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-div1604" type="section" level="1" n="407">
          <pb o="485" file="0501" n="501" rhead="LIBER QVINTVS."/>
          <p style="it">
            <s xml:id="echoid-s30953" xml:space="preserve">VSVS autem huius tabulæ, quæ Generalis eſt, & </s>
            <s xml:id="echoid-s30954" xml:space="preserve">omnibus climatibus accommodata, hic eſt. </s>
            <s xml:id="echoid-s30955" xml:space="preserve">Da-
              <lb/>
              <note position="right" xlink:label="note-0501-01" xlink:href="note-0501-01a" xml:space="preserve">Vſus præceden
                <lb/>
              tis tabulæ lon
                <lb/>
              gitudinum vm
                <lb/>
              brarum.</note>
            ta altitudine Solis, quær antur eius gradus in ſuperiori parte tabulæ, & </s>
            <s xml:id="echoid-s30956" xml:space="preserve">Minuta, ſi qua fuerint, in ſi-
              <lb/>
            niſtro latere. </s>
            <s xml:id="echoid-s30957" xml:space="preserve">Mox enim in angulo communi reperientur Partes, & </s>
            <s xml:id="echoid-s30958" xml:space="preserve">Minuta longitudinis umbræ rectæ,
              <lb/>
            quatenus gnomon ex eiſdem partibus comprehendit duodecim. </s>
            <s xml:id="echoid-s30959" xml:space="preserve">Quod ſi ſumantur gradus in inferiori
              <lb/>
            parte tabulæ, & </s>
            <s xml:id="echoid-s30960" xml:space="preserve">Minuta, ſi qua ſint, in dextro latere, inuenientur in angulo communi Partes, & </s>
            <s xml:id="echoid-s30961" xml:space="preserve">Minu-
              <lb/>
            ta vmbræ verſæ. </s>
            <s xml:id="echoid-s30962" xml:space="preserve">Vt ſi quæratur longitudo vmbræ rectæ ad altitudinẽ Solis gr. </s>
            <s xml:id="echoid-s30963" xml:space="preserve">64. </s>
            <s xml:id="echoid-s30964" xml:space="preserve">inueniemus eam conti
              <lb/>
            nere par. </s>
            <s xml:id="echoid-s30965" xml:space="preserve">5. </s>
            <s xml:id="echoid-s30966" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s30967" xml:space="preserve">51. </s>
            <s xml:id="echoid-s30968" xml:space="preserve">Eadem autem, dum Sol altitudinem habet grad. </s>
            <s xml:id="echoid-s30969" xml:space="preserve">31. </s>
            <s xml:id="echoid-s30970" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s30971" xml:space="preserve">30. </s>
            <s xml:id="echoid-s30972" xml:space="preserve">complectetur par.
              <lb/>
            </s>
            <s xml:id="echoid-s30973" xml:space="preserve">19. </s>
            <s xml:id="echoid-s30974" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s30975" xml:space="preserve">35. </s>
            <s xml:id="echoid-s30976" xml:space="preserve">& </s>
            <s xml:id="echoid-s30977" xml:space="preserve">c. </s>
            <s xml:id="echoid-s30978" xml:space="preserve">Similiter ſi quæratur vmbra verſa ad altitudinem Solis grad. </s>
            <s xml:id="echoid-s30979" xml:space="preserve">26. </s>
            <s xml:id="echoid-s30980" xml:space="preserve">reperiemus eam
              <lb/>
            complecti par. </s>
            <s xml:id="echoid-s30981" xml:space="preserve">5. </s>
            <s xml:id="echoid-s30982" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s30983" xml:space="preserve">51. </s>
            <s xml:id="echoid-s30984" xml:space="preserve">Eadem autem, dum Sol altitudinem habet grad. </s>
            <s xml:id="echoid-s30985" xml:space="preserve">58. </s>
            <s xml:id="echoid-s30986" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s30987" xml:space="preserve">30. </s>
            <s xml:id="echoid-s30988" xml:space="preserve">habebit par. </s>
            <s xml:id="echoid-s30989" xml:space="preserve">
