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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          <p>
            <s xml:id="echoid-s24960" xml:space="preserve">
              <pb o="381" file="0397" n="397" rhead="LIBER TERTIVS."/>
            ni ſectioni Meridiani, & </s>
            <s xml:id="echoid-s24961" xml:space="preserve">Aequatoris parallela, vt conſtat ex demõſtratione propoſ. </s>
            <s xml:id="echoid-s24962" xml:space="preserve">18. </s>
            <s xml:id="echoid-s24963" xml:space="preserve">libri 1. </s>
            <s xml:id="echoid-s24964" xml:space="preserve">Quę
              <lb/>
            cum ita ſint, ſecabunt circuli horarij planum horologij inclinati in ijſdem punctis, in quibus re-
              <lb/>
            ctæ per centrum L, & </s>
            <s xml:id="echoid-s24965" xml:space="preserve">diuiſionum puncta in circulo ex L, deſcripto eductæ, tanquam commu-
              <lb/>
            nes ſectiones dictorum circulorum, & </s>
            <s xml:id="echoid-s24966" xml:space="preserve">Aequatoris, occurrunt lineæ æquinoctiali; </s>
            <s xml:id="echoid-s24967" xml:space="preserve">atque adeo cõ-
              <lb/>
            munes ſectiones eorundem circulorum, & </s>
            <s xml:id="echoid-s24968" xml:space="preserve">plani horologij inclinati, hoc eſt, lineæ horariæ, per
              <lb/>
            eadem puncta erunt ducendæ. </s>
            <s xml:id="echoid-s24969" xml:space="preserve">Cum ergo eædem per coroll. </s>
            <s xml:id="echoid-s24970" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s24971" xml:space="preserve">21. </s>
            <s xml:id="echoid-s24972" xml:space="preserve">primi libri, ſe mutuo ſe-
              <lb/>
            cent in ρ, centro horologii, vel, vbi centrum non habetur, parallelæ ſint inter ſe, ex coroll. </s>
            <s xml:id="echoid-s24973" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s24974" xml:space="preserve">22. </s>
            <s xml:id="echoid-s24975" xml:space="preserve">eiuſdem libri, erunt rectæ per puncta lineæ æquinoctialis, & </s>
            <s xml:id="echoid-s24976" xml:space="preserve">per punctum ρ, ductæ, vel certè,
              <lb/>
            vbi non eſt centrum horologii, ipſi lineæ meridianæ parallelæ, lineæ horarum à meridie, vel me-
              <lb/>
            dia nocte, id eſt, communes ſectiones plani horologij, & </s>
            <s xml:id="echoid-s24977" xml:space="preserve">circulorum horariorum à meridie, vel
              <lb/>
              <note position="left" xlink:label="note-0397-01" xlink:href="note-0397-01a" xml:space="preserve">10</note>
            media nocte. </s>
            <s xml:id="echoid-s24978" xml:space="preserve">Quæ autem ſint horæ à meridie, & </s>
            <s xml:id="echoid-s24979" xml:space="preserve">quæ à media nocte, facile intelligi poteſt, ſi cir-
              <lb/>
            culus ex L, deſcriptus concipiatur vna cum horologio in propria poſitione, & </s>
            <s xml:id="echoid-s24980" xml:space="preserve">ea diligenter con-
              <lb/>
            ſiderentur, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s24981" xml:space="preserve">1. </s>
            <s xml:id="echoid-s24982" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s24983" xml:space="preserve">2. </s>
            <s xml:id="echoid-s24984" xml:space="preserve">ſcripſimus de interſectionibus æquinoctialis lineæ, & </s>
            <s xml:id="echoid-s24985" xml:space="preserve">
              <lb/>
            rectarum circuli ex L, deſcripti, obſeruando ſemper, ſi horologium, & </s>
            <s xml:id="echoid-s24986" xml:space="preserve">dictus circulus intelligan-
              <lb/>
            tur in propria poſitione, puncta diuiſionum, quæ ſequuntur communem ſectionem Meridiani, & </s>
            <s xml:id="echoid-s24987" xml:space="preserve">
              <lb/>
            Aequatoris, (qualis eſt recta L M,) verſus occidentem ex parte ſuperiori, referre horas à meri-
              <lb/>
            die, puncta verò, quæ eandem rectam L M, ſequuntur verſus orientem ex parte inferiori, horas à
              <lb/>
            media nocte. </s>
