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-s25224" xml:space="preserve">
              <pb o="384" file="0400" n="400" rhead="GNOMONICES"/>
            habere debeat diuiſio dicti circuli ex L, deſcripti, ut in horizontali horologio factum eſt, inuenie-
              <lb/>
            mus huiuſimodi ſectionem, ſeu lineam horæ 12. </s>
            <s xml:id="echoid-s25225" xml:space="preserve">in prædicto circulo hac ratione. </s>
            <s xml:id="echoid-s25226" xml:space="preserve">Inquiratur
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s25227" xml:space="preserve">30. </s>
            <s xml:id="echoid-s25228" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25229" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25230" xml:space="preserve">inclinatio Meridiani proprij ipſius plani ad Meridianum Horizontis: </s>
            <s xml:id="echoid-s25231" xml:space="preserve">quam
              <lb/>
            quidem comperimus in prima figura grad. </s>
            <s xml:id="echoid-s25232" xml:space="preserve">14. </s>
            <s xml:id="echoid-s25233" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25234" xml:space="preserve">10. </s>
            <s xml:id="echoid-s25235" xml:space="preserve">In ſecunda grad. </s>
            <s xml:id="echoid-s25236" xml:space="preserve">20. </s>
            <s xml:id="echoid-s25237" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25238" xml:space="preserve">52. </s>
            <s xml:id="echoid-s25239" xml:space="preserve">In terria
              <lb/>
              <note position="left" xlink:label="note-0400-01" xlink:href="note-0400-01a" xml:space="preserve">Quanta ſit in
                <lb/>
              cli
                <unsure/>
              natio Meri
                <lb/>
              diani proprii
                <lb/>
              ipſius plani in
                <lb/>
              clinati ad Meri
                <lb/>
              dianum Hori-
                <lb/>
              zontis in quali
                <lb/>
              bet ſex figura-
                <lb/>
              rum huius pro
                <lb/>
              poſ.</note>
            grad. </s>
            <s xml:id="echoid-s25240" xml:space="preserve">33. </s>
            <s xml:id="echoid-s25241" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25242" xml:space="preserve">47. </s>
            <s xml:id="echoid-s25243" xml:space="preserve">In quarta grad. </s>
            <s xml:id="echoid-s25244" xml:space="preserve">27. </s>
            <s xml:id="echoid-s25245" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25246" xml:space="preserve">30. </s>
            <s xml:id="echoid-s25247" xml:space="preserve">In quinta grad. </s>
            <s xml:id="echoid-s25248" xml:space="preserve">75. </s>
            <s xml:id="echoid-s25249" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25250" xml:space="preserve">46. </s>
            <s xml:id="echoid-s25251" xml:space="preserve">In ſexta denique
              <lb/>
            grad. </s>
            <s xml:id="echoid-s25252" xml:space="preserve">90. </s>
            <s xml:id="echoid-s25253" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25254" xml:space="preserve">o. </s>
            <s xml:id="echoid-s25255" xml:space="preserve">Hęc enim inclinatio numeranda eſt à puncto N, in circulo ex L, deſcripto uſque
              <lb/>
            ad punctum O, hac ſeruata lege. </s>
            <s xml:id="echoid-s25256" xml:space="preserve">Si planum ad Horizontem fuerit inclinatum ad partes boreales,
              <lb/>
            hoc eſt, facies eius ſuperior à meridie declinet in ortum, uel occaſum, ſi quidem à meridie in or-
              <lb/>
            tum declinet, numeranda eſt dicta inclinatio Meridianorum à puncto N, uerſus ſiniſtram, hoc eſt,
              <lb/>
            uerſus partes occidentales, ut in figura prima & </s>
            <s xml:id="echoid-s25257" xml:space="preserve">tertia factum eſt. </s>
            <s xml:id="echoid-s25258" xml:space="preserve">Nam quia tunc circulus maxi-
