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-s17660" xml:space="preserve">
              <pb o="260" file="0276" n="276" rhead="GNOMONICES"/>
            axem hyperbolarum hic eſſe lineam horæ 12. </s>
            <s xml:id="echoid-s17661" xml:space="preserve">& </s>
            <s xml:id="echoid-s17662" xml:space="preserve">non 6. </s>
            <s xml:id="echoid-s17663" xml:space="preserve">vt ibi. </s>
            <s xml:id="echoid-s17664" xml:space="preserve">Idem conſtat ex Analemmate,
              <lb/>
            ex quo arcus ſignorum ſunt deſcripti. </s>
            <s xml:id="echoid-s17665" xml:space="preserve">In eo enim radius ♑, per centrum E, ductus ſecat meridia-
              <lb/>
            nam lineam M L, in ſuperiori horologio prope Horizontem B D. </s>
            <s xml:id="echoid-s17666" xml:space="preserve">In inferiori verò radius ♋, per
              <lb/>
            idem centrum E, tranſiens ſecat lineam meridianam prope Horizontem, vt conſtat. </s>
            <s xml:id="echoid-s17667" xml:space="preserve">Idem dicen-
              <lb/>
              <note position="left" xlink:label="note-0276-01" xlink:href="note-0276-01a" xml:space="preserve">Linea horizon-
                <lb/>
              talis aufert ex
                <lb/>
              pa@te ſuperiore
                <lb/>
              hot
                <unsure/>
              ologu ſupe
                <lb/>
              rioris horolo-
                <lb/>
              gium inf
                <unsure/>
              erius,
                <lb/>
              ſ
                <unsure/>
              i omnes ei
                <unsure/>
              us
                <lb/>
              partes i@uertan
                <lb/>
              tur, vt ſupra di-
                <lb/>
              ctum eſt.</note>
            dum eſt de alijs ſignis auſtralibus, & </s>
            <s xml:id="echoid-s17668" xml:space="preserve">borealibus.</s>
            <s xml:id="echoid-s17669" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17670" xml:space="preserve">ITAQVE portio horologii ſuperioris, quam linea horizontalis amputat, collocata in facie
              <lb/>
            inferiori horologii, ita vt horizontalis linea ſuperiorem locum occupet, infra tamẽ ſtylum, & </s>
            <s xml:id="echoid-s17671" xml:space="preserve">quæ
              <lb/>
            dextra pars tunc eſt, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s17672" xml:space="preserve">è contrario, dabit horologium polare inferius, vna cum ar-
              <lb/>
            cubus ſignorum.</s>
            <s xml:id="echoid-s17673" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17674" xml:space="preserve">EADEM quoque portio abſciſſa in ſuperiori horologio erit horologium nocturnum, vt in
              <lb/>
              <note position="left" xlink:label="note-0276-02" xlink:href="note-0276-02a" xml:space="preserve">Portio Supetio
                <lb/>
              ris horologii
                <lb/>
              abſciſſa à linea
                <lb/>
              horizontali eſt
                <lb/>
              horologium no
                <lb/>
              cturnum.</note>
              <note position="left" xlink:label="note-0276-03" xlink:href="note-0276-03a" xml:space="preserve">10</note>
            ſuperioribus dictum eſt. </s>
            <s xml:id="echoid-s17675" xml:space="preserve">In illud enim caderet vmbra ſtyli mane ante ortum Solis, & </s>
            <s xml:id="echoid-s17676" xml:space="preserve">veſperi ante
              <lb/>
            occaſum, Sole in auſtralibus ſignis exiſtente, niſi terræ denſitas obſiſteret.</s>
            <s xml:id="echoid-s17677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17678" xml:space="preserve">MANIFESTVM autem eſt, quo maior fuerit altitudo poli, eo plures horas recipi in horo
              <lb/>
            logio inferiori, ſeu portione abſciſſa à linea horizontali, eò pauciores verò, quò minor fuerit poli
              <lb/>
              <note position="left" xlink:label="note-0276-04" xlink:href="note-0276-04a" xml:space="preserve">Quo maior eſt
                <lb/>
              poli altitudo, eò
                <lb/>
              plures horæ in
                <lb/>
              horologio pola-
                <lb/>
              r
                <unsure/>
