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-div933" type="section" level="1" n="226">
          <p>
            <s xml:id="echoid-s18492" xml:space="preserve">
              <pb o="272" file="0288" n="288" rhead="GNOMONICES"/>
            duo anguli A B D, A B K, ęquales in triangulis A B D, A B K; </s>
            <s xml:id="echoid-s18493" xml:space="preserve">ſed & </s>
            <s xml:id="echoid-s18494" xml:space="preserve">anguli ad A, ęquales ſunt,
              <lb/>
            vtpote recti, eſtq́ue latus A B, dictis angulis adiacens commune. </s>
            <s xml:id="echoid-s18495" xml:space="preserve">Igitur latera A D, A k, æqualia
              <lb/>
              <note position="left" xlink:label="note-0288-01" xlink:href="note-0288-01a" xml:space="preserve">26. primi.</note>
            erunt; </s>
            <s xml:id="echoid-s18496" xml:space="preserve">atque adeo cum per K, tranſeat linea horę 12. </s>
            <s xml:id="echoid-s18497" xml:space="preserve">ab ortu, vel occaſu, vt demonſtrauimus, per-
              <lb/>
            ſpicuum eſt, ſi ipſi A D, ſumatur æqualis A K, per K, ducendam eſſe dictam lineam horæ 12. </s>
            <s xml:id="echoid-s18498" xml:space="preserve">quę
              <lb/>
            quidem in K, tangit parallelum ſem per apparentium maximum. </s>
            <s xml:id="echoid-s18499" xml:space="preserve">Quamobrem horologium Ita
              <lb/>
            licum polare deſcripſimus. </s>
            <s xml:id="echoid-s18500" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s18501" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div940" type="section" level="1" n="227">
          <head xml:id="echoid-head233" xml:space="preserve">PROBLEMA 47. PROPOSITIO 47.</head>
          <note position="left" xml:space="preserve">10</note>
          <p>
            <s xml:id="echoid-s18502" xml:space="preserve">HOROLOGIVM Babylonicum polare delineare.</s>
            <s xml:id="echoid-s18503" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18504" xml:space="preserve">DESCRIBEMVS hoc horologium eiſdem rationibus fermè, quibus Italicum delineaui-
              <lb/>
              <note position="left" xlink:label="note-0288-03" xlink:href="note-0288-03a" xml:space="preserve">Horologii Ba-
                <lb/>
              bylonici polaris
                <lb/>
              deſcriptio.</note>
            mus: </s>
            <s xml:id="echoid-s18505" xml:space="preserve">ſi tamen in primo modo diuiſio circuli F G H I, in partes 24. </s>
            <s xml:id="echoid-s18506" xml:space="preserve">æquales initium habeat à ter
              <lb/>
            mino orientali arcus diurni tam tropici ♋, quàm tropici ♑, tum in puncto b, tum in e. </s>
            <s xml:id="echoid-s18507" xml:space="preserve">Linea
              <lb/>
            autem horę 12. </s>
            <s xml:id="echoid-s18508" xml:space="preserve">ducenda eſt parallela lineę ęquinoctiali per punctum in tropico ♋, inuentum,
              <lb/>
            vt prius.</s>
            <s xml:id="echoid-s18509" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18510" xml:space="preserve">IN ſecundo modo nullum prorſus diſcrimen eſt, ſi modo pro horis ab occ. </s>
            <s xml:id="echoid-s18511" xml:space="preserve">quarum mentio
              <lb/>
            facta eſt in antecedenti propoſ. </s>
            <s xml:id="echoid-s18512" xml:space="preserve">ſumantur eędem ab ortu, &</s>
            <s xml:id="echoid-s18513" xml:space="preserve">c. </s>
            <s xml:id="echoid-s18514" xml:space="preserve">Exemplum horologij Babylonici
              <lb/>
            habes in figura præcedentis propoſ. </s>
            <s xml:id="echoid-s18515" xml:space="preserve">vbi lineę parallelę inter ſe, & </s>
            <s xml:id="echoid-s18516" xml:space="preserve">ad lineam ęquinoctialem per-
              <lb/>
              <note position="left" xlink:label="note-0288-04" xlink:href="note-0288-04a" xml:space="preserve">20</note>
            pendiculares indicant horas à meridie, vel media nocte, quarum numeri aſcripti ſunt arcui diur-
              <lb/>
            no horarum 24. </s>
            <s xml:id="echoid-s18517" xml:space="preserve">& </s>
            <s xml:id="echoid-s18518" xml:space="preserve">nocturno arcui totidem horarum. </s>
            <s xml:id="echoid-s18519" xml:space="preserve">Deinde lineę, quibus appoſiti ſunt numeri
              <lb/>
            infra lineam ęquinoctialem, indicant horas Italicas. </s>
            <s xml:id="echoid-s18520" xml:space="preserve">Lineę denique, quibus numeri ſupra lineã
              <lb/>
            ęquinoctialem aſcripti ſunt, horis Babylonicis, ſeu ab ortu, tribuendę ſunt. </s>