              <lb/>
              <note position="left" xlink:label="note-0400-02" xlink:href="note-0400-02a" xml:space="preserve">10</note>
            mus per polos Horizontis, & </s>
            <s xml:id="echoid-s25259" xml:space="preserve">polos plani inclinati ductus, qui nimirum inclinationem ad Hori-
              <lb/>
            zontem metitur, cadit ex parte auſtri in quadrantem hemiſphęrii ſuperi orientalem; </s>
            <s xml:id="echoid-s25260" xml:space="preserve">(Vocamus
              <lb/>
            quadrantes hemiſphęrii ſuperi, partes illas, quæ inter Meridianum, Horizontem, & </s>
            <s xml:id="echoid-s25261" xml:space="preserve">Verticalem
              <lb/>
            circulum@ propriè dictum continentur. </s>
            <s xml:id="echoid-s25262" xml:space="preserve">Hi enim tres circuli ſe mutuo ad angulos rectos ſecantes
              <lb/>
            partiuntur totum hemiſphęrium ſuperum in quatuor partes æquales, quarum duæ auſtrales
              <lb/>
            ſunt, una orientalis, & </s>
            <s xml:id="echoid-s25263" xml:space="preserve">occidentalis altera; </s>
            <s xml:id="echoid-s25264" xml:space="preserve">duæ uero boreales, vna orientalis, & </s>
            <s xml:id="echoid-s25265" xml:space="preserve">altera occidenta-
              <lb/>
            lis, ut ex ſphæra materiali conſtat) exiſtet polus plani inclinati in eodem quadrante ſupra Ho-
              <lb/>
            rizontem. </s>
            <s xml:id="echoid-s25266" xml:space="preserve">Cum enim arcus illius circuli maximi ducti per uerticem loci, & </s>
            <s xml:id="echoid-s25267" xml:space="preserve">polum plani incli-
              <lb/>
            nati poſitus inter planum & </s>
            <s xml:id="echoid-s25268" xml:space="preserve">uerticem ſit quadrante minor, arcus autem eiuſdem circuli maximi
              <lb/>
            à plano per verticem uſque ad Horizontem porrectus quadrante maior, propterea quòd arcus
              <lb/>
              <note position="left" xlink:label="note-0400-03" xlink:href="note-0400-03a" xml:space="preserve">20</note>
            dicti circuli maximi inter uerticem & </s>
            <s xml:id="echoid-s25269" xml:space="preserve">Horizontem interiecti quadrantes ſunt; </s>
            <s xml:id="echoid-s25270" xml:space="preserve">perſpicuum eſt,
              <lb/>
            polum plani inclinati, qui terminat quadrantem dicti circuli maximi, quo polus plani inclinati ab
              <lb/>
            ipſo plano, per coroll. </s>
            <s xml:id="echoid-s25271" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s25272" xml:space="preserve">16. </s>
            <s xml:id="echoid-s25273" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25274" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25275" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s25276" xml:space="preserve">abeſt, cadere in quadrantẽ hemiſphęrii ſuperi
              <lb/>
            orientalem, & </s>
            <s xml:id="echoid-s25277" xml:space="preserve">auſtralem. </s>
            <s xml:id="echoid-s25278" xml:space="preserve">Quare Meridianus Horizontis occidentalior erit in Æquatore ſupra
              <lb/>
            Horizontem Meridiano proprio plani inclinati per eius polos, & </s>
            <s xml:id="echoid-s25279" xml:space="preserve">per polosmundi ducto; </s>
            <s xml:id="echoid-s25280" xml:space="preserve">ac pro-
              <lb/>
            pterea cum, poſito circulo ex L, deſcripto in proprio ſitu, Meridianus proprius plani inclinati ſe-
              <lb/>
            cet dictum circulum ſupra Horizontem in puncto N, numeranda erit ab N, uerſus partes occidẽ-
              <lb/>
            tales inclinatio Meridiani huius ad Meridianum Horizontis uſquead punctum O. </s>
            <s xml:id="echoid-s25281" xml:space="preserve">In hoc enim
              <lb/>
            puncto eundem circulum ſecabit Meridianus Horizontis, cum ab illo ſecedat in Æquatore ſupra
              <lb/>
