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-div979" type="section" level="1" n="240">
          <p>
            <s xml:id="echoid-s19095" xml:space="preserve">
              <pb o="282" file="0298" n="298" rhead="GNOMONICES"/>
            tum. </s>
            <s xml:id="echoid-s19096" xml:space="preserve">In inferiori verò habetur idem Meridianus inſularum fortunatarum, ſi longitudo loci ſup-
              <lb/>
            putetur à puncto B, verſus D, vſque ad H. </s>
            <s xml:id="echoid-s19097" xml:space="preserve">Nam ſi horologium inferius propriam habeat poſi-
              <lb/>
            tionem, ita vt linea horizontalis ſuperiorem occupet locum, & </s>
            <s xml:id="echoid-s19098" xml:space="preserve">punctum A, in feriorem, atq; </s>
            <s xml:id="echoid-s19099" xml:space="preserve">pun
              <lb/>
            ctum C, ortum reſpiciat, & </s>
            <s xml:id="echoid-s19100" xml:space="preserve">D, occaſum, ſecabit Meridianus loci planum horologij ſupra Hori-
              <lb/>
            zontem in puncto B, infra verò Horizontem in puncto A, Quare à B, verſus D, ſunt partes oc-
              <lb/>
            cidentales, & </s>
            <s xml:id="echoid-s19101" xml:space="preserve">orientales verſus C, &</s>
            <s xml:id="echoid-s19102" xml:space="preserve">c.</s>
            <s xml:id="echoid-s19103" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19104" xml:space="preserve">SED præſtat Meridianos circulos in horologio inferiori deſcribere ex circulis Meridianis ſu-
              <lb/>
              <note position="left" xlink:label="note-0298-01" xlink:href="note-0298-01a" xml:space="preserve">Quo modo In
                <lb/>
              ferius horolo
                <lb/>
              gium Meridia-
                <lb/>
              norum ex Supe
                <lb/>
              riori ori
                <unsure/>
              um ha
                <lb/>
              beat.</note>
            perioris horologij, vt oſtenſum eſt in ſcholio propoſ. </s>
            <s xml:id="echoid-s19105" xml:space="preserve">14. </s>
            <s xml:id="echoid-s19106" xml:space="preserve">huius libri, & </s>
            <s xml:id="echoid-s19107" xml:space="preserve">in verticali horologio fa-
              <lb/>
            ctum eſt in ſcholio propoſ. </s>
            <s xml:id="echoid-s19108" xml:space="preserve">28. </s>
            <s xml:id="echoid-s19109" xml:space="preserve">huius libri, omnia enim, quæ ibi dicta ſunt, huc transferri poſ-
              <lb/>
            ſunt, intelligendo tamen ſemper pro auſtrali horologio ſuperius æquinoctiale, & </s>
            <s xml:id="echoid-s19110" xml:space="preserve">pro boreali in-
              <lb/>
              <note position="left" xlink:label="note-0298-02" xlink:href="note-0298-02a" xml:space="preserve">10</note>
            ferius. </s>
            <s xml:id="echoid-s19111" xml:space="preserve">Exemplum habes in figura propoſita. </s>
            <s xml:id="echoid-s19112" xml:space="preserve">Vbi vides Meridianum 105. </s>
            <s xml:id="echoid-s19113" xml:space="preserve">vltra centrum E, pro-
              <lb/>
            ductum in ſuperiori horologio habere grad. </s>
            <s xml:id="echoid-s19114" xml:space="preserve">285. </s>
            <s xml:id="echoid-s19115" xml:space="preserve">qui illi opponitur, at vltra lineam horizontalem
              <lb/>
            productum, iterum aſſumere grad 105. </s>
            <s xml:id="echoid-s19116" xml:space="preserve">in inferiori horologio, & </s>
            <s xml:id="echoid-s19117" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s19118" xml:space="preserve">Meridianos ergo,
              <lb/>
            id eſt, circulos longitudinũ, in eodem horologio æquinoctiali deſcripſimus. </s>
            <s xml:id="echoid-s19119" xml:space="preserve">Quod faciendũ erat.</s>
            <s xml:id="echoid-s19120" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div982" type="section" level="1" n="241">
          <head xml:id="echoid-head248" xml:space="preserve">PROBLEMA 55. PROPOSITIO 55.</head>
          <p>
            <s xml:id="echoid-s19121" xml:space="preserve">PARALLELOS ciuitatum, ſiue circulos latitudinum, in eodem
              <lb/>
            æquinoctiali horologio depingere.</s>
            <s xml:id="echoid-s19122" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
          <p>
            <s xml:id="echoid-s19123" xml:space="preserve">PRO parallelis per initia ſignorum Zodiaci ductis accipiantur paralleli per vertices ciuitatũ
              <lb/>
              <note position="left" xlink:label="note-0298-04" xlink:href="note-0298-04a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              rallelorum ciui
                <lb/>
