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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            <s xml:id="echoid-s7377" xml:space="preserve">
              <pb o="122" file="0142" n="142" rhead="GNOMONICES"/>
            le exiſtente in æquinoctijs, per totam noctem crepuſculum, quia minus tunc ab Horizonte ſemper Sol d@@
              <lb/>
            ſtat, quàm grad. </s>
            <s xml:id="echoid-s7378" xml:space="preserve">18.</s>
            <s xml:id="echoid-s7379" xml:space="preserve"/>
          </p>
          <figure number="102">
            <image file="0142-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0142-01"/>
          </figure>
          <note position="left" xml:space="preserve">10</note>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s7380" xml:space="preserve">PORRO ſi quis nolit vti ſinubus verſis, poterit alio modo crepuſculorum magnitudines indagare,
              <lb/>
            & </s>
            <s xml:id="echoid-s7381" xml:space="preserve">fortaſſis commodius. </s>
            <s xml:id="echoid-s7382" xml:space="preserve">Quod vt declaremus, docebimus prius inucſtigare depreſſionem meridianam So-
              <lb/>
            lis, hoc eſt, diſtantiam eius ſub Horizonte in Meridiano. </s>
            <s xml:id="echoid-s7383" xml:space="preserve">Hæc autem ita reperietur. </s>
            <s xml:id="echoid-s7384" xml:space="preserve">In ſignis borealibus
              <lb/>
              <note position="left" xlink:label="note-0142-03" xlink:href="note-0142-03a" xml:space="preserve">Depreſſio meri
                <lb/>
              dſana So ´is quo
                <lb/>
              modo reperia-
                <lb/>
              tur.</note>
            detrahatur declinatio paralleli propoſiti ex complemento altitudinis poli; </s>
            <s xml:id="echoid-s7385" xml:space="preserve">In ſignis verò auſtralibus
              <lb/>
            eadem declinatio ad complementum altitudinis poli addatur. </s>
            <s xml:id="echoid-s7386" xml:space="preserve">Numerus enim ex illa ſubtractione reli-
              <lb/>
              <note position="left" xlink:label="note-0142-04" xlink:href="note-0142-04a" xml:space="preserve">Depreſſio meri-
                <lb/>
              diana cuiusli-
                <lb/>
              bet paralleli æ-
                <lb/>
              qualis eſt altitu
                <lb/>
              dini meridianæ
                <lb/>
              paralleli oppo-
                <lb/>
              ſiti.</note>
            ctus, vel ex hac additione compoſitus, dabit depreſſionem meridianam, vt perſpicuum eſt ex quatuor fi-
              <lb/>
            guris huius propoſ. </s>
            <s xml:id="echoid-s7387" xml:space="preserve">in quibus perpetuò depreſſio meridiana eſt arcus C L. </s>
            <s xml:id="echoid-s7388" xml:space="preserve">Eſt autem depreſſio cuiuslibet
              <lb/>
            paralleli æqualis altitudini meridianæ paralleli oppoſiti. </s>
            <s xml:id="echoid-s7389" xml:space="preserve">Si enim ex L, per centrum E, duceretur diame
              <lb/>
            ter, caderet hæc in quadrante A B, in punctum, per quod diameter paralleli oppoſiti eſſet ducendus, vt
              <lb/>
              <note position="left" xlink:label="note-0142-05" xlink:href="note-0142-05a" xml:space="preserve">30</note>
            patet. </s>
            <s xml:id="echoid-s7390" xml:space="preserve">Cum ergo huiuſmodi diameter vna cum diametro Horizontis A C, ad verticem E, angulos æqua-
              <lb/>
              <note position="left" xlink:label="note-0142-06" xlink:href="note-0142-06a" xml:space="preserve">15. primi.</note>
            les faciat, erunt arcus, quibus inſiſtunt dicti æquales anguli ad centrum E, inter ſe æquales; </s>
            <s xml:id="echoid-s7391" xml:space="preserve">nempe ar-
              <lb/>
              <note position="left" xlink:label="note-0142-07" xlink:href="note-0142-07a" xml:space="preserve">27. tertij.</note>
            cus depreſſionis meridianæ C L, & </s>
            <s xml:id="echoid-s7392" xml:space="preserve">arcus altitudinis meridianæ paralleli oppoſiti. </s>
            <s xml:id="echoid-s7393" xml:space="preserve">Vnde ſi quæratur de-
              <lb/>
