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-div426" type="section" level="1" n="138">
          <p>
            <s xml:id="echoid-s8017" xml:space="preserve">
              <pb o="129" file="0149" n="149" rhead="LIBER PRIMVS."/>
            V Y, pars eſt ſinus totius A E, circuli maximi) ad V Y, quatenus ſinus totus eſt in ſu
              <unsure/>
            o parallelo,
              <lb/>
            ita β Z, quatenus pars eſt eiuſdem ſinus totius A E, maximi circuli (quæ quidem ęqualis eſt ſi-
              <lb/>
            nui μ Z, complementi altitudinis Solis in Verticali, vt demõſtrauimus) ad β Z, quatenus pars eſt
              <lb/>
            ſinus totius V Y. </s>
            <s xml:id="echoid-s8018" xml:space="preserve">Quapropter ſi fiat, ut ſinus complementi declinationis paralleli propoſiti ad
              <lb/>
            ſinum totum, ita ſinus complementi altitudinis Solis in Verticali exiſtentis ad aliud, cognita fiet
              <lb/>
            Z β, nempe ſinus diſtantię Solis à meridie. </s>
            <s xml:id="echoid-s8019" xml:space="preserve">Hac arte, Sole parallelum ♋, percurrente, inuenimus
              <lb/>
            hor. </s>
            <s xml:id="echoid-s8020" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8021" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8022" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8023" xml:space="preserve">paulo amplius ante, & </s>
            <s xml:id="echoid-s8024" xml:space="preserve">poſt meridiem, dum in Verticali circulo exiſtit, ad latitudi-
              <lb/>
            nem grad. </s>
            <s xml:id="echoid-s8025" xml:space="preserve">42. </s>
            <s xml:id="echoid-s8026" xml:space="preserve">Ex quibus horis facile conijcies, quota hora ſit poſt mediam noctem, uel ab occa-
              <lb/>
            ſu, aut ortu Solis, cum Sol Verticalem obtinet, ſi prius tempus meridiei cognoſcatur more Italo-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s8027" xml:space="preserve">Babyloniorum. </s>
            <s xml:id="echoid-s8028" xml:space="preserve">Rurſus colliges ex hora cognita ante, uel p
              <unsure/>
            oſt meridiem quolibet die,
              <lb/>
              <note position="right" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">Num Sol in fi-
                <lb/>
              gnis borealibus
                <lb/>
              exiſtens Verti-
                <lb/>
              calem at@@gerit,
                <lb/>
              necne, quo pa-
                <lb/>
              cto cognoſcat
                <unsure/>
              .</note>
              <note position="left" xlink:label="note-0149-02" xlink:href="note-0149-02a" xml:space="preserve">10</note>
            Sole in ſignis borealibus exiſtente, an Sol attigerit Verticalem circulum, an uerò nondum ad eum
              <lb/>
            peruenerit, uel certe
              <unsure/>
            num eundem pertranſierit. </s>
            <s xml:id="echoid-s8029" xml:space="preserve">Quando enim antemeridiano tempore hora co-
              <lb/>
            gnita indicauerit maiorem diſtantiam à meridie, quàm inuenta eſt in Verticali circulo (ut ſi in
              <lb/>
            noſtro exemplo maiorem indicet, quàm hor. </s>
            <s xml:id="echoid-s8030" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8031" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8032" xml:space="preserve">4.) </s>
            <s xml:id="echoid-s8033" xml:space="preserve">perſpicuum eſt, eum nondum ad Vertica-
