Blancanus, Josephus, Sphaera mvndi, sev cosmographia demonstratiua , ac facile methodo tradita : in qua totius Mundi fabrica, vna cum nouis, Tychonis, Kepleri, Galilaei, aliorumq' ; Astronomorum adinuentis continentur ; Accessere I. Breuis introductio ad geographiam. II. Apparatus ad mathematicarum studium. III. Echometria, idest Geometrica tractatio de Echo. IV. Nouum instrumentum ad Horologia

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    <echo version="1.0RC">
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        <div xml:id="echoid-div33" type="section" level="1" n="22">
          <pb o="10" file="0026" n="26" rhead="De Circulis Sphæræ."/>
          <p>
            <s xml:id="echoid-s1232" xml:space="preserve">Sed vt eius in mundo ſitum, ac poſitionem rectè inueniamus, in quouis terræ loco, vti ſolemus. </s>
            <s xml:id="echoid-s1233" xml:space="preserve">Libella,
              <lb/>
            inſtrumento Architectis familiari, vulgo Liuello, quo ipſi pauimenta, & </s>
            <s xml:id="echoid-s1234" xml:space="preserve">plura alia plana in modum Hori-
              <lb/>
            zontis, ſeu Horizonti æquidiſtantia conſtituunt: </s>
            <s xml:id="echoid-s1235" xml:space="preserve">quæ plana dicũtur Horizontalia. </s>
            <s xml:id="echoid-s1236" xml:space="preserve">eſt autem horum plano-
              <lb/>
            rum ea poſitio, vt ad nullam partem ſint inclinata, aut eleuata, verum æquè proſtrata ſint; </s>
            <s xml:id="echoid-s1237" xml:space="preserve">qualis apparet eſ-
              <lb/>
            ſe aquæ quieſcentis ſuperficies. </s>
            <s xml:id="echoid-s1238" xml:space="preserve">hæc enim ad omnes partes æqualiter iacet. </s>
            <s xml:id="echoid-s1239" xml:space="preserve">Libella autem inſtrumentum eſt
              <lb/>
              <figure xlink:label="fig-0026-01" xlink:href="fig-0026-01a" number="14">
                <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01"/>
              </figure>
            talis conditionis, vt in eo vna linea ſit alteri perpendicularis, vt in figura
              <lb/>
            linea A D. </s>
            <s xml:id="echoid-s1240" xml:space="preserve">eſt perpendicularis lineæ B C. </s>
            <s xml:id="echoid-s1241" xml:space="preserve">eamque in D. </s>
            <s xml:id="echoid-s1242" xml:space="preserve">bifariam ſecet. </s>
            <s xml:id="echoid-s1243" xml:space="preserve">a
              <lb/>
            ſummo autem lineæ A D. </s>
            <s xml:id="echoid-s1244" xml:space="preserve">ideſt à puncto A. </s>
            <s xml:id="echoid-s1245" xml:space="preserve">deſcendat liberè perpendicu-
              <lb/>
            lum A E. </s>
            <s xml:id="echoid-s1246" xml:space="preserve">vſus eius talis eſt; </s>
            <s xml:id="echoid-s1247" xml:space="preserve">cum planum aliquod conſtituendum eſt Hori-
              <lb/>
            zontale, aut ad L@bellam, id prius per ſenſus æſtimationem iuxta Horizon
              <lb/>
            tem ſternunt; </s>
            <s xml:id="echoid-s1248" xml:space="preserve">ei deinde Libellam ſic ſuperponunt, vt linea B C. </s>
            <s xml:id="echoid-s1249" xml:space="preserve">quæ baſis
              <lb/>
            eſt inſtrumenti, plano illi tota applicetur, inſtrumẽtum vero ſic ſuper eum
              <lb/>
            erigatur, vt perpendiculum A E. </s>
            <s xml:id="echoid-s1250" xml:space="preserve">liberè cadens, & </s>
            <s xml:id="echoid-s1251" xml:space="preserve">ſuperficiem inſtrumen-
              <lb/>
            ti radens, lineæ A D. </s>
            <s xml:id="echoid-s1252" xml:space="preserve">ad vnguem reſpondeat quod vt melius efficiat, ex-
              <lb/>
            cauari ſolet feneſtella è regione perpendiculi E. </s>
            <s xml:id="echoid-s1253" xml:space="preserve">intra quam in hac opera-
              <lb/>
            tione, ipſum perpendiculum excipitur, ne inſtrumento occurrens a libera
              <lb/>
            demiſſione impediatur. </s>
            <s xml:id="echoid-s1254" xml:space="preserve">ſic igitur perpendiculo ſtante, erit neceſſario ba-
              <lb/>
            fis B C. </s>
            <s xml:id="echoid-s1255" xml:space="preserve">in ſitu Horizontis, eum enim cum perpendiculo A E. </s>
            <s xml:id="echoid-s1256" xml:space="preserve">faciat angu-
