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-s7314" xml:space="preserve">
              <pb o="121" file="0141" n="141" rhead="LIBER PRIMVS."/>
            bit, vt patet in eadem ſecunda figura, in qua declinatio auſtralis H K, maior eſt complemento altitudinis
              <lb/>
              <note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">auſtralis maior
                <lb/>
              eſt complemen
                <lb/>
              to altitudinis
                <lb/>
              poli, exiſtit to-
                <lb/>
              tus parallelus
                <lb/>
              ſub Horizonte,
                <lb/>
              nullamq́; habet
                <lb/>
              altitudinẽ meri
                <lb/>
              dianam.</note>
            poli A H. </s>
            <s xml:id="echoid-s7315" xml:space="preserve">Quòd ſi a
              <unsure/>
            rcus A K, differentia inter complementum altitudinis poli A H, & </s>
            <s xml:id="echoid-s7316" xml:space="preserve">declinationem
              <lb/>
            auſtralem H K, minor fuerit arcu A X, qui inter Horizontem & </s>
            <s xml:id="echoid-s7317" xml:space="preserve">parallelum, qui incedit per initium
              <lb/>
              <figure xlink:label="fig-0141-01" xlink:href="fig-0141-01a" number="101">
                <image file="0141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0141-01"/>
              </figure>
              <note position="left" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0141-03" xlink:href="note-0141-03a" xml:space="preserve">20</note>
              <note position="right" xlink:label="note-0141-04" xlink:href="note-0141-04a" xml:space="preserve">Crepuſculum
                <lb/>
              quantum ſit,
                <lb/>
              dum parallelus
                <lb/>
              auſtralis totus
                <lb/>
              ſub Horizont
                <unsure/>
              e
                <lb/>
              la@er.</note>
            crepuſculi matutini, & </s>
            <s xml:id="echoid-s7318" xml:space="preserve">per finem veſpertini, interijcitur, erit crepuſculum, dum @ol arcum k R, & </s>
            <s xml:id="echoid-s7319" xml:space="preserve">alte-
              <lb/>
            rum ſibi æqualem percurrit, ita vt K R, ſit crepuſculi dimidium; </s>
            <s xml:id="echoid-s7320" xml:space="preserve">quia in arcu K R, & </s>
            <s xml:id="echoid-s7321" xml:space="preserve">in alio ſibi æqua-
              <lb/>
              <note position="right" xlink:label="note-0141-05" xlink:href="note-0141-05a" xml:space="preserve">Crepuſeulum,
                <lb/>
              quando paralle
                <lb/>
              lus auſtralis to-
                <lb/>
              tus ſub Horizõ-
                <lb/>
              te latet, quo pa-
                <lb/>
              cto in@eniatur.</note>
            li Sol minus diſtat ab Horizonte, quàm grad. </s>
            <s xml:id="echoid-s7322" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7323" xml:space="preserve">Huius autem arcus quantitatem it a inueniemus. </s>
            <s xml:id="echoid-s7324" xml:space="preserve">Ex
              <lb/>
            puncto L, paralleli auſtralis in posteriori figura huius ſcholij, ducatur ad A C, perpendicularis L N, ſe-
              <lb/>
            cans X Y, in O. </s>
            <s xml:id="echoid-s7325" xml:space="preserve">Item per K, & </s>
            <s xml:id="echoid-s7326" xml:space="preserve">M, agantur ipſi A C, parallelæ K θ, M λ, ſecantes L N, in θ, & </s>
            <s xml:id="echoid-s7327" xml:space="preserve">λ. </s>
            <s xml:id="echoid-s7328" xml:space="preserve">An-
              <lb/>
            te omnia veniemus in cognitionem rectarum L λ, L O, hoc pacto. </s>
            <s xml:id="echoid-s7329" xml:space="preserve">Totus arcus C L, quem appellare poſ-
              <lb/>
            ſumus depreſſionem Solis ſub Horizonte, hoc eſt, distantiam ipſius in Meridiano ſub Horizonte maio-
              <lb/>
              <note position="left" xlink:label="note-0141-06" xlink:href="note-0141-06a" xml:space="preserve">30</note>
              <note position="right" xlink:label="note-0141-07" xlink:href="note-0141-07a" xml:space="preserve">Depreſſio Solis