              <lb/>
            lem motu primi mobilis perueniſſe, quando autem ęqualem diſtantiam monſtrauerit, in Verticali
              <lb/>
              <note position="right" xlink:label="note-0149-03" xlink:href="note-0149-03a" xml:space="preserve">Altitudo Soli@
                <lb/>
              ſupra Horizon-
                <lb/>
              tem ex hora co
                <lb/>
              gnita quomodo
                <lb/>
              aliter, quàm ſu-
                <lb/>
              pra, inueſtige-
                <lb/>
              tur.</note>
            eum exiſtere, quando denique minorem ſignificauerit, eundem iam pertranſiiſſe Verticalẽ, atque
              <lb/>
            inter Verticalem, & </s>
            <s xml:id="echoid-s8034" xml:space="preserve">Meridianum ex parte auſtrali eſſe poſitum. </s>
            <s xml:id="echoid-s8035" xml:space="preserve">Contrarium intelligas tempore
              <lb/>
            pomeridiano.</s>
            <s xml:id="echoid-s8036" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8037" xml:space="preserve">TOTVM hoc problema expedire poſſumus hoc etiam modo. </s>
            <s xml:id="echoid-s8038" xml:space="preserve">Quia in eiſdem figuris om-
              <lb/>
            nibus ſuprapoſitis eſt, ut K S, ſinus verſus arcus ſemidiurni ad R S, differentiam inter ſinum
              <lb/>
              <note position="left" xlink:label="note-0149-04" xlink:href="note-0149-04a" xml:space="preserve">20</note>
            uerſum arcus ſemidiurni, & </s>
            <s xml:id="echoid-s8039" xml:space="preserve">ſinum verſum diſtantię Solis à meridie, ita K N, ſinus altitudinis me
              <lb/>
              <note position="right" xlink:label="note-0149-05" xlink:href="note-0149-05a" xml:space="preserve">2. vel 4. ſexti</note>
            ridianę ad T N, ſinum altitudinis Solis: </s>
            <s xml:id="echoid-s8040" xml:space="preserve">Si fiat, vt ſinus uerſus arcus ſemidiurni ad differentiam
              <lb/>
            inter ſinum uerſum ſemidiurni arcus, & </s>
            <s xml:id="echoid-s8041" xml:space="preserve">ſinum uerſum diſtantię Solis à meridie, ita ſinus al-
              <lb/>
            titudinis meridianę ad aliud, inuenietur finus altitudinis Solis quæſitę, atque adeò altitudo ipſa
              <lb/>
            maniſeſta erit.</s>
            <s xml:id="echoid-s8042" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Altitudo Solis
            <lb/>
          in æquinoctiis
            <lb/>
          quo modo ex
            <lb/>
          hora nota co-
            <lb/>
          gnoſcatur.</note>
          <p>
            <s xml:id="echoid-s8043" xml:space="preserve">IN Aequatore autem, vt ex ſexta figura apparet, ſinus uerſus arcus ſemidiurni eſt ſinus totus
              <lb/>
            H E, & </s>
            <s xml:id="echoid-s8044" xml:space="preserve">differentia inter ipſum, & </s>
            <s xml:id="echoid-s8045" xml:space="preserve">ſinum uerſum diſtantię Solis à meridie eſt R E, ſinus cõplemen-
              <lb/>
            ti diſtantię Solis à meridie, & </s>
            <s xml:id="echoid-s8046" xml:space="preserve">ſinus altitudinis meridianę eſt ſinus complementi altitudinis po-
              <lb/>
            li. </s>
            <s xml:id="echoid-s8047" xml:space="preserve">Vnde ſi tunc fiat, vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita ſinus
              <lb/>
            complementi altitudinis poli ad aliud, habebitur ſinus altitudinis Solis tempore obſeruationis,
              <lb/>