            <s xml:id="echoid-s18521" xml:space="preserve">Horologium igitur
              <lb/>
            Babylonicum polare delineauimus. </s>
            <s xml:id="echoid-s18522" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s18523" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div943" type="section" level="1" n="228">
          <head xml:id="echoid-head234" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">Quomodo ho-
            <lb/>
          rologium Itali
            <lb/>
          cum polare dif-
            <lb/>
          ferat a Eabylo-
            <lb/>
          nico polari.</note>
          <p style="it">
            <s xml:id="echoid-s18524" xml:space="preserve">EX figura præcedentis horologii manifeſtum eſt, horologium Babylonicum non differre ab Italico,
              <lb/>
            niſi ſitu, & </s>
            <s xml:id="echoid-s18525" xml:space="preserve">ordine horarum, quemadmodum in horizontali horologio expoſuimus.</s>
            <s xml:id="echoid-s18526" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p style="it">
            <s xml:id="echoid-s18527" xml:space="preserve">HABET autem inferius horologium polare à ſuperiori ortum, ſi omnium horarum lineæ vltra ho-
              <lb/>
              <note position="left" xlink:label="note-0288-07" xlink:href="note-0288-07a" xml:space="preserve">Qua ratione
                <lb/>
              Infcrius horo-
                <lb/>
              logium polare
                <lb/>
              iam Italicum,
                <lb/>
              quàm Babylo-
                <lb/>
              nicum à Supe-
                <lb/>
              riore ortum ha
                <lb/>
              beat.</note>
            rizontalem lineam producantur, & </s>
            <s xml:id="echoid-s18528" xml:space="preserve">ſuperior pars mutetur in inferiorem, & </s>
            <s xml:id="echoid-s18529" xml:space="preserve">quæ dextra eſt poſt hanc mu
              <lb/>
            tationem, vertatur in ſiniſtram, vt oſtendimus in ſcholio propoſ. </s>
            <s xml:id="echoid-s18530" xml:space="preserve">14. </s>
            <s xml:id="echoid-s18531" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s18532" xml:space="preserve">Quæ autem horæ in infe-
              <lb/>
            riori horologio numerandę ſint ab occaſu, & </s>
            <s xml:id="echoid-s18533" xml:space="preserve">quæ ab ortu, cognoſcemus ex iis, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s18534" xml:space="preserve">23.
              <lb/>
            </s>
            <s xml:id="echoid-s18535" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s18536" xml:space="preserve">ſcripſimus.</s>
            <s xml:id="echoid-s18537" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s18538" xml:space="preserve">NON eſt etiam prætereundum hoc loco, in ea regione, vbi altitudo poli æqualis eſt complemento
              <lb/>
              <note position="left" xlink:label="note-0288-08" xlink:href="note-0288-08a" xml:space="preserve">In latitudine
                <lb/>
              loci gr. 66. Min.
                <lb/>
              30. horæ ab or.
                <lb/>
              & occ. tangunt
                <lb/>
              duos tropicos.
                <lb/>
              In maiori vero
                <lb/>
              latitudine horę
                <lb/>
              ab or. & occ. nõ
                <lb/>
              perueniunt ad
                <lb/>
              tropicos, ſed tan
                <lb/>
              gunt alios pa-
                <lb/>
              rallelos propin-
                <lb/>
              quiores lineæ
                <lb/>
              æquinoctiali, tã
                <lb/>
              in horologio
                <lb/>
              Meridiano, q̃
                <lb/>
              in polari.</note>
            maximæ declinationis Solis, hoc eſt, grad. </s>
            <s xml:id="echoid-s18539" xml:space="preserve">66. </s>
            <s xml:id="echoid-s18540" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s18541" xml:space="preserve">30. </s>
            <s xml:id="echoid-s18542" xml:space="preserve">duos tropicos fungi munere duorum parallelorum,
              <lb/>
            quorum vnus ſemper apparentium, alter verò ſemper latentium maximus eſt. </s>
            <s xml:id="echoid-s18543" xml:space="preserve">Vnde lineę horarum ab
              <lb/>
            ortu, vel occaſu tangent duos tropicos in horis à meridie, vel media nocte tam in utroque horologio Me-
              <lb/>
            ridiano, quàm in Polari. </s>
            <s xml:id="echoid-s18544" xml:space="preserve">In ea autem regione, ubi altitudo poli maior eſt, quàm grad. </s>