                <lb/>
              quid.</note>
            rem, (Habet enim Sol in illo parallelo duas depreſſiones ſub Horizonte, maiorem C L, & </s>
            <s xml:id="echoid-s7330" xml:space="preserve">minorẽ A K,
              <lb/>
            quarum illa ad ſeptentrionem, hæc verò ad auſtrum vergit) compoſitus ex C I, complemento altitudinis
              <lb/>
            poli, & </s>
            <s xml:id="echoid-s7331" xml:space="preserve">I L, declinatione auſtrali, notus eſt. </s>
            <s xml:id="echoid-s7332" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s7333" xml:space="preserve">eius ſinus L N, notus erit. </s>
            <s xml:id="echoid-s7334" xml:space="preserve">Rurſus arcus A K,
              <lb/>
            depreſſionis minoris notus eſt, cum ſit differentia inter arcum declinationis auſtralis H K, & </s>
            <s xml:id="echoid-s7335" xml:space="preserve">arcum
              <lb/>
            complementi altitudinis poli A H. </s>
            <s xml:id="echoid-s7336" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s7337" xml:space="preserve">eius ſinus θ N, cognitus erit. </s>
            <s xml:id="echoid-s7338" xml:space="preserve">Ablato ergo ſinu θ N, ex
              <lb/>
            L N, ſinu, qui iam cognitus eſt, remanebit & </s>
            <s xml:id="echoid-s7339" xml:space="preserve">L θ, nota, quæ differentia eſt inter ſinum maioris depreſ-
              <lb/>
            ſionis, & </s>
            <s xml:id="echoid-s7340" xml:space="preserve">ſinum minoris depreſſionis ſub Horizonte. </s>
            <s xml:id="echoid-s7341" xml:space="preserve">Quoniam verò eſt vt L M, ad M K, it a L λ, ad λ θ;
              <lb/>
            </s>
            <s xml:id="echoid-s7342" xml:space="preserve">
              <note position="right" xlink:label="note-0141-08" xlink:href="note-0141-08a" xml:space="preserve">2. ſexti.</note>
            eſt autem L M, æqualis ipſi M K; </s>
            <s xml:id="echoid-s7343" xml:space="preserve">erit quoque L λ, ipſi λ θ, æqualis. </s>
            <s xml:id="echoid-s7344" xml:space="preserve">Cum ergo L θ, recta nota ſit, erit
              <lb/>
            & </s>
            <s xml:id="echoid-s7345" xml:space="preserve">eius medietas L λ, nota. </s>
            <s xml:id="echoid-s7346" xml:space="preserve">At vero L O, nota eſt, cum ſit differentia inter L N, ſinum maioris depreſ-
              <lb/>
            ſionis, & </s>
            <s xml:id="echoid-s7347" xml:space="preserve">O N, ſinum grad. </s>
            <s xml:id="echoid-s7348" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7349" xml:space="preserve">nempe arcus A X, vel C Y. </s>
            <s xml:id="echoid-s7350" xml:space="preserve">Vtraque ergo L λ, L O, nota eſt.</s>
            <s xml:id="echoid-s7351" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p style="it">
            <s xml:id="echoid-s7352" xml:space="preserve">IAM verò quoniam eſt, vt L λ, ad L O, ita L M, ad L T; </s>
            <s xml:id="echoid-s7353" xml:space="preserve">ſi fiat, vt L λ, medietas differentiæ in-
              <lb/>
              <note position="right" xlink:label="note-0141-10" xlink:href="note-0141-10a" xml:space="preserve">4. ſexti.</note>
            ter ſinum maioris depreſſionis & </s>
            <s xml:id="echoid-s7354" xml:space="preserve">ſinũ minoris, ad L O, differentiam inter ſinum maioris depreſſionis, & </s>
            <s xml:id="echoid-s7355" xml:space="preserve">
              <lb/>
            ſinum grad. </s>
            <s xml:id="echoid-s7356" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7357" xml:space="preserve">it a L M, ſinus totus ad aliud, inuenietur L T, ſinus verſus arcus L R. </s>
            <s xml:id="echoid-s7358" xml:space="preserve">Ex quo ſinu verſo
              <lb/>
            L T, ita perueſtigabimus arcum K R, dimidiati crepuſculi. </s>
            <s xml:id="echoid-s7359" xml:space="preserve">Quando ſinus verſus L T, inuentus maior
              <lb/>
            eſt ſinu toto L M, auferemus ex eo ſinum totum, vt habeamus ſinum rectum M T, cuius arcum P R, ex
              <lb/>
            tabula ſinuum acceptum auferemus ex quadrante K P, remanebitq́, arcus K R, dimidij crepuſculinotus.