              <note position="left" xlink:label="note-0149-07" xlink:href="note-0149-07a" xml:space="preserve">30</note>
              <note position="right" xlink:label="note-0149-08" xlink:href="note-0149-08a" xml:space="preserve">Qua ratio ne. ex
                <lb/>
              altitudine Solis
                <lb/>
              ſupra Horizon-
                <lb/>
              tem cognita in-
                <lb/>
              ueſtige. u@ ho-
                <lb/>
              ra.</note>
            ut & </s>
            <s xml:id="echoid-s8048" xml:space="preserve">ſupra demonſtratum eſt.</s>
            <s xml:id="echoid-s8049" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8050" xml:space="preserve">RVRSVS quia eſt, ut k N, ſinus altitud nis meridianę ad T N, ſinum altitudinis Solis,
              <lb/>
            ita K S, ſinus uerſus arcus ſemidiurni ad R S, differentiam inter ſinum uerſum arcus ſemidiur-
              <lb/>
            ni, & </s>
            <s xml:id="echoid-s8051" xml:space="preserve">ſinum uerſum diſtantiæ Solis à meridie: </s>
            <s xml:id="echoid-s8052" xml:space="preserve">Si ſiat, ut ſinus altitudinis meridianę ad ſinum
              <lb/>
              <note position="right" xlink:label="note-0149-09" xlink:href="note-0149-09a" xml:space="preserve">2. vel 4. ſexti</note>
            altitudinis Solis tempore obſeruationis inuentę, ita ſinus uerſus arcus ſemidiurni ad aliud, re-
              <lb/>
            perietur numerus, qui ex ſinu uerſo arcus ſemidiurni ſublatus relinquit ſinum uerſum diſtan-
              <lb/>
            tiæ Solis à meridie. </s>
            <s xml:id="echoid-s8053" xml:space="preserve">Ex hoc autem ſinu uerſo diſtantiam Solis à meridie, atque adeò horam in-
              <lb/>
            ueniemus hac ratione. </s>
            <s xml:id="echoid-s8054" xml:space="preserve">Quando ſinus uerſus diſtantiæ Solis à meridie inuentus minor fuerit ſi-
              <lb/>
            nu toto, vt contingit ſemper in ſignis auſtralibus, & </s>
            <s xml:id="echoid-s8055" xml:space="preserve">in ſignis etiam borealibus, cum diſtantia So-
              <lb/>
            lis à meridie minor eſt quadrante, auferemus @um ex ſinu toto, & </s>
            <s xml:id="echoid-s8056" xml:space="preserve">reſidui ſinus recti arcum ex
              <lb/>
              <note position="left" xlink:label="note-0149-10" xlink:href="note-0149-10a" xml:space="preserve">40</note>
            quadrante auferemus, remanebitq́ue diſtantia Solis à meridie. </s>
            <s xml:id="echoid-s8057" xml:space="preserve">Si autem dictus ſinus verſus
              <lb/>
            ęqualis fuerit ſinui toti, quod bis duntaxat in quolibet arcu diurno parallelorum borealium eue-
              <lb/>
            nire poteſt, erit diſtantia Solis à meridie quadrans complectens ſex horas. </s>
            <s xml:id="echoid-s8058" xml:space="preserve">Si denique ſinus ver-
              <lb/>
            ſus inuentus extiterit maior ſinu toto, auferemus ex eo ſinum totum, & </s>
            <s xml:id="echoid-s8059" xml:space="preserve">reſidui ſinus recti arcum
              <lb/>
            ad quadrantem adijciemus, conficiemusq́; </s>
            <s xml:id="echoid-s8060" xml:space="preserve">diſtantiam Solis à meridie.</s>
            <s xml:id="echoid-s8061" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quota hora ſi@,
            <lb/>
          quo modo in
            <lb/>
          æquinoctiis ex
            <lb/>
          data altitudine
            <lb/>
          Solis cognoſce@.