              <lb/>
            los hinc indè æquales, hoc eſt ſit æqualiter inclinata, quæ eſt poſitio Horizontalis, erit & </s>
            <s xml:id="echoid-s1257" xml:space="preserve">ipſa in ſitu Hori-
              <lb/>
            zontis fita, & </s>
            <s xml:id="echoid-s1258" xml:space="preserve">conſequenter planum cui adhęret ſecundum illam dimenſionem erit Horizontaie. </s>
            <s xml:id="echoid-s1259" xml:space="preserve">yt autem
              <lb/>
            conſtet ipſum eſſe Horizontale ſecundum omnes partes, oportet vt libella eidem plano ſuperpoſita, & </s>
            <s xml:id="echoid-s1260" xml:space="preserve">cir-
              <lb/>
            cumuoluta circa lineam perpendicularem, tanquam axem, ſemper perpendiculũ ſuæ lineæ, exactè reſpon-
              <lb/>
            deat, ſic enim planum illud ſecundum omnes ſui partes, ac dimenſionem ad libellam ſitum erit, & </s>
            <s xml:id="echoid-s1261" xml:space="preserve">conſe-
              <lb/>
            quenter Horizontale dici merebitur. </s>
            <s xml:id="echoid-s1262" xml:space="preserve">talis autem plani alicuius conſtitutio, cum ad multa alia ſit vtilis, tum
              <lb/>
            etiam vt rectè Horizontis concipiamus. </s>
            <s xml:id="echoid-s1263" xml:space="preserve">Reliquum eſt, vt nonnulla, etiam de Horizontis habitatore dica-
              <lb/>
            mus, atque in primis notandum quemlibet Horizontem propriè loquendo, vnicum habere tantum habita-
              <lb/>
            torem, cum enim vti diximus, quot ſunt loca, tot etiam Horizontes, quotque loca, tot etiam habitatores
              <lb/>
            ſint, ſequitur ſingulos habitatores proprios etiam Horizontem nanciſci. </s>
            <s xml:id="echoid-s1264" xml:space="preserve">Quilibet porrò habitator, cum-
              <lb/>
            ſtat, ſuo Horizonti perpendiculariter in centro eius inſiſtit, ideſt, linea ducta ſecundum hominis longitu-
              <lb/>
            dinem altitudinemuè Horizonti perpendiculariter eſt, quę linea ſi producatur vtrinque, trãſit per Zenith,
              <lb/>
            centrum Horizontis, centrum terræ, ac Nadir; </s>
            <s xml:id="echoid-s1265" xml:space="preserve">qualis in figura eſt linea C G F. </s>
            <s xml:id="echoid-s1266" xml:space="preserve">ad habitatorem G. </s>
            <s xml:id="echoid-s1267" xml:space="preserve">reliqua
              <lb/>
            pariter corpora, quæ in altum eriguntur, vt turres, columnæ, parietes, debent eſſe in hac linea, quæ ne ca-
              <lb/>
            dant, debet etiam per eorum grauitatis centrum eadem linea, & </s>
            <s xml:id="echoid-s1268" xml:space="preserve">præterea per baſim eorum tranſire; </s>
            <s xml:id="echoid-s1269" xml:space="preserve">aliter
              <lb/>
            erecta ſtare nequeunt, ſed concidunt & </s>
            <s xml:id="echoid-s1270" xml:space="preserve">proſternuntur. </s>
            <s xml:id="echoid-s1271" xml:space="preserve">hæc linea, Directionis linea dicitur. </s>
            <s xml:id="echoid-s1272" xml:space="preserve">eadem ratione
              <lb/>
            homines minime ſtare queunt, niſi hæc linea per centrum grauitatis, ac ſimul per baſim eorum, hoc eſt per
              <lb/>
            interuallum intra p@antas interiectum, quæ eſt eorum baſis, deſcendat. </s>
            <s xml:id="echoid-s1273" xml:space="preserve">prædicta omnia in figura, vbi ſunt
              <lb/>
            varij habitatore cum ſuis Horizontibus, ac lineis Directionis contemplari poſſumus.</s>
            <s xml:id="echoid-s1274" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1275" xml:space="preserve">Officia autem, ſiue vſus Horizontis ſunt hi; </s>
            <s xml:id="echoid-s1276" xml:space="preserve">Primo totam mundi Sphæram diuidit vt dictum eſt, in duo
              <lb/>
            hemiſpæria; </s>
            <s xml:id="echoid-s1277" xml:space="preserve">in ſuperum ſcilicet, & </s>
            <s xml:id="echoid-s1278" xml:space="preserve">inferum, ſeu in cõſpicuum a ſuo habitatore, & </s>
            <s xml:id="echoid-s1279" xml:space="preserve">in eidem occultum.</s>
            <s xml:id="echoid-s1280" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1281" xml:space="preserve">2 Concurrit ad Sphæram rectam, obliquam, ac paralellam conſtituendam vti ſupra expoſuimus.</s>