              <lb/>
            </s>
            <s xml:id="echoid-s7360" xml:space="preserve">Si verò ſinus verſus L T, fuerit repertus æqualis ſinui toti, erit arcus dimidij crepuſculi quadrans inte-
              <lb/>
            ger, quia tunc diameter K L, tranſit per punctum, vbi axis diametrum X Y, interſecat, ac proinde pun
              <lb/>
            ctum T, in punctum M, cadet. </s>
            <s xml:id="echoid-s7361" xml:space="preserve">Si denique deprehenſus fuerit ſinus verſus L T, minor ſinu toto, aufere-
              <lb/>
            mus eum ex ſin@ toto, & </s>
            <s xml:id="echoid-s7362" xml:space="preserve">reliqui ſinus recti arcum ex tabula ſinuum acceptum adijciemus ad quadran-
              <lb/>
              <note position="left" xlink:label="note-0141-11" xlink:href="note-0141-11a" xml:space="preserve">50</note>
            tem, vt habeamus arcum dimidij crepuſculi: </s>
            <s xml:id="echoid-s7363" xml:space="preserve">quia tunc diameter K L, ſecat axem inter E, centrum,
              <lb/>
            Analemmatis & </s>
            <s xml:id="echoid-s7364" xml:space="preserve">diametrum X Y, at que adeo punctum T, cadet inter M, centrum paralleli, & </s>
            <s xml:id="echoid-s7365" xml:space="preserve">pun-
              <lb/>
            ctum L, vt patet.</s>
            <s xml:id="echoid-s7366" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7367" xml:space="preserve">SI verò arcus A K, infra Horizontem, nempe differentia inter cõplementum altitudinis poli A H,
              <lb/>
              <note position="right" xlink:label="note-0141-12" xlink:href="note-0141-12a" xml:space="preserve">Crepuſeulum
                <lb/>
              quãdo nu llum
                <lb/>
              ſit, Sole exiſten
                <lb/>
              te in auſtrali-
                <lb/>
              bus ſignis.</note>
            & </s>
            <s xml:id="echoid-s7368" xml:space="preserve">declinationem auſtralem H K, (quando in ſignis auſtralibus declinatio maior eſt, quàm complemen-
              <lb/>
            tum altitudinis poli) æqualis fuerit, vel maior arcu A X, nullum erit crepuſculum, Sole illum paralle-
              <lb/>
            lum auſtralem percurrente; </s>
            <s xml:id="echoid-s7369" xml:space="preserve">quia tunc Sol ſub Horizonte ſemper plus diſtat ab Horizonte, quàm grad. </s>
            <s xml:id="echoid-s7370" xml:space="preserve">18.
              <lb/>
            </s>
            <s xml:id="echoid-s7371" xml:space="preserve">niſi dicere velimus crepuſculum, punctum illud temporis, in quo Sol in puncto X, existit in media nocte,
              <lb/>
            quando nimirum arcus A K, æqualis eſt arcui A X.</s>
            <s xml:id="echoid-s7372" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Crepuſculum
            <lb/>
          quãdo nullum
            <lb/>
          ſit, Sole in æqui
            <lb/>
          noctijs exiſtẽte.</note>
          <p style="it">
            <s xml:id="echoid-s7373" xml:space="preserve">QVOD ſi complementum altitudinis poli minus fuerit arcu grad. </s>
            <s xml:id="echoid-s7374" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7375" xml:space="preserve">vt in ſecunda figura huius
              <lb/>
            ſcholij contingit, (eſt enim arcus C I, complementi altitudinis poli minor arcu C Y, grad. </s>
            <s xml:id="echoid-s7376" xml:space="preserve">18.) </s>
            <s xml:id="echoid-s7377" xml:space="preserve">erit, </s>
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