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-div56" type="section" level="1" n="18">
          <pb o="17" file="0037" n="37" rhead="LIBER PRIMVS."/>
          <p style="it">
            <s xml:id="echoid-s1242" xml:space="preserve">CAETERVM quainduſtria poli eleuatio in quacunque regione inueſtigari debeat, quod quidem
              <lb/>
              <note position="right" xlink:label="note-0037-01" xlink:href="note-0037-01a" xml:space="preserve">Cognitio altit
                <lb/>
              dinis poli ad
                <lb/>
              Analemmatisu
                <lb/>
              deſcriptionẽ no
                <unsure/>
                <lb/>
              ceſſalia eſt.</note>
            ad rectam Analemmatis conſtructionem requiritur, (neque enim axis F G, duci poterit, ſi quantus eſſe
              <lb/>
            debeat altitudinis poli arcus D F, ignoretur.) </s>
            <s xml:id="echoid-s1243" xml:space="preserve">oſtendimus & </s>
            <s xml:id="echoid-s1244" xml:space="preserve">in vſu Aſtrolabij, & </s>
            <s xml:id="echoid-s1245" xml:space="preserve">in Coſmographia, nec
              <lb/>
            non in commentarijs in Sphæram, cum de Meridiani circuli officijs verba faceremus. </s>
            <s xml:id="echoid-s1246" xml:space="preserve">Eandem tamen al-
              <lb/>
            titudinem poli alio modo per Analemma inueniemus in ſcholio 2. </s>
            <s xml:id="echoid-s1247" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s1248" xml:space="preserve">28. </s>
            <s xml:id="echoid-s1249" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s1250" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1251" xml:space="preserve">HAEC igitur ſigura, quam hactenus conſtruximus, continens dictorum circulorum ſectiones commu-
              <lb/>
            nes cum Meridiano circulo, apud veteres, & </s>
            <s xml:id="echoid-s1252" xml:space="preserve">recẽtiores potiſſimum Analemma nuncupatur, quamuis ip-
              <lb/>
            ſum non vno modo deſinierint omnes, cum alius alium in eo definiendo ſcopum habuerit. </s>
            <s xml:id="echoid-s1253" xml:space="preserve">Placuit ta-
              <lb/>
            men nobis illud explicare per communes ſectiones, quas circuli præcipui ſphæræ in plano Meridia-
              <lb/>
            ni faciunt.</s>
            <s xml:id="echoid-s1254" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <note position="right" xml:space="preserve">Alij etiam cir-
            <lb/>
          culi, præter di-
            <lb/>
          ctos in Analem
            <lb/>
          mate deſcribi
            <lb/>
          poſſunt.</note>
          <p style="it">
            <s xml:id="echoid-s1255" xml:space="preserve">POSSVNT autem & </s>
            <s xml:id="echoid-s1256" xml:space="preserve">aliorum circulorũ ſectiones cum eodem Meridiano (quales ſunt paralleli
              <lb/>
            Horizontis, paralleli Eclipticæ, &</s>
            <s xml:id="echoid-s1257" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s1258" xml:space="preserve">deſcribi in eodem Meridiano, ut in deſcriptione Aftrolabij fit, & </s>
            <s xml:id="echoid-s1259" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0037-04" xlink:href="note-0037-04a" xml:space="preserve">Alia acceptio
                <lb/>
              Analemmatis.</note>
            in ſequentibus etiam nonnunquam fiet. </s>
            <s xml:id="echoid-s1260" xml:space="preserve">Immo verò & </s>
            <s xml:id="echoid-s1261" xml:space="preserve">figura circularis, cuius circulus referat alium
              <lb/>
            quempiam circulum maximum, præter Meridianum, continens ſectiones communes aliorum circulorum
              <lb/>
            cum illo circulo maximo, Analemma dici conſueuit, vt ſuo loco docebimus. </s>