              <lb/>
            19. </s>
            <s xml:id="echoid-s30990" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s30991" xml:space="preserve">35. </s>
            <s xml:id="echoid-s30992" xml:space="preserve">& </s>
            <s xml:id="echoid-s30993" xml:space="preserve">c.</s>
            <s xml:id="echoid-s30994" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p style="it">
            <s xml:id="echoid-s30995" xml:space="preserve">EX hac eadem tabula cognoſcemus longitudines vmbrarum Solſtitialium, æquinoctialium, & </s>
            <s xml:id="echoid-s30996" xml:space="preserve">bru-
              <lb/>
              <note position="right" xlink:label="note-0501-03" xlink:href="note-0501-03a" xml:space="preserve">Longitudin es
                <lb/>
              vmbrarum Sol
                <lb/>
              ſtitialium, æqui
                <lb/>
              noctialium, atq;
                <lb/>
              brumaliũ, qua
                <lb/>
              ratione ex præ-
                <lb/>
              ce denti t
                <unsure/>
              abula
                <lb/>
              co gnoſcantur,
                <lb/>
              ad quam@unq;
                <lb/>
              loci latitudinẽ.</note>
            malium ad quamcunque latitudinem loci, pro qua re multi auctores peculiares tabulas condiderunt. </s>
            <s xml:id="echoid-s30997" xml:space="preserve">Si
              <lb/>
            enim in Solſtitio vtroque accipiatur altitudo meridiana, dicto citius ex ea longitudinem vmbræ inue-
              <lb/>
            niemus. </s>
            <s xml:id="echoid-s30998" xml:space="preserve">Pro vmbra autem æquinoctiali quærendum eſt in tabula complementum altitudinis poli. </s>
            <s xml:id="echoid-s30999" xml:space="preserve">Tan-
              <lb/>
            ta enim tunc eſt altitudo meridiana, & </s>
            <s xml:id="echoid-s31000" xml:space="preserve">c. </s>
            <s xml:id="echoid-s31001" xml:space="preserve">Vt ad latitudinem grad. </s>
            <s xml:id="echoid-s31002" xml:space="preserve">42. </s>
            <s xml:id="echoid-s31003" xml:space="preserve">altitudo meridiana principij ♋,
              <lb/>
            continet grad. </s>
            <s xml:id="echoid-s31004" xml:space="preserve">71. </s>
            <s xml:id="echoid-s31005" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s31006" xml:space="preserve">30. </s>
            <s xml:id="echoid-s31007" xml:space="preserve">cui in tabula reſpondent partes 4. </s>
            <s xml:id="echoid-s31008" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s31009" xml:space="preserve">1. </s>
            <s xml:id="echoid-s31010" xml:space="preserve">pro longitudine vmbræ rectæ Sol-
              <lb/>
            stitialis. </s>
            <s xml:id="echoid-s31011" xml:space="preserve">Rurſus altitudo meridiana principij ♈, aut ♎, comprehendit grad. </s>
            <s xml:id="echoid-s31012" xml:space="preserve">48. </s>
            <s xml:id="echoid-s31013" xml:space="preserve">Cui in eadem tabula
              <lb/>
            conueniunt par. </s>
            <s xml:id="echoid-s31014" xml:space="preserve">10. </s>
            <s xml:id="echoid-s31015" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s31016" xml:space="preserve">48. </s>
            <s xml:id="echoid-s31017" xml:space="preserve">pro vmbr a recta æquinoctiali. </s>
            <s xml:id="echoid-s31018" xml:space="preserve">Altitudo deniq; </s>
            <s xml:id="echoid-s31019" xml:space="preserve">meridiana principij ♑, eſt
              <lb/>
            grad. </s>
            <s xml:id="echoid-s31020" xml:space="preserve">24. </s>
            <s xml:id="echoid-s31021" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s31022" xml:space="preserve">30. </s>