            <s xml:id="echoid-s24988" xml:space="preserve">Et quoniam, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s24989" xml:space="preserve">1. </s>
            <s xml:id="echoid-s24990" xml:space="preserve">ſuperioris libri docuimus, lineæ rectæ prius trã-
              <lb/>
            ſire debent per centrum L, quàm occurrant lineæ æquinoctiali, facile cognoſci poterit, quænam
              <lb/>
            puncta æquinoctialis lineæ indicent horas à meridie, & </s>
            <s xml:id="echoid-s24991" xml:space="preserve">quæ à media nocte: </s>
            <s xml:id="echoid-s24992" xml:space="preserve">Ita vt rectè ordo ho-
              <lb/>
              <note position="left" xlink:label="note-0397-02" xlink:href="note-0397-02a" xml:space="preserve">20</note>
            rarum à nobis ſupra deſcriptus ſit. </s>
            <s xml:id="echoid-s24993" xml:space="preserve">Nam ſi rectè diligenterq́ue rem perpendamus, deprehende-
              <lb/>
              <note position="right" xlink:label="note-0397-03" xlink:href="note-0397-03a" xml:space="preserve">Quomodo iudi
                <lb/>
              ca
                <unsure/>
              dum ſit, quæ
                <lb/>
              horę à mer. &
                <lb/>
              quę@à med noc.
                <lb/>
              co
                <unsure/>
              putãdæ ſint.</note>
            mus lineam æquinoctialem in horologiis, quæ ad Zenith pertinent, & </s>
            <s xml:id="echoid-s24994" xml:space="preserve">auſtrum reſpiciunt, eſſe ſe-
              <lb/>
            ctionem plani horologij, & </s>
            <s xml:id="echoid-s24995" xml:space="preserve">Aequatoris, in quam cadunt radij Solis in ſemicirculo Aequatoris ſu-
              <lb/>
            pra Horizontem exiſtentis. </s>
            <s xml:id="echoid-s24996" xml:space="preserve">Vndelineæ meridianæ portio lineam æquinoctialem ſecans in illis
              <lb/>
            horologijs horam 12. </s>
            <s xml:id="echoid-s24997" xml:space="preserve">meridiei indicabit; </s>
            <s xml:id="echoid-s24998" xml:space="preserve">lineæ verò verſus partes orientales monſtrabunt horas
              <lb/>
            poſt meridiem, quales ſunt illæ, quæ nobis ad horologia conuerſis ad dextram ſunt poſitæ. </s>
            <s xml:id="echoid-s24999" xml:space="preserve">Idem
              <lb/>
            contingit in horologijs, quæ ad Zenith pertinent, ſpectantq́ue in boream, & </s>
            <s xml:id="echoid-s25000" xml:space="preserve">habent lineam æqui
              <lb/>
            noctialem infra centrum horologij, ſed partes orientales ſitæ ſunt nobis ad horologia conuerſis.
              <lb/>
            </s>
            <s xml:id="echoid-s25001" xml:space="preserve">ad ſiniſtram. </s>
            <s xml:id="echoid-s25002" xml:space="preserve">In horologijs autem ad Zenith pertinentibus, & </s>
            <s xml:id="echoid-s25003" xml:space="preserve">quæ boream reſpiciunt, habentq́; </s>
            <s xml:id="echoid-s25004" xml:space="preserve">
              <lb/>
            æquinoctialem lineam ſupra centrum horologij, linea æquinoctialis communis ſectio eſt Aequa-
              <lb/>
              <note position="left" xlink:label="note-0397-04" xlink:href="note-0397-04a" xml:space="preserve">30</note>
            toris, & </s>
            <s xml:id="echoid-s25005" xml:space="preserve">plani horologij, in quam vmbræ cadunt, Sole exiſtente in ſemicirculo Aequatoris infra
              <lb/>
            Horizontem. </s>
            <s xml:id="echoid-s25006" xml:space="preserve">Quamobrem portio lineæ meridianæ lineam æquinoctialem ſecans oſtendet in his
              <lb/>
            horologiis horam 12. </s>
            <s xml:id="echoid-s25007" xml:space="preserve">mediæ noctis, & </s>
            <s xml:id="echoid-s25008" xml:space="preserve">lineæ verſus partes occidentales, quæ nobis dextræ ſunt, ſi
              <lb/>
            faciem ad horologia conuertamus, horas poſt mediam noctem dabunt, vt ſupra diximus.</s>
            <s xml:id="echoid-s25009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25010" xml:space="preserve">QVOD ſi ex F, egrediantur rectæ efficientes cum E F, linea declinationis, quam oſtendimus
