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-s35249" xml:space="preserve">
              <pb o="546" file="0562" n="562" rhead="GNOMONICES"/>
            næ eiuſdem loci, vel complementi depreſſionis meridianæ in data regione, & </s>
            <s xml:id="echoid-s35250" xml:space="preserve">ſinum complemen
              <lb/>
            ti circunferentiæ horariæ. </s>
            <s xml:id="echoid-s35251" xml:space="preserve">Si igitur ab hac differentia, cum Sol eſt vltta Verticalem datæ regio-
              <lb/>
            nis, (vt contingit in parallelis auſtralibus, & </s>
            <s xml:id="echoid-s35252" xml:space="preserve">in ſecunda figura cap. </s>
            <s xml:id="echoid-s35253" xml:space="preserve">4.) </s>
            <s xml:id="echoid-s35254" xml:space="preserve">auferatur ſinus rectus alti-
              <lb/>
            tudinis meridianæ dicti illius loci, aut ſinus complementi depreſſionis meridianæ in data regio-
              <lb/>
            ne; </s>
            <s xml:id="echoid-s35255" xml:space="preserve">vel ſi hæc differentia, cum Sol in parallelis borealibus citra Verticalem datæ regionis exiſtit,
              <lb/>
            (vt in figura 4.</s>
            <s xml:id="echoid-s35256" xml:space="preserve">5. </s>
            <s xml:id="echoid-s35257" xml:space="preserve">& </s>
            <s xml:id="echoid-s35258" xml:space="preserve">6. </s>
            <s xml:id="echoid-s35259" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s35260" xml:space="preserve">4. </s>
            <s xml:id="echoid-s35261" xml:space="preserve">apparet) ex ſinu recto altitudinis meridianæ eiuſdem loci, vel ex ſinu
              <lb/>
            complementi depreſſionis meridianæ in data regione dematur, reliquus erit ſinus complementi
              <lb/>
            circunferentiæ horariæ. </s>
            <s xml:id="echoid-s35262" xml:space="preserve">Hoc ergo complementum, vnà cum ipſa horaria circunferentia, non
              <lb/>
            ignorabitur.</s>
            <s xml:id="echoid-s35263" xml:space="preserve"/>
          </p>
          <figure number="347">
            <image file="0562-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0562-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s35264" xml:space="preserve">EANDEM cir-
              <lb/>
              <note position="left" xlink:label="note-0562-01" xlink:href="note-0562-01a" xml:space="preserve">Alis innentio
                <lb/>
              h@rariæ, & br@-
                <lb/>
              @io@.</note>
              <note position="left" xlink:label="note-0562-02" xlink:href="note-0562-02a" xml:space="preserve">10</note>
            cunferentiam horariã
              <lb/>
            inueniemus, etiamſi
              <lb/>
            Verticalem non pona-
              <lb/>
            mus eſſe Horizontem,
              <lb/>
            hoc modo. </s>
            <s xml:id="echoid-s35265" xml:space="preserve">Inueſtige-
              <lb/>
            tur per propoſ. </s>
            <s xml:id="echoid-s35266" xml:space="preserve">36. </s>
            <s xml:id="echoid-s35267" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s35268" xml:space="preserve">1. </s>
            <s xml:id="echoid-s35269" xml:space="preserve">diſtantia Solis à me-
              <lb/>
            ridie, cum in Verticali
              <lb/>
            circulo exiſtit, (quod
              <lb/>
            quidem in parallelis
              <lb/>
              <note position="left" xlink:label="note-0562-03" xlink:href="note-0562-03a" xml:space="preserve">20</note>
            auſtralibus infra Hori-
              <lb/>
            zontem contingit, ſed
              <lb/>
            in borealibus ſupra Ho
              <lb/>
            rizontem) & </s>
            <s xml:id="echoid-s35270" xml:space="preserve">huius
              <lb/>
            diſtantiæ ſinus verſus
              <lb/>
            a n, ex diametro a b,
              <lb/>
            hoc eſt, ex ſinu toto du-
              <lb/>
            plicato, detrahatur, vt
              <lb/>
            nota relinquatur recta
              <lb/>
            n b. </s>
            <s xml:id="echoid-s35271" xml:space="preserve">Si enim fiat, vt
              <lb/>
              <note position="left" xlink:label="note-0562-04" xlink:href="note-0562-04a" xml:space="preserve">30</note>
            hæc recta n b, inuenta
              <lb/>
              <note position="left" xlink:label="note-0562-05" xlink:href="note-0562-05a" xml:space="preserve">4. ſexti.</note>
            ad b q, ſinum comple-
              <lb/>
            menti depreſſionis me
              <lb/>
            ridianæ (quam ex ſcho
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s35272" xml:space="preserve">35. </s>
            <s xml:id="echoid-s35273" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35274" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s35275" xml:space="preserve">inueniemus) ita L b,
              <lb/>
            ſinus verſus diſtantiæ Solis à media nocte ad aliud, inuenietur b p, differentia inter b q, ſinum cõ-
              <lb/>
            plementi depreſſionis meridianæ, & </s>
            <s xml:id="echoid-s35276" xml:space="preserve">p q, ſinum complementi circunferentiæ horariæ, &</s>
            <s xml:id="echoid-s35277" xml:space="preserve">c. </s>
            <s xml:id="echoid-s35278" xml:space="preserve">Vel
              <lb/>