            <s xml:id="echoid-s31023" xml:space="preserve">Igitur vmbra recta brumalis complectetur partes 26. </s>
            <s xml:id="echoid-s31024" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s31025" xml:space="preserve">20. </s>
            <s xml:id="echoid-s31026" xml:space="preserve">& </s>
            <s xml:id="echoid-s31027" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s31028" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s31029" xml:space="preserve">GEOMETRICE quoque longitudo vmbræ rectæ ad quamcun altitudinem Solis reperietur
              <lb/>
              <note position="left" xlink:label="note-0501-04" xlink:href="note-0501-04a" xml:space="preserve">20</note>
              <note position="right" xlink:label="note-0501-05" xlink:href="note-0501-05a" xml:space="preserve">Quomodo Geo
                <lb/>
              metricè ex alti-
                <lb/>
              tudine Solis lõ-
                <lb/>
              gitudo vmbræ
                <lb/>
              inueniatur.</note>
            hoc modo. </s>
            <s xml:id="echoid-s31030" xml:space="preserve">Ductis in quocunque circulo, vt in eo, quem in hac propoſ. </s>
            <s xml:id="echoid-s31031" xml:space="preserve">ſupra deſcripſimus, duabus re-
              <lb/>
            ctis A C, B D, ſeſe ad angulos rectos ſecantibus in centro E; </s>
            <s xml:id="echoid-s31032" xml:space="preserve">ſumatur in A C, recta E F, æqualis gno
              <lb/>
            moni, cuius longitudo vmbræ inquiritur, & </s>
            <s xml:id="echoid-s31033" xml:space="preserve">per F, ipſi B D, parallela agatur F G. </s>
            <s xml:id="echoid-s31034" xml:space="preserve">Poſtremo à puncto
              <lb/>
            D, vel B, verſus A, numeretur altitudo Solis vſque ad punctum I, quæ in dato exemplo comprehendit
              <lb/>
            ferme grad. </s>
            <s xml:id="echoid-s31035" xml:space="preserve">38. </s>
            <s xml:id="echoid-s31036" xml:space="preserve">Nam ductarecta I E, ex I, per centrum E, quæ rectam F G, ſecet in G, erit F G, lon-
              <lb/>
            gitudo vmbræ rectæ ad datam altitudinem Solis D I, vt ſupra demonstrauimus. </s>
            <s xml:id="echoid-s31037" xml:space="preserve">Eodem pacto erit H G,
              <lb/>
            vmbra verſa, ſi recta E H, ſumpta ſit æqualis gnomoni, & </s>
            <s xml:id="echoid-s31038" xml:space="preserve">per H, ipſi A C, parallela agatur H G.</s>
            <s xml:id="echoid-s31039" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1608" type="section" level="1" n="408">
          <head xml:id="echoid-head422" xml:space="preserve">PROBLEMA 3. PROPOSITIO 3.</head>
          <note position="left" xml:space="preserve">30</note>
          <p>
            <s xml:id="echoid-s31040" xml:space="preserve">ARCVM cuiuſuis circuli maximi interceptum inter Verticalem
              <lb/>
            eius circulum propriè dictum, & </s>
            <s xml:id="echoid-s31041" xml:space="preserve">Verticalem illum, qui qualibet hora
              <lb/>
            per centrum Solis ducitur, inueſtigare.</s>
            <s xml:id="echoid-s31042" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s31043" xml:space="preserve">REPETATVR tertia figura propoſ. </s>
            <s xml:id="echoid-s31044" xml:space="preserve">36. </s>
            <s xml:id="echoid-s31045" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s31046" xml:space="preserve">1. </s>
            <s xml:id="echoid-s31047" xml:space="preserve">in qua A B C D, ſit circulus maximus propoſi-
              <lb/>
              <note position="right" xlink:label="note-0501-07" xlink:href="note-0501-07a" xml:space="preserve">Qua via arcus
                <lb/>
              cuiuſuis circuli
                <lb/>
              maxi
                <unsure/>
              mi interce
                <lb/>
              pt