              tatum, latitudi-
                <lb/>
              numve, in eodẽ
                <lb/>
              horologio æqui
                <lb/>
              noctiali.</note>
            intra tropicos exiſtentium tranſeuntes, & </s>
            <s xml:id="echoid-s19124" xml:space="preserve">alia omnia fiant, quæ de parallelis ſignorum Zodiaci de-
              <lb/>
            ſcribendis propoſ. </s>
            <s xml:id="echoid-s19125" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19126" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s19127" xml:space="preserve">præcepimus; </s>
            <s xml:id="echoid-s19128" xml:space="preserve">factumq́ue erit, quod proponitur. </s>
            <s xml:id="echoid-s19129" xml:space="preserve">Igitur parallelos
              <lb/>
            cíuitatum, ſiue circulos latitudinum, &</s>
            <s xml:id="echoid-s19130" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19131" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s19132" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div984" type="section" level="1" n="242">
          <head xml:id="echoid-head249" xml:space="preserve">PROBLEMA 56. PROPOSITIO 56.</head>
          <p>
            <s xml:id="echoid-s19133" xml:space="preserve">DOMOS cœleſtes in codem horologio æquinoctiali de-
              <lb/>
              <note position="left" xlink:label="note-0298-05" xlink:href="note-0298-05a" xml:space="preserve">30</note>
            ſcribere.</s>
            <s xml:id="echoid-s19134" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19135" xml:space="preserve">SECETVR circulus A C B D, principio facto à linea meridiana, in 12. </s>
            <s xml:id="echoid-s19136" xml:space="preserve">partes æquales, vel
              <lb/>
              <note position="left" xlink:label="note-0298-06" xlink:href="note-0298-06a" xml:space="preserve">Cœleſtium do-
                <lb/>
              morum in eo-
                <lb/>
              dẽ æquinoctiali
                <lb/>
              horologio de-
                <lb/>
              ſcriptio ſecun-
                <lb/>
              dum
                <unsure/>
              loan. Re-
                <lb/>
              giom.</note>
            in plures, ſi ſingularum domorum partes etiam defideremus. </s>
            <s xml:id="echoid-s19137" xml:space="preserve">Nos illum diuiſimus in 12. </s>
            <s xml:id="echoid-s19138" xml:space="preserve">vt inte-
              <lb/>
            græ domus duntaxat deſcribantur. </s>
            <s xml:id="echoid-s19139" xml:space="preserve">Per puncta autem diuiſionum, & </s>
            <s xml:id="echoid-s19140" xml:space="preserve">centrum E, ducantnr rectæ
              <lb/>
            lineæ occultæ. </s>
            <s xml:id="echoid-s19141" xml:space="preserve">Deinde per punctum m, vbi meridiana linea horizontalem interſecat, dictis lineis
              <lb/>
            agantur lineæ parallelæ, deſcriptæq́ue erunt domus cœleſtes in vtroque horologio ſecundum do-
              <lb/>
            ctrinam Ioan, Regiom. </s>
            <s xml:id="echoid-s19142" xml:space="preserve">Quoniam enim circuli domorum cœleſtium ſecundum Ioan. </s>
            <s xml:id="echoid-s19143" xml:space="preserve">Regiom.
              <lb/>
            </s>
            <s xml:id="echoid-s19144" xml:space="preserve">
              <note position="left" xlink:label="note-0298-07" xlink:href="note-0298-07a" xml:space="preserve">Demonſtratio
                <lb/>
              deſcriptionis
                <lb/>
              domorum cœle
                <lb/>
              ſtium ſecundũ
                <lb/>
              10. Regiom.</note>
            diuidunt Aequatorem in partes æquales, initio facto à Meridiano, qui vnus eſt ex dictis circulis,
              <lb/>
            tranſeuntq́ue per centrum mundi, ſiue Æquatoris, tranſibunt neceſſario per communes ſectiones
              <lb/>
              <note position="left" xlink:label="note-0298-08" xlink:href="note-0298-08a" xml:space="preserve">40</note>
            Aequatoris, & </s>
            <s xml:id="echoid-s19145" xml:space="preserve">circulorum horariorum à meridie, vel media nocte, cum hi quoque per centrum
              <lb/>
            mundi incedentes ſecent Aequatorem in partes æquales, principio facto à Meridiano; </s>
            <s xml:id="echoid-s19146" xml:space="preserve">ita vt com-
              <lb/>
            munes ſectiones circulorum domorum cœleſtium & </s>
            <s xml:id="echoid-s19147" xml:space="preserve">Aequatoris à communibus ſectionibus cir-
              <lb/>
            culorum horariorum & </s>
            <s xml:id="echoid-s19148" xml:space="preserve">Aequatoris non diſcrepent. </s>
            <s xml:id="echoid-s19149" xml:space="preserve">Sed communes ſectiones plani horologij,