            inueniatur, per propoſ. </s>
            <s xml:id="echoid-s35279" xml:space="preserve">1. </s>
            <s xml:id="echoid-s35280" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35281" xml:space="preserve">5. </s>
            <s xml:id="echoid-s35282" xml:space="preserve">altitudo Solis ſupra Verticalem circulum. </s>
            <s xml:id="echoid-s35283" xml:space="preserve">Nam eius complemen
              <lb/>
            tum dabit circunferentiam horariam, vt patet.</s>
            <s xml:id="echoid-s35284" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p>
            <s xml:id="echoid-s35285" xml:space="preserve">RVRSVS quoniam in triangulis a h d, a l L, eſt vt a d, ſinus verſus arcus ſemidiurni a e, ad
              <lb/>
              <note position="left" xlink:label="note-0562-07" xlink:href="note-0562-07a" xml:space="preserve">4. ſexti.</note>
            a h, ſinum rectum altitudinis meridianæ, ita a L, ſinus verſus diſtantiæ Solis à meridiead a l, dif-
              <lb/>
            ferentiam inter a h, ſinum altitudinis meridianæ, & </s>
            <s xml:id="echoid-s35286" xml:space="preserve">l h, ſinum arcus B P, complementi circunfe-
              <lb/>
            rentiæ deſcenſiuæ A P: </s>
            <s xml:id="echoid-s35287" xml:space="preserve">Si fiat, vt ſinus verſus arcus ſemidiurni ad ſinum altitudinis meridianæ,
              <lb/>
              <note position="left" xlink:label="note-0562-08" xlink:href="note-0562-08a" xml:space="preserve">Deſcenſiua.</note>
            ita ſinus verſus diſtantiæ Solis à meridie ad aliud, inuenietur numerus, qui ex ſinu altitudinis
              <lb/>
            meridianæ ſubductus relinquet ſinum complementi deſcenſiuæ circunferentiæ. </s>
            <s xml:id="echoid-s35288" xml:space="preserve">Hoc ergo com-
              <lb/>
            plementum, vna cum circunferentia deſcenſiua, cognitum erit. </s>
            <s xml:id="echoid-s35289" xml:space="preserve">Vel inueniatur, per vltimum mo
              <lb/>
            dum in propoſ. </s>
            <s xml:id="echoid-s35290" xml:space="preserve">36. </s>
            <s xml:id="echoid-s35291" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35292" xml:space="preserve">1. </s>
            <s xml:id="echoid-s35293" xml:space="preserve">ante triangula ſphærica traditum, altitudo Solis ſupra Horizontem. </s>
            <s xml:id="echoid-s35294" xml:space="preserve">Eius
              <lb/>
            enim complementum deſcenſiuam circunferentiam exhibebit, vt perſpicuum eſt.</s>
            <s xml:id="echoid-s35295" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s35296" xml:space="preserve">PRAETEREA cum in triangulis E L N, E Y S, ſit, vt E L, ſinus circunferentiæ hectemo-
              <lb/>
              <note position="left" xlink:label="note-0562-09" xlink:href="note-0562-09a" xml:space="preserve">4. ſexti.</note>
              <note position="left" xlink:label="note-0562-10" xlink:href="note-0562-10a" xml:space="preserve">50</note>
            riæ, hoceſt, ſinus complementi altitudinis Solis ſupra Meridianum, ad L N, ſinum complemen-
              <lb/>
            ti circunferentiæ deſcenſiuæ, hoc eſt, ad ſinum altitudinis Solis ſupra Horizontem, ita E Y, ſinus
              <lb/>
            totus ad Y ſ, ſinum meridianæ circunferentiæ B Y: </s>
            <s xml:id="echoid-s35297" xml:space="preserve">Si fiat vt ſinus circunferentiæ hectemoriæ
              <lb/>
              <note position="left" xlink:label="note-0562-11" xlink:href="note-0562-11a" xml:space="preserve">Meridiana.</note>
            inuentæ, hoc eſt, vt ſinus complementi altitudinis Solis ſupra Meridianum, ad ſinum comple-
              <lb/>
            menti circunferentiæ deſcenſiuæ, id eſt, ad ſinum altitudinis Solis ſupra Horizontem, ita ſinus
              <lb/>
            totus ad aliud, inuenietur ſinus circunferentię meridianæ; </s>
            <s xml:id="echoid-s35298" xml:space="preserve">atque adeo ipſa meridiana circunfe-
              <lb/>
            rentia nota fiet.</s>
            <s xml:id="echoid-s35299" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s35300" xml:space="preserve">AD hæc, quia in triangulo k L N, latera K L, L N, æqualia ſunt lateribus R O, O E, in trian-
              <lb/>
            gulo R O E, (ſumpta enim fuit in cap. </s>
            <s xml:id="echoid-s35301" xml:space="preserve">4. </s>
            <s xml:id="echoid-s35302" xml:space="preserve">recta O R, rectæ K L. </s>
            <s xml:id="echoid-s35303" xml:space="preserve">ęqualis: </s>
            <s xml:id="echoid-s35304" xml:space="preserve">recta autem L N, rectæ
              <lb/>
            O E, æqualis eſt in parallelogrammo N O) continentq́ue angulos æquales, vtpote rectos; </s>
            <s xml:id="echoid-s35305" xml:space="preserve">(Nam,
              <lb/>
              <note position="left" xlink:label="note-0562-12" xlink:href="note-0562-12a" xml:space="preserve">14. primi</note>
            per deſin. </s>
            <s xml:id="echoid-s35306" xml:space="preserve">4. </s>
            <s xml:id="echoid-s35307" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s35308" xml:space="preserve">11. </s>
            <s xml:id="echoid-s35309" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s35310" xml:space="preserve">K L, ad planum Meridiani recta eſt, ſi ſemicirculus a K b, rectus </s>
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