                <unsure/>
              us inter eius
                <lb/>
              Verticalem pro
                <lb/>
              p@@è dictum,
                <lb/>
              & alium Verti-
                <lb/>
              calem, qui per
                <lb/>
              Solem ducitur,
                <lb/>
              inquirendus ſit.</note>
            tus, ſiue is Horizon ſit, ſiue nõ; </s>
            <s xml:id="echoid-s31048" xml:space="preserve">Meridianus ipſius proprius B E D, per polos nimirũ eius, & </s>
            <s xml:id="echoid-s31049" xml:space="preserve">per po
              <lb/>
            los mundi ductus; </s>
            <s xml:id="echoid-s31050" xml:space="preserve">A F C, Aequator; </s>
            <s xml:id="echoid-s31051" xml:space="preserve">G I, parallelus Solis ſiue borealis, ſiue auſtralis; </s>
            <s xml:id="echoid-s31052" xml:space="preserve">A E C, Vertica
              <lb/>
            lis circuli propoſiti proprie dictus, trãſiens videlicet per polos ipſius, & </s>
            <s xml:id="echoid-s31053" xml:space="preserve">per polos Meridiani pro-
              <lb/>
            prij; </s>
            <s xml:id="echoid-s31054" xml:space="preserve">E L O, Verticalis per centrũ Solis in L, conſtituti ductus; </s>
            <s xml:id="echoid-s31055" xml:space="preserve">& </s>
            <s xml:id="echoid-s31056" xml:space="preserve">N L, circulus horarius per polos
              <lb/>
              <note position="left" xlink:label="note-0501-08" xlink:href="note-0501-08a" xml:space="preserve">40</note>
            mundi, & </s>
            <s xml:id="echoid-s31057" xml:space="preserve">centrũ Solis tranſiens hora propoſita. </s>
            <s xml:id="echoid-s31058" xml:space="preserve">Erit igitur A O, arcus inter dictos duos Verticales
              <lb/>
              <figure xlink:label="fig-0501-01" xlink:href="fig-0501-01a" number="313">
                <image file="0501-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0501-01"/>
              </figure>
              <note position="left" xlink:label="note-0501-09" xlink:href="note-0501-09a" xml:space="preserve">50</note>
            circulos poſitus: </s>
            <s xml:id="echoid-s31059" xml:space="preserve">quẽita inueniemus. </s>
            <s xml:id="echoid-s31060" xml:space="preserve">Quoniã in triangulo ſphęrico E N L, per propoſ. </s>
            <s xml:id="echoid-s31061" xml:space="preserve">17. </s>
            <s xml:id="echoid-s31062" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s31063" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s31064" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s31065" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s31066" xml:space="preserve">de triangulis, vel per propoſ. </s>
            <s xml:id="echoid-s31067" xml:space="preserve">13. </s>
            <s xml:id="echoid-s31068" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s31069" xml:space="preserve">1. </s>
            <s xml:id="echoid-s31070" xml:space="preserve">Gebri, aut per propoſ. </s>
            <s xml:id="echoid-s31071" xml:space="preserve">41. </s>
            <s xml:id="echoid-s31072" xml:space="preserve">noſtrorum trian
              <lb/>
            gulorum ſphæricorum, eſt vt ſinus arcus E L, complementi altitudinis Solis ſupra circulum pro-
              <lb/>
            poſitum, ad ſinũ anguli E N L, diſtantię Solis à Meridiano circuli propoſiti, ita ſinus arcus N L,
              <lb/>
            complementi declinationis ( Sole enim in parallelo auſtrali exiſtente, vt in quarto circulo, arcus
              <lb/>
            N L, eundem ſinum habet, quem reliquus arcus ex ſemicirculo, qui inter L, & </s>
            <s xml:id="echoid-s31073" xml:space="preserve">polum </s>
          </p>
        </div>
      </text>
    </echo>
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