            <lb/>
          dum.</note>
          <p>
            <s xml:id="echoid-s8062" xml:space="preserve">SOLE in æquinoctiis exiſtente, vt ex ſexta figura eſt manifeſtum, ſinus altitudinis meri-
              <lb/>
            dianæ eſt ſinus complementi altitudinis poli, & </s>
            <s xml:id="echoid-s8063" xml:space="preserve">ſinus uerſus arcus ſemidiurni eſt ſinus totus
              <lb/>
            H E, & </s>
            <s xml:id="echoid-s8064" xml:space="preserve">differentia inter ſinum uerſum arcus ſemidiurni, & </s>
            <s xml:id="echoid-s8065" xml:space="preserve">ſinum verſum diſtantiæ Solis à me-
              <lb/>
            ridie, eſt ſinus complementi diſtantiæ Solis à meridie. </s>
            <s xml:id="echoid-s8066" xml:space="preserve">Quamobrem, ſi tunc ſiat, vt ſinus com-
              <lb/>
            plementi altitudinis poli ad ſinum altitudinis Solis tempore obſeruationis, ita ſinus totus ad
              <lb/>
              <note position="left" xlink:label="note-0149-12" xlink:href="note-0149-12a" xml:space="preserve">50</note>
            aliud, habebitur ſinus complementi diſtantiæ Solis à meridie. </s>
            <s xml:id="echoid-s8067" xml:space="preserve">Id quod ſupra quoque demon-
              <lb/>
            ſtratum eſt.</s>
            <s xml:id="echoid-s8068" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8069" xml:space="preserve">EXEMPLVM. </s>
            <s xml:id="echoid-s8070" xml:space="preserve">Ponamus Solem in parallelo ♐, uel ♒, habere poſt meridiem altitudinẽ
              <lb/>
              <note position="right" xlink:label="note-0149-13" xlink:href="note-0149-13a" xml:space="preserve">Exemplum.</note>
            ſupra Horizontem grad. </s>
            <s xml:id="echoid-s8071" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8072" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8073" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8074" xml:space="preserve">Fiat ut 46638. </s>
            <s xml:id="echoid-s8075" xml:space="preserve">ſinus altitudinis meridianę ad 11753. </s>
            <s xml:id="echoid-s8076" xml:space="preserve">ſinum
              <lb/>
            altitudinis Solis inuentę
              <unsure/>
            , ita 66867. </s>
            <s xml:id="echoid-s8077" xml:space="preserve">ſinus uerſus arcus ſemidiurni ad aliud, prodibitq́; </s>
            <s xml:id="echoid-s8078" xml:space="preserve">hic fermè
              <lb/>
            numerus 16851. </s>
            <s xml:id="echoid-s8079" xml:space="preserve">qui ex 66867. </s>
            <s xml:id="echoid-s8080" xml:space="preserve">ſinu uerfo arcus ſemidiurni ſubtractus relinquet 50016. </s>
            <s xml:id="echoid-s8081" xml:space="preserve">ſinum
              <lb/>
            uerſum diſtantię Solis à meridie. </s>
            <s xml:id="echoid-s8082" xml:space="preserve">Hunc ergo quia minor eſt ſinu toto, ex 100000. </s>
            <s xml:id="echoid-s8083" xml:space="preserve">ſinu toto ſubdu-
              <lb/>
            cemus, & </s>
            <s xml:id="echoid-s8084" xml:space="preserve">reſidui ſinus recti 49984. </s>
            <s xml:id="echoid-s8085" xml:space="preserve">arcũ grad. </s>
            <s xml:id="echoid-s8086" xml:space="preserve">29. </s>
            <s xml:id="echoid-s8087" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8088" xml:space="preserve">59. </s>
            <s xml:id="echoid-s8089" xml:space="preserve">ex quadrante dememus, habebimusq́;
              <lb/>
            </s>
            <s xml:id="echoid-s8090" xml:space="preserve">diſtantiam Solis à meridie grad. </s>
            <s xml:id="echoid-s8091" xml:space="preserve">60. </s>
            <s xml:id="echoid-s8092" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8093" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8094" xml:space="preserve">hoc eſt, hor. </s>
            <s xml:id="echoid-s8095" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8096" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8097" xml:space="preserve">o, poſt meridiẽ, quia obſeruatio
              <lb/>
            ponitur facta poſt meridiem. </s>
            <s xml:id="echoid-s8098" xml:space="preserve">Ante meridiem eſſet hora 8. </s>
            <s xml:id="echoid-s8099" xml:space="preserve">poſt med. </s>
            <s xml:id="echoid-s8100" xml:space="preserve">noct. </s>
            <s xml:id="echoid-s8101" xml:space="preserve">Cognita autem hora
              <lb/>
            meridiei more Italorũ, & </s>
            <s xml:id="echoid-s8102" xml:space="preserve">Babyloniorum ex quantitate diei, facile comperiemus, quęnam hora </s>
          </p>
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    </echo>
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