              i Inferioti, ſeu
                <lb/>
              noctutno com-
                <lb/>
              prehenduntur,
                <lb/>
              quò aũt minor,
                <lb/>
              eò
                <unsure/>
              pauciores.</note>
            altitudo. </s>
            <s xml:id="echoid-s17679" xml:space="preserve">Nam quò maior eſt altitudo poli, eò minor fiet angulus complementi altitudinis poli
              <lb/>
            D B A, atque adeo punctum D, vicinius erit æquinoctiali lineæ. </s>
            <s xml:id="echoid-s17680" xml:space="preserve">quare plures horas linea hori-
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            zontalis interſecabit, &</s>
            <s xml:id="echoid-s17681" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17682" xml:space="preserve">Quod idem ex eo patere poteſt, quòd quanto maior eſt altitudo poli,
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            tanto propius ad Verticalem circulum accedit circulus horæ 6. </s>
            <s xml:id="echoid-s17683" xml:space="preserve">cui horologiũ polare æquidiſtat,
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            ac proinde pluribus horis Sol Borealem faciem illuminabit, &</s>
            <s xml:id="echoid-s17684" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17685" xml:space="preserve">Igitur parallelos, ſiue arcus ſigno
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            ruin Zodiaci in prædicto horologio polari deſcripſimus. </s>
            <s xml:id="echoid-s17686" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s17687" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
        </div>
        <div xml:id="echoid-div900" type="section" level="1" n="217">
          <head xml:id="echoid-head223" xml:space="preserve">PROBLEMA 39. PROPOSITIO 39.</head>
          <p>
            <s xml:id="echoid-s17688" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem polari horolo-
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            gio deſcribere.</s>
            <s xml:id="echoid-s17689" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17690" xml:space="preserve">QVEMADMODVM paralleli ſignorum, ita & </s>
            <s xml:id="echoid-s17691" xml:space="preserve">paralleli arcuum diurnorum deſcribun-
              <lb/>
              <note position="left" xlink:label="note-0276-06" xlink:href="note-0276-06a" xml:space="preserve">De ſcriptio ar-
                <lb/>
              arcuum diur-
                <lb/>
              no@um in eo-
                <lb/>
              dem horologio
                <lb/>
              polaii.</note>
            tur in horologio, cum tam hi, quàm illi Æquatori ſint æquidiſtantes; </s>
            <s xml:id="echoid-s17692" xml:space="preserve">dummodo loco parallelo-
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            rum per ſignorum principia deſcriptorum accipiantur paralleli arcuum diurnorum, &</s>
            <s xml:id="echoid-s17693" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17694" xml:space="preserve">Paralle-
              <lb/>
              <note position="left" xlink:label="note-0276-07" xlink:href="note-0276-07a" xml:space="preserve">30</note>
            los igitur arcuum diurnorum in eodem polari horologio deſcripſimus. </s>
            <s xml:id="echoid-s17695" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s17696" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div902" type="section" level="1" n="218">
          <head xml:id="echoid-head224" xml:space="preserve">PROBLEMA 40. PROPOSITIO 40.</head>
          <p>
            <s xml:id="echoid-s17697" xml:space="preserve">CIRCVLOS Verticales in eodem horologio polari deſcribere.</s>
            <s xml:id="echoid-s17698" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17699" xml:space="preserve">IN horologio auferatur ex linea æquinoctiali recta A B, æqualis ſtylo, cuiuſmodi eſt recta in-
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            ter lineam horæ 12. </s>
            <s xml:id="echoid-s17700" xml:space="preserve">& </s>
            <s xml:id="echoid-s17701" xml:space="preserve">lineam horæ 3. </s>
            <s xml:id="echoid-s17702" xml:space="preserve">vel 9 interiecta, vt demonſtrauimus in ſcholio propoſ. </s>
            <s xml:id="echoid-s17703" xml:space="preserve">25.