            <s xml:id="echoid-s1262" xml:space="preserve">Cæterum Analemma hacte
              <lb/>
              <note position="right" xlink:label="note-0037-05" xlink:href="note-0037-05a" xml:space="preserve">Quæ lineamen
                <lb/>
              ta Analemma-
                <lb/>
              tis eadem per-
                <lb/>
              maneantin om
                <lb/>
              ni climate, &
                <lb/>
              quæ non.</note>
            nus conſtructum, quod attinet ad parallelos per circulum M P N Q, inuentos, omnibus mundi climati-
              <lb/>
            bus inſeruit. </s>
            <s xml:id="echoid-s1263" xml:space="preserve">Hi enim paralleli nunquam mutantur, in quocunque Horizonte Analemma conſtituatur,
              <lb/>
            niſi prius maxima declinatio Solis mutata ſit, cum eorum deſcriptio ex hac ſola maxima declinatione
              <lb/>
            pendeat, vt conſtat. </s>
            <s xml:id="echoid-s1264" xml:space="preserve">Cæteræautem ſectiones, vel rectæ lineæ, variantur pro varia altitudine poli ſupra
              <lb/>
            Horizontem. </s>
            <s xml:id="echoid-s1265" xml:space="preserve">Nec enim vbique eadem poli altitudo ſupra Horizontem reperitur. </s>
            <s xml:id="echoid-s1266" xml:space="preserve">Vnde ſi prius in Ana-
              <lb/>
              <note position="left" xlink:label="note-0037-06" xlink:href="note-0037-06a" xml:space="preserve">20</note>
            lemmate deſcribantur paralleli per ſigna Zodiaci ducti, tanquam immutabiles in quocunque climate,
              <lb/>
              <note position="right" xlink:label="note-0037-07" xlink:href="note-0037-07a" xml:space="preserve">Initium deſcri-
                <lb/>
              ptienis Analẽ-
                <lb/>
              matis à paralle
                <lb/>
              lis per ſigna Zo
                <lb/>
              diaci tranſeun-
                <lb/>
              tibus quomodo
                <lb/>
              fiat.</note>
            (ducendo nimirum primum pro diametro Aequatoris rectam H I, deinde maximas Solis declinationes
              <lb/>
            ſupputando H M, H N, &</s>
            <s xml:id="echoid-s1267" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s1268" xml:space="preserve">abſoluemus reliquas eius partes pro data altitudine poli, hac ratione.
              <lb/>
            </s>
            <s xml:id="echoid-s1269" xml:space="preserve">Per centrum E, ducatur ad diametrum Acquatoris H I, perpendicularis F G, pro axe mundi. </s>
            <s xml:id="echoid-s1270" xml:space="preserve">Deinde
              <lb/>
            à punctis F, G, in diuerſas partes numerata altitudine poli, vſque ad D, B, ducatur diameter B D, pro
              <lb/>
            Horizonte, & </s>
            <s xml:id="echoid-s1271" xml:space="preserve">pro Verticali ducatur alia diameter A C, ſecans B D, ad angulos rectos. </s>
            <s xml:id="echoid-s1272" xml:space="preserve">Ex punctis
              <lb/>
            denique D, B, educantur Aequatoris diametro H I, parallelæ D K, B L, pro diametris parallelorum,
              <lb/>
            qui inter perpetuo apparentes, & </s>
            <s xml:id="echoid-s1273" xml:space="preserve">deliteſcentes maximi ſunt.</s>
            <s xml:id="echoid-s1274" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1275" xml:space="preserve">INCREDIBILE porrò eſt, quàm multiplicem, ac varium vſum in rebus Aſtronomicis habeat
              <lb/>
              <note position="right" xlink:label="note-0037-08" xlink:href="note-0037-08a" xml:space="preserve">Vtilitates Ana-
                <lb/>
              lẽmatis uariæ.</note>
            Analemma. </s>