            <s xml:id="echoid-s18545" xml:space="preserve">66. </s>
            <s xml:id="echoid-s18546" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s18547" xml:space="preserve">30. </s>
            <s xml:id="echoid-s18548" xml:space="preserve">duos
              <lb/>
              <note position="left" xlink:label="note-0288-09" xlink:href="note-0288-09a" xml:space="preserve">40</note>
            prędictos parallelos cadere intra duos tropicos, ita vt lineæ horarum ab ortu, vel occaſu illos parallelos
              <lb/>
            tangentes ad ipſos tropicos nullo modo perueniant. </s>
            <s xml:id="echoid-s18549" xml:space="preserve">Vmbra enim ſtyli monſtrare tunc non poteſt horas
              <lb/>
            ab ortu, uel occaſu Solis elapſas, cum Sol exiſtens in tropicis neque oriatur, neque occidat, ſed perpetuo
              <lb/>
            ſupra Horizontem exiſtat, uel infra.</s>
            <s xml:id="echoid-s18550" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div946" type="section" level="1" n="229">
          <head xml:id="echoid-head235" xml:space="preserve">PROBLEMA 48. PROPOSITIO 48.</head>
          <p>
            <s xml:id="echoid-s18551" xml:space="preserve">HOROLOGIVM Antiquum polare conſtituere.</s>
            <s xml:id="echoid-s18552" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18553" xml:space="preserve">SECETVR arcus diurnus tam tropici ♋, a F b, quàm tropici ♑, d F e, in circulo F G H I,
              <lb/>
              <note position="left" xlink:label="note-0288-10" xlink:href="note-0288-10a" xml:space="preserve">50</note>
              <note position="left" xlink:label="note-0288-11" xlink:href="note-0288-11a" xml:space="preserve">Deſcriptio ho-
                <lb/>
              rologii Antiqui
                <lb/>
              polaris.</note>
            in 12. </s>
            <s xml:id="echoid-s18554" xml:space="preserve">partes ęquales. </s>
            <s xml:id="echoid-s18555" xml:space="preserve">Ex his enim inueniemus in vtroque tropico puncta, per quæ ducendę erunt
              <lb/>
            horę inęquales, non aliter, ac in præcedentibus duabus propoſitionibus puncta horarum ab ortu,
              <lb/>
            & </s>
            <s xml:id="echoid-s18556" xml:space="preserve">occaſu Solis in eiſdem tropicis inueſtigauimus. </s>
            <s xml:id="echoid-s18557" xml:space="preserve">Tranſibunt autem neceſſario horæ inæqua-
              <lb/>
            les per puncta horarum à meridie, vel media nocte in linea ęquinoctiali, vt ſupra docuimus in ho-
              <lb/>
            rizontali horologio propoſ. </s>
            <s xml:id="echoid-s18558" xml:space="preserve">12. </s>
            <s xml:id="echoid-s18559" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s18560" xml:space="preserve">Certum autem eſt, vt ex figura appoſita apparet, ho-
              <lb/>
            ram 1. </s>
            <s xml:id="echoid-s18561" xml:space="preserve">& </s>
            <s xml:id="echoid-s18562" xml:space="preserve">11. </s>
            <s xml:id="echoid-s18563" xml:space="preserve">non cadere in horologium ſuperius, cum Sol in principio ♋, exiſtit.</s>
            <s xml:id="echoid-s18564" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18565" xml:space="preserve">PER arcus quoque duos diurnos in horologio deſcriptos, quorum vnus horas 18. </s>
            <s xml:id="echoid-s18566" xml:space="preserve">& </s>
            <s xml:id="echoid-s18567" xml:space="preserve">al-
              <lb/>
              <note position="left" xlink:label="note-0288-12" xlink:href="note-0288-12a" xml:space="preserve">Deſcriptio An-
                <lb/>
              tiqui horologii
                <lb/>
              polaris per ar-
                <lb/>
              cus diurnos ho
                <lb/>
              rarum 6. & 18.</note>
            ter ſex comprehendat, conſtruemus idem horologium Antiquum, vt in ſuperioribus factum
              <lb/>
            eſt, propoſ. </s>
            <s xml:id="echoid-s18568" xml:space="preserve">12. </s>
            <s xml:id="echoid-s18569" xml:space="preserve">24. </s>
            <s xml:id="echoid-s18570" xml:space="preserve">& </s>
            <s xml:id="echoid-s18571" xml:space="preserve">36. </s>
            <s xml:id="echoid-s18572" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s18573" xml:space="preserve">Id quod figura appoſita perſpicuè docet. </s>
            <s xml:id="echoid-s18574" xml:space="preserve">Horologiũ igitur
              <lb/>
            Antiquum polare conſtituimus. </s>
            <s xml:id="echoid-s18575" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s18576" xml:space="preserve"/>
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