q, & </s>
            <s xml:id="echoid-s16252" xml:space="preserve">c.</s>
            <s xml:id="echoid-s16253" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p style="it">
            <s xml:id="echoid-s16254" xml:space="preserve">SATIS autem eſt, ſi ſolum horologiũ ad ortum ſpectans deſcribatur. </s>
            <s xml:id="echoid-s16255" xml:space="preserve">Hoc enim ſi ita inuertatur,
              <lb/>
            vt ſuperiora in inferiora, & </s>
            <s xml:id="echoid-s16256" xml:space="preserve">dextra in ſiniſtra mutentur, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s16257" xml:space="preserve">14. </s>
            <s xml:id="echoid-s16258" xml:space="preserve">huius libri docuimus,
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            præbebit nobis alterum horologium, quod ad occaſum ſpectat. </s>
            <s xml:id="echoid-s16259" xml:space="preserve">Quod hac etiam ratione faciemus perſpi-
              <lb/>
            cuum. </s>
            <s xml:id="echoid-s16260" xml:space="preserve">Quoniam in triangulo A E C, in orientali horologio, & </s>
            <s xml:id="echoid-s16261" xml:space="preserve">in triangulo A E S, in occidentali, anguli
              <lb/>
            ad A, æquales ſunt, nempe recti, & </s>
            <s xml:id="echoid-s16262" xml:space="preserve">anguli quoque ad E, æquales, ob æquales arcus inter H, & </s>
            <s xml:id="echoid-s16263" xml:space="preserve">rectas
              <lb/>
            E C, E S, poſitos, quibus inſistunt, necnon & </s>
            <s xml:id="echoid-s16264" xml:space="preserve">latera A E, A E, dictis angulis adiacentia ſunt æqualia,
              <lb/>
            cum vtrumq; </s>
            <s xml:id="echoid-s16265" xml:space="preserve">ſit longitudo ſtyli; </s>
            <s xml:id="echoid-s16266" xml:space="preserve">erunt quoque latera A C, A S, æqualia. </s>
            <s xml:id="echoid-s16267" xml:space="preserve">Quoniam vero, ſi horologium
              <lb/>
            orientale occidentali ſuperponatur, ita vt punctum A, puncto A, & </s>
            <s xml:id="echoid-s16268" xml:space="preserve">linea horizontalis A B, lineæ hori
              <lb/>
              <note position="right" xlink:label="note-0257-16" xlink:href="note-0257-16a" xml:space="preserve">27. tertij.</note>
            zontali A B, congruat, & </s>
            <s xml:id="echoid-s16269" xml:space="preserve">pars ſuperior Orientalis horologij cadat infra horizontalem lineam, & </s>
            <s xml:id="echoid-s16270" xml:space="preserve">infe
              <lb/>
              <note position="right" xlink:label="note-0257-17" xlink:href="note-0257-17a" xml:space="preserve">26. primi.</note>
            rior ſupra: </s>
            <s xml:id="echoid-s16271" xml:space="preserve">Item in co ſitu pars dextra mutetur in ſiniſtram, & </s>
            <s xml:id="echoid-s16272" xml:space="preserve">contra, æquinoctialis linea A C, Orien
              <lb/>
              <note position="left" xlink:label="note-0257-18" xlink:href="note-0257-18a" xml:space="preserve">50</note>
            talis horologij lineæ æquinoctiali A S, horologij occidentalis congruit, propter æqualitatem angulorum,
              <lb/>
            quos vtraq; </s>
            <s xml:id="echoid-s16273" xml:space="preserve">linea æquinoctialis cum horizontali facit verſus eaſdem partes in hoc ſitu, quem orienta-
              <lb/>
            le horologium habet eo modo inuerſum, vt diximus; </s>
            <s xml:id="echoid-s16274" xml:space="preserve">cadet quoque punctum C, in punctum S, propter
              <lb/>
            æquales lineas A C, A S. </s>
            <s xml:id="echoid-s16275" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s16276" xml:space="preserve">linea primæ horæ orientalis horologii per punctum C, ducta lineæ
              <lb/>
            primæ horæ occidentalis horologii per punctum S, ductæ congruet, cum vtraq; </s>
            <s xml:id="echoid-s16277" xml:space="preserve">cum æquinoctiali linea an
              <lb/>
            gulum rectum conſtituat, vt ſupra ostendimus. </s>
            <s xml:id="echoid-s16278" xml:space="preserve">Eodem modo reliquas lineas horarias horologii orienta-
              <lb/>
            lis reliquis lineis horariis occidentalis horologii demonſtrabimus congruere. </s>
            <s xml:id="echoid-s16279" xml:space="preserve">Quocirca orientale horolo-
              <lb/>
            gium inuerſum, vt dictum eſt, exhibebit horologium occidentale, cum illud hac ratione eundem ſitum,
              <lb/>
            quem hoc, ſortiatur, ei{q́ue} æquale ſit omni ex parte, vt oſtendimus.</s>
            <s xml:id="echoid-s16280" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16281" xml:space="preserve">SED horæ, quæ in orientali horologio numer antur à media nocte, ſunt poſt illam inuerſionem compu
              <lb/>
            tandæ à meridie, cum iam factum ſit occidentale.</s>
            <s xml:id="echoid-s16282" xml:space="preserve"/>
          </p>
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