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-s12729" xml:space="preserve">
              <pb o="193" file="0213" n="213" rhead="LIBER SECVNDVS."/>
            b N, ſimilem eſſe, quòd hic ſimilis ſit arcui ſemidiurno tropici ♋. </s>
            <s xml:id="echoid-s12730" xml:space="preserve">Et quoniã arcus inter b, & </s>
            <s xml:id="echoid-s12731" xml:space="preserve">pro-
              <lb/>
            ximum punctum diuiſionis verſus N, ſimilis eſt etiam arcui tropici ♋, inter duos maximos circu
              <lb/>
            los, qui per polos ducuntur, interiecto, quorum vnus per horam 24. </s>
            <s xml:id="echoid-s12732" xml:space="preserve">ab occaſu, id eſt, per pun-
              <lb/>
              <figure xlink:label="fig-0213-01" xlink:href="fig-0213-01a" number="150">
                <image file="0213-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0213-01"/>
              </figure>
              <note position="left" xlink:label="note-0213-01" xlink:href="note-0213-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0213-02" xlink:href="note-0213-02a" xml:space="preserve">20</note>
            ctum b, alter autem per horam 23. </s>
            <s xml:id="echoid-s12733" xml:space="preserve">aboccaſu in tropico ♋, ducitur, quòd vterque arcus ſit pars
              <lb/>
              <note position="left" xlink:label="note-0213-03" xlink:href="note-0213-03a" xml:space="preserve">30</note>
            24. </s>
            <s xml:id="echoid-s12734" xml:space="preserve">ſui circuli; </s>
            <s xml:id="echoid-s12735" xml:space="preserve">tranſibit quoque per proximum punctum diuiſionis, à puncto b, verſus N, proce-
              <lb/>
            dendo, circulus maximus per polos mundi, & </s>
            <s xml:id="echoid-s12736" xml:space="preserve">horam 23. </s>
            <s xml:id="echoid-s12737" xml:space="preserve">ab occaſu in tropico ♋, ductus: </s>
            <s xml:id="echoid-s12738" xml:space="preserve">qu ia
              <lb/>
            hac ratione rectæ ex centro E, ductæ per b, & </s>
            <s xml:id="echoid-s12739" xml:space="preserve">per punctum proximum verſus N, hoc eſt, ſectiones
              <lb/>
            factę à duobus illis circulis maximis per polos, ac per horas 24. </s>
            <s xml:id="echoid-s12740" xml:space="preserve">& </s>
            <s xml:id="echoid-s12741" xml:space="preserve">23. </s>
            <s xml:id="echoid-s12742" xml:space="preserve">ab occaſu in tropico ♋, du-
              <lb/>
            ctis, auferent ex Aequatore arcũ ſimilem arcui tropici inter horas 24. </s>
            <s xml:id="echoid-s12743" xml:space="preserve">& </s>
            <s xml:id="echoid-s12744" xml:space="preserve">23. </s>
            <s xml:id="echoid-s12745" xml:space="preserve">poſito, vt vult Theod.
              <lb/>
            </s>
            <s xml:id="echoid-s12746" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s12747" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12748" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12749" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12750" xml:space="preserve">quod alioquin non contingeret, Si enim per aliud punctum tranſiret dictus cir-
              <lb/>
            culus, eſſet arcus circuli M a N b, inter b, & </s>
            <s xml:id="echoid-s12751" xml:space="preserve">illud punctum, maior vel minor quàm vigeſimaquar
              <lb/>
            ta pars; </s>
            <s xml:id="echoid-s12752" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s12753" xml:space="preserve">arcus Aequatoris huic ſimilis, (vt conſtat ex demonſtratis à nobis ad finem
              <lb/>
            cap. </s>
            <s xml:id="echoid-s12754" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12755" xml:space="preserve">ſphæræ) foret maior, vel minor quàm pars vigeſimaquarta; </s>
            <s xml:id="echoid-s12756" xml:space="preserve">atque adeo non ſimilis prædi
              <lb/>
            cto arcui ttopici ♋. </s>
            <s xml:id="echoid-s12757" xml:space="preserve">Quod eſt abſurdum. </s>
            <s xml:id="echoid-s12758" xml:space="preserve">Eadem ratione ſequens punctum verſus N, horam 22. </s>
            <s xml:id="echoid-s12759" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0213-04" xlink:href="note-0213-04a" xml:space="preserve">40</note>
            & </s>
            <s xml:id="echoid-s12760" xml:space="preserve">reliqua reliquas horas indicabunt.</s>
            <s xml:id="echoid-s12761" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12762" xml:space="preserve">IAM verò ex circulo M a N b, ita diuiſo, inueniemus in arcu ♋, puncta horarum ab occaſu,
              <lb/>