              <note position="left" xlink:label="note-0142-08" xlink:href="note-0142-08a" xml:space="preserve">Quando nume
                <lb/>
              rus compoſitus
                <lb/>
              ex complemen-
                <lb/>
              to altitudinis
                <lb/>
              poli, & declina-
                <lb/>
              tione auſtrali
                <lb/>
              quadrãrem ex-
                <lb/>
              ceſſerit.</note>
            preſſio meridiana alicuius paralleli, poterit pro ea aſſumi altitudo meridiana paralleli oppoſiti.</s>
            <s xml:id="echoid-s7394" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7395" xml:space="preserve">VERVM hic quoque obſeruanda nonnulla ſunt. </s>
            <s xml:id="echoid-s7396" xml:space="preserve">Si enim in ſignis auſtralibus numerus ex comple-
              <lb/>
            mento altitudinis poli, & </s>
            <s xml:id="echoid-s7397" xml:space="preserve">declinatione conflatus maior fuerit quadrante, numerus conflatus ex ſemicir-
              <lb/>
            culo erit auferendus, vt depreſſio meridiana habeatur, ceu videre eſt in prima figura huius ſcholij. </s>
            <s xml:id="echoid-s7398" xml:space="preserve">Simi-
              <lb/>
            liter@ ſi in ſignis borealibus declinatio paralleli fuerit maior complemento altitudinis poli, ita vt illa ab
              <lb/>
              <note position="left" xlink:label="note-0142-09" xlink:href="note-0142-09a" xml:space="preserve">Quando decli-
                <lb/>
              natio borealis
                <lb/>
              maior fuerit cõ
                <unsure/>
                <lb/>
              plemento altitu
                <lb/>
              dinis poli, nulla
                <lb/>
              eſt depreſſio me
                <lb/>
              ridiana, ſed to-
                <lb/>
              tus parallelus
                <lb/>
              ſupra Horizon-
                <lb/>
              @em extat.</note>
            hoc detrahi nequeat, extabit totus parallelus ſupra Horizontem, vt in ſecunda figura huius ſcholij appa-
              <lb/>
            ret. </s>
            <s xml:id="echoid-s7399" xml:space="preserve">Quare nulla erit tunc depreſſio meridiana, ſed parallelus duas meridianas altitudines habebit, vt
              <lb/>
              <note position="left" xlink:label="note-0142-10" xlink:href="note-0142-10a" xml:space="preserve">40</note>
            paulo ante dictum eſt. </s>
            <s xml:id="echoid-s7400" xml:space="preserve">Quando denique in ſignis auſtralibus declinatio paralleli maior fuerit comple-
              <lb/>
            mento altitudinis poli, vt in eadem ſecunda figura huius ſcholij apparet, dictum iam eſt paulo ante, pa-
              <lb/>
            rallelum tunc eſſe totum ſub Horizonte, habereq́, duas depreſſiones meridianas, quas ibidem inueſtiga-
              <lb/>
            uimus; </s>
            <s xml:id="echoid-s7401" xml:space="preserve">& </s>
            <s xml:id="echoid-s7402" xml:space="preserve">aliquando poſſe eſſe crepuſculum, aliquando autem non; </s>
            <s xml:id="echoid-s7403" xml:space="preserve">Item quo pacto illud crepuſculum
              <lb/>
            inueſtigari debeat.</s>
            <s xml:id="echoid-s7404" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quando decli-
            <lb/>
          natio aũ
            <unsure/>
          ſtralis
            <lb/>
          maior fuerit cõ
            <lb/>
          plemento altitu
            <lb/>
          dinis poli, totus
            <lb/>
          parallelus au-
            <lb/>
          ſtralis ſub Hori
            <lb/>
          zonte latet, ha-
            <lb/>
          betq́; duas de-
            <lb/>
          preſſiones meri
            <lb/>
          dianas.</note>
          <p style="it">
            <s xml:id="echoid-s7405" xml:space="preserve">HIS ita poſitis, ducatur ex L, ad rectam K O, productam in omnibus figuris (excepta ſecunda figu-
              <lb/>
            ra huius ſcholij) perpendicularis L θ; </s>
            <s xml:id="echoid-s7406" xml:space="preserve">Item ex M, centro paralleli alia perpendicularis M λ. </s>
            <s xml:id="echoid-s7407" xml:space="preserve">Et quo-