            Horizontem, atque adeo in circulo ex L, deſcripto, ab N, uerſus occidentẽ, ut dictum eſt. </s>
            <s xml:id="echoid-s25282" xml:space="preserve">Igitur à
              <lb/>
              <note position="left" xlink:label="note-0400-04" xlink:href="note-0400-04a" xml:space="preserve">30</note>
            puncto O, inchoanda erit diuiſio circuli ex L, deſcripti. </s>
            <s xml:id="echoid-s25283" xml:space="preserve">Si uerò planum eiuſdem generis, quod
              <lb/>
            nimirum ex parte boreali ad Horizontem eſt inclinatum, à meridie deflectat in occaſum, nume-
              <lb/>
            randa erit dicta inclinatio duorum Meridianorum ab N, uerſus orientales partes, uſque ad O,
              <lb/>
            punctum, quod initium prębeat diuiſionis circuli ex L, deſcripti: </s>
            <s xml:id="echoid-s25284" xml:space="preserve">quia tunc polus plani inclinati
              <lb/>
            exiſtit in quadrante hemiſphęrii ſuperi occidentali; </s>
            <s xml:id="echoid-s25285" xml:space="preserve">(quod nõ aliter probabimus, quàm proximè
              <lb/>
            oſtendimus, polum plani eſle in quadrãte oriẽtali, quando planum declinabat à meridie in ortũ)
              <lb/>
            atque adeò Meridianus Horizontis in Æquatore ſupra Horizontem orientalior eſt Meridiano
              <lb/>
            proprii plani inclinati, & </s>
            <s xml:id="echoid-s25286" xml:space="preserve">c.</s>
            <s xml:id="echoid-s25287" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25288" xml:space="preserve">IN planis autem, quæ ex parte auſtrali inclinata ſunt ad Horizontem, hoc eſt, quorum ſupe-
              <lb/>
            riores facies à ſeptentrione deflectunt in ortum, occaſumue, ut ſciamus, quamnã in partem ſuppu-
              <lb/>
              <note position="left" xlink:label="note-0400-05" xlink:href="note-0400-05a" xml:space="preserve">40</note>
            tare debeamus dictam inclinationem Meridianorum, inquirẽdi erunt primum per propoſ. </s>
            <s xml:id="echoid-s25289" xml:space="preserve">32. </s>
            <s xml:id="echoid-s25290" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s25291" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25292" xml:space="preserve">arcus circulorum maximorum inclinationes planorum ad Horizontem metientium inter Ho-
              <lb/>
            rizontem, & </s>
            <s xml:id="echoid-s25293" xml:space="preserve">circulũ horæ 6. </s>
            <s xml:id="echoid-s25294" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s25295" xml:space="preserve">uel med. </s>
            <s xml:id="echoid-s25296" xml:space="preserve">nocte interiecti. </s>
            <s xml:id="echoid-s25297" xml:space="preserve">In quarta figura huius propoſ. </s>
            <s xml:id="echoid-s25298" xml:space="preserve">inue-
              <lb/>
            nimus eiuſmodi arcum (in prioribus enim tribus figuris hiſce arcubus non indigemus, cum
              <lb/>
              <note position="left" xlink:label="note-0400-06" xlink:href="note-0400-06a" xml:space="preserve">Quanti ſint at
                <lb/>
              cus circulorum
                <lb/>
              maximorũ in-
                <lb/>
              clinationes pla
                <lb/>
              norum metien
                <lb/>
              tium, inter Ho
                <lb/>
              rizontem & cir
                <lb/>
              culum horæ 6.
                <lb/>
              à mer. vel med.
                <lb/>
              noc. interiecti
                <lb/>
              in poſteriorib’
                <lb/>
              tribus ſiguris
                <lb/>
              huius propoſ.</note>
            earum plana ad Horizontem inclinata ſint ex parte boreali) grad. </s>
            <s xml:id="echoid-s25299" xml:space="preserve">40. </s>
            <s xml:id="echoid-s25300" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25301" xml:space="preserve">14. </s>
            <s xml:id="echoid-s25302" xml:space="preserve">In quinta grad.