              <lb/>
              <note position="right" xlink:label="note-0397-05" xlink:href="note-0397-05a" xml:space="preserve">Alia deſcriptio
                <lb/>
              horarum ex ho
                <lb/>
              rologio horizõ-
                <lb/>
              tali.</note>
            eſſe lineam meridianam in horologio horizontali, eoſdem angulos, quos cum linea meridiana
              <lb/>
            conſtituunt lineæ horariæ in horizontali horologio, nempelinea horæ 6. </s>
            <s xml:id="echoid-s25011" xml:space="preserve">qualis eſt F α, angulum
              <lb/>
            rectum α F E, & </s>
            <s xml:id="echoid-s25012" xml:space="preserve">c. </s>
            <s xml:id="echoid-s25013" xml:space="preserve">ſecabitur recta A B, in punctis, per quæ rectæ emiſſæ ex centro ρ, vel, vbi non eſt
              <lb/>
            centrum, ipſi meridianæ lineæ parallelæ ductæ, dabunt horarias lineas, vt prius; </s>
            <s xml:id="echoid-s25014" xml:space="preserve">veluti demonſtra
              <lb/>
            uimus propoſ. </s>
            <s xml:id="echoid-s25015" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25016" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s25017" xml:space="preserve">Qua de re vide, quæ ibi ſcripſimus circa perpendicularem F α, vt per
              <lb/>
              <note position="left" xlink:label="note-0397-06" xlink:href="note-0397-06a" xml:space="preserve">40</note>
            illam, vel aliquam aliam lineam ex F, egredientem diuiſio circuli ex L, deſcripti recte inſtituatur,
              <lb/>
            quemadmodum ſupra quoque in hac propoſ. </s>
            <s xml:id="echoid-s25018" xml:space="preserve">monuimus.</s>
            <s xml:id="echoid-s25019" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Conſtructio a-
            <lb/>
          lia horologii de
            <lb/>
          clinantis ſi
            <unsure/>
          mul
            <lb/>
          & inclinati, ad
            <lb/>
          ſimilitudinem
            <lb/>
          horologii hori-
            <lb/>
          zontalis.</note>
          <p>
            <s xml:id="echoid-s25020" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s25021" xml:space="preserve">Conſtruemus quoque horologium idem declinans ſimul & </s>
            <s xml:id="echoid-s25022" xml:space="preserve">inclinatum, ad ſi-
              <lb/>
            militudinem horizontalis horologij, quemadmodum & </s>
            <s xml:id="echoid-s25023" xml:space="preserve">in declinante horologio à Verticali ſcri-
              <lb/>
            pſimus propoſ. </s>
            <s xml:id="echoid-s25024" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25025" xml:space="preserve">huius libri, hacarte. </s>
            <s xml:id="echoid-s25026" xml:space="preserve">Conſtituatur primum portio Analemmatis, vt in propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s25027" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25028" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s25029" xml:space="preserve">in qua contineantur ſectiones communes Meridiani proprii ipſius plani decli-
              <lb/>
            nanus ſimul & </s>
            <s xml:id="echoid-s25030" xml:space="preserve">inclinati cum Horizonte, Verticali, & </s>
            <s xml:id="echoid-s25031" xml:space="preserve">Aequatore, & </s>
            <s xml:id="echoid-s25032" xml:space="preserve">c. </s>
            <s xml:id="echoid-s25033" xml:space="preserve">(circulus autem maximus,
              <lb/>
            cui planum horologij declinantis ſimul & </s>
            <s xml:id="echoid-s25034" xml:space="preserve">inclinati æquidiſtat, vices gerit Horizontis, & </s>
            <s xml:id="echoid-s25035" xml:space="preserve">alius
              <lb/>
            circulus maximus ſecans illum ad angulos rectos, tranſiensq́ue per communes ſectiones Aequa-
              <lb/>
            toris, & </s>
            <s xml:id="echoid-s25036" xml:space="preserve">dicti Horizontis, munere Verticalis circuli fungitur) ita vt arcus C E, metiatur altitudi-