            <s xml:id="echoid-s1276" xml:space="preserve">Ex eo enim non ſolum conſtructio Aſtrolabij, quod planiſphærium Ptolemæus appellat, Geo-
              <lb/>
              <note position="left" xlink:label="note-0037-09" xlink:href="note-0037-09a" xml:space="preserve">30</note>
            metricis demonſtrationibus perficitur, verum etiã omnia ferè, quæ ad phænomcna primi mobilis demon-
              <lb/>
            stranda pertinent, ſine magno labore eruuntur: </s>
            <s xml:id="echoid-s1277" xml:space="preserve">quod non eſt huius loci explicare. </s>
            <s xml:id="echoid-s1278" xml:space="preserve">In hoc etiã opere noſtro
              <lb/>
            Gnomonico non obſcurè eius excellentia, inſignis{q́ue} vtilitas eluceſcet, cum propemodũ omnes demonſtra-
              <lb/>
            tiones, quæ in horologiorum deſcriptionibus vſurpantur, ex Analemmate eliciantur, vt ex ſequentibus
              <lb/>
            fiet perſpicuum, maximè cum de Analemmate Ptolemæi, ex quo miraiucundit ate horologia deſcribun-
              <lb/>
            tur, agemus. </s>
            <s xml:id="echoid-s1279" xml:space="preserve">Nunc contentus ero, ſi quàm facile ex Analemmate dierum magnitudines & </s>
            <s xml:id="echoid-s1280" xml:space="preserve">noctium;
              <lb/>
            </s>
            <s xml:id="echoid-s1281" xml:space="preserve">tempus ortus, & </s>
            <s xml:id="echoid-s1282" xml:space="preserve">occaſus Solis, quoad horas Italicas, & </s>
            <s xml:id="echoid-s1283" xml:space="preserve">Babylonicas, & </s>
            <s xml:id="echoid-s1284" xml:space="preserve">tempus Meridiei; </s>
            <s xml:id="echoid-s1285" xml:space="preserve">tempus itẽ
              <lb/>
            ortus & </s>
            <s xml:id="echoid-s1286" xml:space="preserve">occaſus ratione horarum aſtronomicarum, nec non latitudines ortiuæ, & </s>
            <s xml:id="echoid-s1287" xml:space="preserve">occiduæ omnium pun-
              <lb/>
            ctorum Eclipticæ quolibet anni tempore, & </s>
            <s xml:id="echoid-s1288" xml:space="preserve">ad quamcunque latitudinem loci cognoſcantur, breui-
              <lb/>
              <note position="right" xlink:label="note-0037-10" xlink:href="note-0037-10a" xml:space="preserve">Inuentio arcus
                <lb/>
              diurni, noctur-
                <lb/>
              n@q́; ex Analẽ
                <lb/>
              mate, & horæ
                <lb/>
              ortus occaſusq;
                <lb/>
              Solis.</note>
            ter declarem.</s>
            <s xml:id="echoid-s1289" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p style="it">
            <s xml:id="echoid-s1290" xml:space="preserve">SIT ergo propoſitum hæc omnia perdiſcere, cum ſol parallelum ♋ vel ♑ percurrit motu pri-
              <lb/>
            mi mobilis. </s>
            <s xml:id="echoid-s1291" xml:space="preserve">Circa diametrum paralleli ♋, M θ, vel ♑, N ρ, ex centro b, (cum enim axis F G,
              <lb/>
            ſecet omnes parallelos ad angulos rectos, quòd & </s>
            <s xml:id="echoid-s1292" xml:space="preserve">Aequatoris diametrum, cui æquidiſtant, ad angulos
              <lb/>
              <note position="right" xlink:label="note-0037-12" xlink:href="note-0037-12a" xml:space="preserve">29. primi.</note>
            rectos ſecet, ac proinde & </s>
            <s xml:id="echoid-s1293" xml:space="preserve">bifariam, erit b, centrum circuli circa M θ, deſcribendi) ſeorſum circulus de-
              <lb/>
              <note position="right" xlink:label="note-0037-13" xlink:href="note-0037-13a" xml:space="preserve">3. tertij.</note>
            ſcribatur M d θ e, ſumpta{q́ue} recta M a, ipſi M a, in Analemmate æquali, ducatur per a, ad M θ, perpen-
              <lb/>
            dicularis d e, quæ communis ſectio erit Horizontis, & </s>