            hac ratione. </s>
            <s xml:id="echoid-s12763" xml:space="preserve">Per puncta diuiſionum, & </s>
            <s xml:id="echoid-s12764" xml:space="preserve">centrum E, rectas lineas occultas educemus ſecantes æqui-
              <lb/>
            noctialem lineam in punctis, per quæ ſi rectæ occultæ ducantur ex H, centro horologij, ſecabitur
              <lb/>
            tropicus ♋, in punctis horarum ab occaſu. </s>
            <s xml:id="echoid-s12765" xml:space="preserve">Verbi gratia, per punctum f, horæ 18. </s>
            <s xml:id="echoid-s12766" xml:space="preserve">ab occaſu, & </s>
            <s xml:id="echoid-s12767" xml:space="preserve">per
              <lb/>
            centrum E, ducta recta f E, ſecat lineam æquinoctialem in g; </s>
            <s xml:id="echoid-s12768" xml:space="preserve">Recta autem H g, ducta ſecat arcum
              <lb/>
            ♋, in h, puncto, quod dico pertinere ad horam 18. </s>
            <s xml:id="echoid-s12769" xml:space="preserve">ab occaſu. </s>
            <s xml:id="echoid-s12770" xml:space="preserve">Quoniam enim recta f g, commu
              <lb/>
            nis ſectio eſt Aequatoris, & </s>
            <s xml:id="echoid-s12771" xml:space="preserve">circuli maximi per polos mundi, & </s>
            <s xml:id="echoid-s12772" xml:space="preserve">horam 18. </s>
            <s xml:id="echoid-s12773" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s12774" xml:space="preserve">in tropico ♋,
              <lb/>
            ducti; </s>
            <s xml:id="echoid-s12775" xml:space="preserve">propterea quòd, vt oſtendimus, dictus circulus maximus per punctum f, horę 18. </s>
            <s xml:id="echoid-s12776" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s12777" xml:space="preserve">ſi
              <lb/>
            circulus M a N b, in proprio ſitu ſtatuatur, ac per centrum mundi E, tranſit; </s>
            <s xml:id="echoid-s12778" xml:space="preserve">occurret dictus cir-
              <lb/>
              <note position="left" xlink:label="note-0213-05" xlink:href="note-0213-05a" xml:space="preserve">50</note>
            culus maximus plano horologii in puncto g. </s>
            <s xml:id="echoid-s12779" xml:space="preserve">Quia verò circulus idem per H, centrum horologij
              <lb/>
            tranſit, per propoſ. </s>
            <s xml:id="echoid-s12780" xml:space="preserve">18. </s>
            <s xml:id="echoid-s12781" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s12782" xml:space="preserve">quòd per axem ducatur, erit recta Hg, cõmunis ſectio eiuſ-
              <lb/>
            dem maximi circuli, & </s>
            <s xml:id="echoid-s12783" xml:space="preserve">plani horologii. </s>
            <s xml:id="echoid-s12784" xml:space="preserve">Quare cum, Sole exiſtente in illo circulo maximo, vmbra
              <lb/>
            ſtyli, per propoſ. </s>
            <s xml:id="echoid-s12785" xml:space="preserve">11. </s>
            <s xml:id="echoid-s12786" xml:space="preserve">eiuſdem libri ſuperioris, cadat in rectam Hg, & </s>
            <s xml:id="echoid-s12787" xml:space="preserve">eodem exiſtente in tropico
              <lb/>
            ♋, proijciatur, per propoſ. </s>
            <s xml:id="echoid-s12788" xml:space="preserve">12. </s>
            <s xml:id="echoid-s12789" xml:space="preserve">eiuſdem ſuperioris libri, in arcum ♋; </s>
            <s xml:id="echoid-s12790" xml:space="preserve">fit vt Sole poſſidente punctũ
              <lb/>
            horæ 18. </s>
            <s xml:id="echoid-s12791" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s12792" xml:space="preserve">in tropico ♋, vbi dictus circulus maximus, & </s>
            <s xml:id="echoid-s12793" xml:space="preserve">tropicus ♋, ſe interſecant, vmbra
              <lb/>
            ſtyli proijciatur in punctum h, ac proinde per h, ducenda erit linea horæ 18. </s>
            <s xml:id="echoid-s12794" xml:space="preserve">ab occaſu. </s>
            <s xml:id="echoid-s12795" xml:space="preserve">Eademq́;
              <lb/>
            </s>
            <s xml:id="echoid-s12796" xml:space="preserve">de cæteris ratio eſt ha benda.</s>
            <s xml:id="echoid-s12797" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12798" xml:space="preserve">VERVM hac ratione, vt vides, inueniuntur in tropico ♋, puncta illarum duntaxat horarũ,
              <lb/>
            quæ in ſemicirculo t N u, continentur, propterea quòd communes ſectiones illorum maximorũ
              <lb/>
            circulorum, & </s>
            <s xml:id="echoid-s12799" xml:space="preserve">Aequatoris, indicant in linea æquinoctiali illas horas, è quibus per centrum E, </s>
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