              <lb/>
            & </s>
            <s xml:id="echoid-s19150" xml:space="preserve">circulorum domorum cœleſtium parallelæ ſunt communibus ſectionibus Aequatoris, & </s>
            <s xml:id="echoid-s19151" xml:space="preserve">eo-
              <lb/>
              <note position="left" xlink:label="note-0298-09" xlink:href="note-0298-09a" xml:space="preserve">16. vndec.</note>
            rundem circulorum; </s>
            <s xml:id="echoid-s19152" xml:space="preserve">his autem parallelæ quoque ſunt (cum ſint oſtenſæ eædem, quæ ſectiones
              <lb/>
              <note position="left" xlink:label="note-0298-10" xlink:href="note-0298-10a" xml:space="preserve">16. vndec.</note>
            communes Aequatoris, & </s>
            <s xml:id="echoid-s19153" xml:space="preserve">horariorum circulorum) communes ſectiones plani horologij, & </s>
            <s xml:id="echoid-s19154" xml:space="preserve">cir-
              <lb/>
            culorum horarum à meridie, vel media nocte. </s>
            <s xml:id="echoid-s19155" xml:space="preserve">Igitur communes ſectiones plani horologii, & </s>
            <s xml:id="echoid-s19156" xml:space="preserve">
              <lb/>
            circulorum domorum cœleſtium parallelæ quoque erunt communibus ſectionibus eiuſdem pla-
              <lb/>
              <note position="left" xlink:label="note-0298-11" xlink:href="note-0298-11a" xml:space="preserve">9. vndec.</note>
            ni horologii, & </s>
            <s xml:id="echoid-s19157" xml:space="preserve">horariorum circulorum. </s>
            <s xml:id="echoid-s19158" xml:space="preserve">Cum ergo rectæ per centrum E, ductæ, diuidentesq́ue
              <lb/>
              <note position="left" xlink:label="note-0298-12" xlink:href="note-0298-12a" xml:space="preserve">50</note>
            circulum A C B D, in 12. </s>
            <s xml:id="echoid-s19159" xml:space="preserve">partes æquales, vel etiam in plures, vel pauciores, ſint communes ſectio-
              <lb/>
            nes plani horologii, & </s>
            <s xml:id="echoid-s19160" xml:space="preserve">circulorum horariorum, vt propoſ. </s>
            <s xml:id="echoid-s19161" xml:space="preserve">49. </s>
            <s xml:id="echoid-s19162" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s19163" xml:space="preserve">demonſtrauimus; </s>
            <s xml:id="echoid-s19164" xml:space="preserve">erunt
              <lb/>
            his rectis parallelæ, communes ſectiones plani horologii, & </s>
            <s xml:id="echoid-s19165" xml:space="preserve">circulorum domorum cœleſtium.
              <lb/>
            </s>
            <s xml:id="echoid-s19166" xml:space="preserve">Quocirca cum communes ſectiones hæ tranſeant omnes per punctum m, vt conſtat ex propoſ. </s>
            <s xml:id="echoid-s19167" xml:space="preserve">
              <lb/>
            18. </s>
            <s xml:id="echoid-s19168" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s19169" xml:space="preserve">propterea quòd cõmunis ſectio omnium circulorum cœleſtium domorum, hoc
              <lb/>
            eſt, axis Verticalis circuli, ſeu cõmunis ſectio Meridiani, & </s>
            <s xml:id="echoid-s19170" xml:space="preserve">Horizontis, plano horologii occurrit
              <lb/>
            in eodem puncto m, vt patet ex figura propoſ. </s>
            <s xml:id="echoid-s19171" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19172" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s19173" xml:space="preserve">in qua communis iſta ſectio eſt recta
              <lb/>
            l m, ſi triangulum E l m, intelligatur rectum ad planum horologii, hoc eſt, in plano Meridiani; </s>
            <s xml:id="echoid-s19174" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0298-13" xlink:href="note-0298-13a" xml:space="preserve">Quibus horis à
                <lb/>
              mer vel med.
                <lb/>
              noc initia do-
                <lb/>
              morum cœle-
                <lb/>
              ſtium parallela
                <lb/>
              ſint.</note>
            erunt rectæ per m, ductæ rectis per E, emiſſis parallelæ, communes ſectiones plani horologii, & </s>
            <s xml:id="echoid-s19175" xml:space="preserve">
              <lb/>
            circulorum cœleſtium domorum. </s>
            <s xml:id="echoid-s19176" xml:space="preserve">Quod eſt propoſitum. </s>
            <s xml:id="echoid-s19177" xml:space="preserve">Manifeſtum autem eſt, initia domo-
              <lb/>
            rum cœleſtium parallela eſſe lineis horarum à meridiana linea diſtantibus duabus, quatuor, & </s>
            <s xml:id="echoid-s19178" xml:space="preserve"/>
          </p>
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