            <s xml:id="echoid-s1294" xml:space="preserve">propoſiti par alleli. </s>
            <s xml:id="echoid-s1295" xml:space="preserve">Quoniam enim tam Horizon,
              <lb/>
            quàm parallelus ♋ ad Meridianum rectus eſt, erit ad eundem communis eorum ſectio quoque recta,
              <lb/>
              <note position="right" xlink:label="note-0037-14" xlink:href="note-0037-14a" xml:space="preserve">19. vndec.</note>
            ac proinde ex defin. </s>
            <s xml:id="echoid-s1296" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1297" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1298" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1299" xml:space="preserve">Euclidis, ad rectam M θ, in Analemmatis Meridiano exiſtentem perpen-
              <lb/>
            dicularis in puncto a, vbi ſe mutuo ſecant in Meridiano Horizon, & </s>
            <s xml:id="echoid-s1300" xml:space="preserve">parallelus. </s>
            <s xml:id="echoid-s1301" xml:space="preserve">Quare recta d e, quæ in
              <lb/>
            circulo M d θ e, per a, ad M θ, ducta eſt perpendicularis, communis ſectio erit Horizontis, & </s>
            <s xml:id="echoid-s1302" xml:space="preserve">paralleli
              <lb/>
              <note position="left" xlink:label="note-0037-15" xlink:href="note-0037-15a" xml:space="preserve">50</note>
            ♋; </s>
            <s xml:id="echoid-s1303" xml:space="preserve">adeò vt, ſi intelligatur circulus M d θ e, circa diametrum M θ, in Analemmate circumuerti, do-
              <lb/>
            nec rectus ſit ad planum Meridiani, atque idcirco & </s>
            <s xml:id="echoid-s1304" xml:space="preserve">recta d e, huius circuli ſeorſum deſcripti ad
              <lb/>
            idem perpendicularis, Horizon ad idem planum Meridiani exiſtens rectus tranſeat per puncta d, e, ac
              <lb/>
            proinde per rectam d e. </s>
            <s xml:id="echoid-s1305" xml:space="preserve">Hanc autem rationem repetemus in propoſ. </s>
            <s xml:id="echoid-s1306" xml:space="preserve">33. </s>
            <s xml:id="echoid-s1307" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s1308" xml:space="preserve">vbi fortaſſis planior
              <lb/>
            fiet, cum ibi parallelus Solis in ipſo Analemmate circa propriam diametrum deſcriptus ſit. </s>
            <s xml:id="echoid-s1309" xml:space="preserve">Itaque arcus
              <lb/>
            d M e, erit arcus diurnus ♋, nempe qui ſupra terram extat, & </s>
            <s xml:id="echoid-s1310" xml:space="preserve">d θ c, nocturnus. </s>
            <s xml:id="echoid-s1311" xml:space="preserve">Vel ille erit arcus
              <lb/>
            nocturnus ♑, & </s>
            <s xml:id="echoid-s1312" xml:space="preserve">hic diurnus. </s>
            <s xml:id="echoid-s1313" xml:space="preserve">Vnde ſi totus circulus M d θ e, ſecetur in horas 24. </s>
            <s xml:id="echoid-s1314" xml:space="preserve">æquales, initio facto
              <lb/>
            a puncto d, vele, (Nos ab e, incepimus, quod nunc refert punctum ortus in Horizonte pro horis Babylo-
              <lb/>
            nicis, nunc vero punctum occaſus pro horis Italicis) confeſtim apparebit, quot horas comprehendat tam
              <lb/>
            arcus d M e, quàm d θ e. </s>
            <s xml:id="echoid-s1315" xml:space="preserve">Ita vides arcum diurnum ♋ d M e, complecti horas quindecim, & </s>
            <s xml:id="echoid-s1316" xml:space="preserve">paulo
              <lb/>
            amplius, arcum verò nocturnum d θ e, non omnino horas 9. </s>
            <s xml:id="echoid-s1317" xml:space="preserve">ſed paulo minus. </s>
            <s xml:id="echoid-s1318" xml:space="preserve">Sic etiam intelligis, </s>
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