              <lb/>
            </s>
            <s xml:id="echoid-s25303" xml:space="preserve">24. </s>
            <s xml:id="echoid-s25304" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25305" xml:space="preserve">14. </s>
            <s xml:id="echoid-s25306" xml:space="preserve">In ſexta denique grad. </s>
            <s xml:id="echoid-s25307" xml:space="preserve">37. </s>
            <s xml:id="echoid-s25308" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25309" xml:space="preserve">57. </s>
            <s xml:id="echoid-s25310" xml:space="preserve">Deinde explorandum erit, an polus plani inclina-
              <lb/>
            ti ex parte auſtrali ad Horizontem (qui quidem in huiuſmodi planis perpetuo in alterutrum
              <lb/>
            quadrantum borealium hemiſphęrii ſuperi cadit, quemadmodum in planis ex parte boreali ad
              <lb/>
            Horizontem inclinatis ſemper cadit in alterutrum quadrantum auſtralium, ut paulo ante oſten-
              <lb/>
            dimus) exiſtat infra circulum horæ 6. </s>
            <s xml:id="echoid-s25311" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s25312" xml:space="preserve">uel med. </s>
            <s xml:id="echoid-s25313" xml:space="preserve">nocte, uel in ipſomer circulo, uel deni-
              <lb/>
              <note position="left" xlink:label="note-0400-07" xlink:href="note-0400-07a" xml:space="preserve">50</note>
            que ſupra eundem. </s>
            <s xml:id="echoid-s25314" xml:space="preserve">Hoc autem facile aſſequemur, ſi cum arcu proxime inuento conferamus ar-
              <lb/>
            cum circuli maximi inclinationem plani ad Horizontem metientis (in quo etiam exiſtit arcus
              <lb/>
            proximè inuentus) poſitum inter polum plani inclinati, & </s>
            <s xml:id="echoid-s25315" xml:space="preserve">Horizontem, quem mox reperiemus.
              <lb/>
            </s>
            <s xml:id="echoid-s25316" xml:space="preserve">Si enim hic arcus minor repertus fuerit illo, manifeſtum eſt, polum plani inclinati cadere infra
              <lb/>
              <note position="left" xlink:label="note-0400-08" xlink:href="note-0400-08a" xml:space="preserve">An polus plani
                <lb/>
              inclinati in tri
                <lb/>
              bus poſteriori-
                <lb/>
              bus figuris hu-
                <lb/>
              ius propoſ. ca-
                <lb/>
              dat infra circu
                <lb/>
              lum horæ 6. an
                <lb/>
              ſupra, an vero
                <lb/>
              in ipſummet
                <lb/>
              circulum, qua
                <lb/>
              ratione cogno-
                <lb/>
              @catur.</note>
            circulum horæ 6. </s>
            <s xml:id="echoid-s25317" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s25318" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s25319" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s25320" xml:space="preserve">Si autem æqualis extiterit, polum plani in ipſomer circu
              <lb/>
            lo locari: </s>
            <s xml:id="echoid-s25321" xml:space="preserve">ſi denique maior fuerit inuentus, polum plani ſupra eundem circulum cadere, vt per-
              <lb/>
            ſpicuum eſt ex figura propoſ. </s>
            <s xml:id="echoid-s25322" xml:space="preserve">32. </s>
            <s xml:id="echoid-s25323" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25324" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25325" xml:space="preserve">vbi M, polus plani inclinati E, cadit infra circulum horæ
              <lb/>
            6. </s>
            <s xml:id="echoid-s25326" xml:space="preserve">B K D, quia arcus H M, inter polum plani, & </s>
            <s xml:id="echoid-s25327" xml:space="preserve">Horizontem minor eſt arcu H L, inter circulum
              <lb/>
            horæ 6. </s>
            <s xml:id="echoid-s25328" xml:space="preserve">& </s>
            <s xml:id="echoid-s25329" xml:space="preserve">Horizontem: </s>
            <s xml:id="echoid-s25330" xml:space="preserve">quòd ſi æqualis eſlet, caderet polus in L, ſi verò maior, ſupra L, vt patet.
              <lb/>
            </s>
            <s xml:id="echoid-s25331" xml:space="preserve">Cæterum arcus dictus inter polum plani, & </s>
            <s xml:id="echoid-s25332" xml:space="preserve">Horizontem dicto citius reperitur, cum perpetuo
              <lb/>
            ęqualis ſit complemento inclinationis plani ad Horizontem, ut ex eadem figura propoſ. </s>
            <s xml:id="echoid-s25333" xml:space="preserve">32. </s>
            <s xml:id="echoid-s25334" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25335" xml:space="preserve">1.</s>
            <s xml:id="echoid-s25336" xml:space="preserve"/>
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