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            </s>
            <s xml:id="echoid-s17704" xml:space="preserve">huius libri, & </s>
            <s xml:id="echoid-s17705" xml:space="preserve">ad punctum B, conſtituatur angulus A B C, altitudini poli æqualis, ſecetq́ue recta
              <lb/>
              <note position="left" xlink:label="note-0276-08" xlink:href="note-0276-08a" xml:space="preserve">40</note>
            B C, lineam meridianam infra lineam æquinoctialem in C, in ſuperiori horologio, in inferiori
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            autem ſupra lineam æquinoctialem. </s>
            <s xml:id="echoid-s17706" xml:space="preserve">Ducta deinde recta B D, quæ faciat angulum A B D, com-
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            plemento altitudinis poli æqualem, aut (quod idem eſt) angulum rectum cum recta B C, ita vt ſe-
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            cet meridianam lineam in puncto D, per quod linea horizontalis ducitur, vt propoſ. </s>
            <s xml:id="echoid-s17707" xml:space="preserve">38. </s>
            <s xml:id="echoid-s17708" xml:space="preserve">huius
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            libri oſtenſum eſt, ſumatur in linea meridiana ipſi B D, æqualis D E, ſiue ſupra horizontalem li-
              <lb/>
            neam, ſiue inſra. </s>
            <s xml:id="echoid-s17709" xml:space="preserve">Ex centro autem E, deſcripto circulo cuiuſcunque magnitudinis, eoq́ue diuiſo
              <lb/>
            in partes 360. </s>
            <s xml:id="echoid-s17710" xml:space="preserve">vel in pauciores, ſi horologium omnium Verticalium non eſt capax, (Nos eum ſe-
              <lb/>
            cuimus in partes 24. </s>
            <s xml:id="echoid-s17711" xml:space="preserve">vt ſingulæ grad. </s>
            <s xml:id="echoid-s17712" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17713" xml:space="preserve">complectantur) ducantur per puncta diuiſionum, & </s>
            <s xml:id="echoid-s17714" xml:space="preserve">cen-
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            trum E, rectæ occultæ ſecantes lineam horizontalem in punctis, per quæ, & </s>
            <s xml:id="echoid-s17715" xml:space="preserve">per punctum C, re-
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            ctæ emiſſæ dabunt circulos Verticales, hoc eſt, communes Verticalium, & </s>
            <s xml:id="echoid-s17716" xml:space="preserve">plani horologii ſectio-
              <lb/>
              <note position="left" xlink:label="note-0276-09" xlink:href="note-0276-09a" xml:space="preserve">50</note>
            nes, quarum initium ſumitur à Verticali linea, quæ per C, ipſi A B, vel lineæ horizontali paralle-
              <lb/>
            la ducitur, ita vt linea meridiana det nonageſimum Verticalem. </s>
            <s xml:id="echoid-s17717" xml:space="preserve">Quæ omnia hoc modo de-
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            monſtrabimus.</s>
            <s xml:id="echoid-s17718" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17719" xml:space="preserve">INTELLIGATVR triangulum C B D, vnà cum recta A B, circa C D, circumduci, do-
              <lb/>
              <note position="left" xlink:label="note-0276-10" xlink:href="note-0276-10a" xml:space="preserve">Demonſtratio
                <lb/>
              deſcriprionis
                <lb/>
              citculorũ Ver-
                <lb/>
              ticalium in ho-
                <lb/>
              rologio polati.</note>
            nec rectum ſit ad planum horologii, atque cum Meridiano coniungatur, punctumq́ue B, idem
              <lb/>
            fiat, quod centrum mundi. </s>
            <s xml:id="echoid-s17720" xml:space="preserve">Quoniam igitur, vt propoſitione 38. </s>
            <s xml:id="echoid-s17721" xml:space="preserve">huius libri demonſtrauimus,
              <lb/>
            Horizon per rectam B D, tranſit, ita vt B D, communis ſectio ſit Horizontis ac Meridiani; </s>
            <s xml:id="echoid-s17722" xml:space="preserve">eſtq́ue
              <lb/>
            angulus D B C, rectus, quippe qui ex altitudine poli, & </s>
            <s xml:id="echoid-s17723" xml:space="preserve">complemento eiuſdem componatur, erit
              <lb/>
            recta B C, communis ſectio Verticalis proprie dicti, & </s>
            <s xml:id="echoid-s17724" xml:space="preserve">Meridiani, ita vt C, ſit Zenith, ſeu vertex
              <lb/>
            capitis. </s>
            <s xml:id="echoid-s17725" xml:space="preserve">Cum enim tam Meridianus, quàm Verticalis ad Horizontem rectus ſit, erit & </s>
            <s xml:id="echoid-s17726" xml:space="preserve">eorum ſe-
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            ctio communis, axis nimirum Horizontis, ad eundem Horizontem perpendicularis, atque </s>
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