              <lb/>
              <note position="left" xlink:label="note-0397-08" xlink:href="note-0397-08a" xml:space="preserve">50</note>
            nem poli ſupra planum declinãs ſimul & </s>
            <s xml:id="echoid-s25037" xml:space="preserve">inclinatum, & </s>
            <s xml:id="echoid-s25038" xml:space="preserve">recta D G, ſitæqualis ſtylo horologij de-
              <lb/>
            clinantis ſimul & </s>
            <s xml:id="echoid-s25039" xml:space="preserve">inclinati cuiusuis magnitudinis aſſumpto, & </s>
            <s xml:id="echoid-s25040" xml:space="preserve">c. </s>
            <s xml:id="echoid-s25041" xml:space="preserve">In noſtro exemplo, quod ſextæ
              <lb/>
            figuræ accõmodauimus, prope quam dictam portionem Analemmatis deſcripſimus, arcus C E,
              <lb/>
              <note position="right" xlink:label="note-0397-09" xlink:href="note-0397-09a" xml:space="preserve">Altitu dines po
                <lb/>
              li ſupra plana
                <lb/>
              ſex figuratum
                <lb/>
              huiuſce propo-
                <lb/>
              ſiu
                <unsure/>
              onis.</note>
            continet grad. </s>
            <s xml:id="echoid-s25042" xml:space="preserve">66. </s>
            <s xml:id="echoid-s25043" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25044" xml:space="preserve">47. </s>
            <s xml:id="echoid-s25045" xml:space="preserve">Tanta enim ferè eſt altitudo poli inuenta ſupra planum illud inclina-
              <lb/>
            rum; </s>
            <s xml:id="echoid-s25046" xml:space="preserve">& </s>
            <s xml:id="echoid-s25047" xml:space="preserve">recta D G, ſumpta eſt æqualis ſtylo I K, eiuſdem horologij. </s>
            <s xml:id="echoid-s25048" xml:space="preserve">In prima autem figura idem
              <lb/>
            arcus C E, ſi portio Analemmatis conſtruatur figuræ illi reſpondens, continebit grad. </s>
            <s xml:id="echoid-s25049" xml:space="preserve">25. </s>
            <s xml:id="echoid-s25050" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25051" xml:space="preserve">43.
              <lb/>
            </s>
            <s xml:id="echoid-s25052" xml:space="preserve">In ſecunda grad. </s>
            <s xml:id="echoid-s25053" xml:space="preserve">25. </s>
            <s xml:id="echoid-s25054" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25055" xml:space="preserve">18. </s>
            <s xml:id="echoid-s25056" xml:space="preserve">In tertia grad. </s>
            <s xml:id="echoid-s25057" xml:space="preserve">0. </s>
            <s xml:id="echoid-s25058" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25059" xml:space="preserve">0. </s>
            <s xml:id="echoid-s25060" xml:space="preserve">In quarta grad. </s>
            <s xml:id="echoid-s25061" xml:space="preserve">68. </s>
            <s xml:id="echoid-s25062" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25063" xml:space="preserve">13. </s>
            <s xml:id="echoid-s25064" xml:space="preserve">In quinta de-
              <lb/>
            nique grad. </s>
            <s xml:id="echoid-s25065" xml:space="preserve">27. </s>
            <s xml:id="echoid-s25066" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25067" xml:space="preserve">50. </s>
            <s xml:id="echoid-s25068" xml:space="preserve">Tantæ enim ferè ſunt altitudines poli ſupra illa plana inclinata repertæ,
              <lb/>
            iuxta doctrinam propoſ. </s>
            <s xml:id="echoid-s25069" xml:space="preserve">29. </s>
            <s xml:id="echoid-s25070" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25071" xml:space="preserve">1.</s>
            <s xml:id="echoid-s25072" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25073" xml:space="preserve">POST hæc ducãtur rectæ G N, G H, ſeſe ad rectos angulos ſecantes in G, quarum G N, re-
              <lb/>
            ferat ſectionem communem plani horologii, & </s>
            <s xml:id="echoid-s25074" xml:space="preserve">Meridiani proprii ipſius plani, inſtar lineæ </s>
          </p>
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