              <lb/>
            niam eſt in triangulo K θ L, vt K M, ad M L, ita K λ, ad λ θ: </s>
            <s xml:id="echoid-s7408" xml:space="preserve">Eſt autem K M, ipſi M L, æqualis; </s>
            <s xml:id="echoid-s7409" xml:space="preserve">erit
              <lb/>
            quoque k λ, ipſi λ θ, æqualis. </s>
            <s xml:id="echoid-s7410" xml:space="preserve">Cum ergo K N, ſinus ſit altitudinis meridianæ, & </s>
            <s xml:id="echoid-s7411" xml:space="preserve">θ N, ſinus depreſſio-
              <lb/>
            nis meridianæ, (quia θ N, æqualis est ſinui depreſſionis, qui ex L, ad A C, duceretur perpendicularis)
              <lb/>
              <note position="left" xlink:label="note-0142-12" xlink:href="note-0142-12a" xml:space="preserve">50</note>
            erit K λ, medietas rectæ compoſitæ ex ſinubus altitudinis, & </s>
            <s xml:id="echoid-s7412" xml:space="preserve">depreſſionis meridianæ. </s>
            <s xml:id="echoid-s7413" xml:space="preserve">At vero λ O, dif-
              <lb/>
            ferentia erit inter dictam medietatem, & </s>
            <s xml:id="echoid-s7414" xml:space="preserve">rectam compoſitam ex ſinubus altitudinis meridianæ, & </s>
            <s xml:id="echoid-s7415" xml:space="preserve">grad.
              <lb/>
            </s>
            <s xml:id="echoid-s7416" xml:space="preserve">
              <note position="left" xlink:label="note-0142-13" xlink:href="note-0142-13a" xml:space="preserve">2. ſexti.</note>
            18. </s>
            <s xml:id="echoid-s7417" xml:space="preserve">Quia verò eſt, vt K λ, ad λ O, ita K M, ad M T; </s>
            <s xml:id="echoid-s7418" xml:space="preserve">Si fiat, vt K λ, medietas rectæ compoſitæ ex ſinu
              <lb/>
              <note position="left" xlink:label="note-0142-14" xlink:href="note-0142-14a" xml:space="preserve">34. primi.</note>
              <note position="left" xlink:label="note-0142-15" xlink:href="note-0142-15a" xml:space="preserve">2. ſexti.</note>
            altitudinis meridianæ, & </s>
            <s xml:id="echoid-s7419" xml:space="preserve">ſinu depreſſionis meridianæ, ad λ O, differentiam inter medietatem prædictam,
              <lb/>
              <note position="left" xlink:label="note-0142-16" xlink:href="note-0142-16a" xml:space="preserve">Crepuſculum
                <lb/>
              qua ratione ali
                <lb/>
              ter, quàm ſu-
                <lb/>
              pra, inueſtigan-
                <lb/>
              @um.</note>
            & </s>
            <s xml:id="echoid-s7420" xml:space="preserve">rectam compoſitam ex ſinu altitudinis meridianæ, & </s>
            <s xml:id="echoid-s7421" xml:space="preserve">ſinu grad. </s>
            <s xml:id="echoid-s7422" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7423" xml:space="preserve">ita K M, ſinus totus ad aliud,
              <lb/>
            prodibit M T, ſinus rectus arcus P R, qui quidem arcus additus quadranti conſtituit arcum K R, ex ar-
              <lb/>
            cu ſemidiurno, & </s>
            <s xml:id="echoid-s7424" xml:space="preserve">arcu crepuſculi compoſito, ſi videlicet prædicta medietas K λ, minor deprehc
              <unsure/>
            nſa fue-
              <lb/>
            rit, quàm recta compoſita ex ſinu altitudinis meridianæ, & </s>
            <s xml:id="echoid-s7425" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s7426" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7427" xml:space="preserve">vt in ſignis borealibus ſemper con-
              <lb/>
            tingit, & </s>
            <s xml:id="echoid-s7428" xml:space="preserve">nonnunquam in auſtralibus, ceu videre licet in duabus prioribus figuris huius propoſ. </s>
            <s xml:id="echoid-s7429" xml:space="preserve">& </s>
            <s xml:id="echoid-s7430" xml:space="preserve">in prio-
              <lb/>
            vi huius ſcholij, vel ſubtractus ex quadrante relinquit arcum K R, compoſitum ex arcu ſemidiurno, & </s>
            <s xml:id="echoid-s7431" xml:space="preserve">
              <lb/>
            @@rcu crepuſculi, ſi nimir@m medietas dicta deprehenſa ſuerit maior, quàm recta ex ſinu meridianę </s>
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