            <s xml:id="echoid-s1282" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1283" xml:space="preserve">3 Determinat Ortum, & </s>
            <s xml:id="echoid-s1284" xml:space="preserve">Occaſum ſyderum; </s>
            <s xml:id="echoid-s1285" xml:space="preserve">cum enim motu primi mobilis, ſeu motu diurno, Aſtra ab
              <lb/>
            Oriente, in Occidentem circumferantur, oriri tunc dicuntur quando ſupra Horizontem emergunt; </s>
            <s xml:id="echoid-s1286" xml:space="preserve">occi-
              <lb/>
            dere autem quando infra eumdem demergũtur. </s>
            <s xml:id="echoid-s1287" xml:space="preserve">Duo verò puncta, quæ in limbo Horizontis notantur ho-
              <lb/>
            minibus, Ortus, & </s>
            <s xml:id="echoid-s1288" xml:space="preserve">Occaſus, ſuntque apud ſectiones communes Horizontis, & </s>
            <s xml:id="echoid-s1289" xml:space="preserve">Æquatoris, dicuntur Ortus,
              <lb/>
            & </s>
            <s xml:id="echoid-s1290" xml:space="preserve">Occaſus veri, ſeu Æquinoctialis, eo quod ortiuarum, & </s>
            <s xml:id="echoid-s1291" xml:space="preserve">occiduarum latitudinem medium teneant, ſintq;
              <lb/>
            </s>
            <s xml:id="echoid-s1292" xml:space="preserve">prope Æquatore; </s>
            <s xml:id="echoid-s1293" xml:space="preserve">vt mox exponam.</s>
            <s xml:id="echoid-s1294" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1295" xml:space="preserve">4 In Horizonte ſumuntur, vel menſurantur latitudines ortiuæ, & </s>
            <s xml:id="echoid-s1296" xml:space="preserve">occiduæ; </s>
            <s xml:id="echoid-s1297" xml:space="preserve">eſt enim amplitudo, ſeu la-
              <lb/>
            titudo ortiua, occiduauè, arcus Horizontis inter punctum Ortus, & </s>
            <s xml:id="echoid-s1298" xml:space="preserve">Occaſus Æquinoctialis, & </s>
            <s xml:id="echoid-s1299" xml:space="preserve">punctum il-
              <lb/>
            lud in Horizonte, vbi ſydus oritur occidituè: </s>
            <s xml:id="echoid-s1300" xml:space="preserve">eſt autem amplitudo ortiua, æqualis amplitudini occiduæ,
              <lb/>
            v.</s>
            <s xml:id="echoid-s1301" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1302" xml:space="preserve">latitudo ortiua Solis, quando eſt in principio Cancri, tropicumque eius percurrit, eſt in el
              <unsure/>
            euatione po-
              <lb/>
            li gr. </s>
            <s xml:id="echoid-s1303" xml:space="preserve">44. </s>
            <s xml:id="echoid-s1304" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s1305" xml:space="preserve">qualis eſt Parmæ graduum fere 37. </s>
            <s xml:id="echoid-s1306" xml:space="preserve">totidemque graduũ erit latitudo occidua tunc temporis: </s>
            <s xml:id="echoid-s1307" xml:space="preserve">vt ex
              <lb/>
            Sphęra materiali, eleuato polo Arctico gr. </s>
            <s xml:id="echoid-s1308" xml:space="preserve">44. </s>
            <s xml:id="echoid-s1309" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s1310" xml:space="preserve">ſupra Horizontem videre eſt. </s>
            <s xml:id="echoid-s1311" xml:space="preserve">ſi ad quodlibet tempus vis
              <lb/>
            ſcire latitud nem ortiuam, occiduamue Solis, pone gradum Eclypticæ, quem Sol tunc percurrit in Hori-
              <lb/>
            zonte, eleuato polo Sphæræ, vt conuenit tuæ habitationi; </s>
            <s xml:id="echoid-s1312" xml:space="preserve">nam arcus Horizontis inter Æquatorem, & </s>
            <s xml:id="echoid-s1313" xml:space="preserve">gra-
              <lb/>
            dum illum, erit quæſita latitudo. </s>
            <s xml:id="echoid-s1314" xml:space="preserve">porrò infra docebo inuenire gradum Solis, & </s>
            <s xml:id="echoid-s1315" xml:space="preserve">poli altitudinem.</s>
            <s xml:id="echoid-s1316" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1317" xml:space="preserve">5 Sequitur ex prædictis de Ortu, & </s>
            <s xml:id="echoid-s1318" xml:space="preserve">Occaſu, Horizontem etiam determinare quantitatem diei, ac no-
              <lb/>
            ctis artificialis; </s>
            <s xml:id="echoid-s1319" xml:space="preserve">eſt enim dies artificialis mora Solis ſupra Horizontem, ideſt tempus ab Ortu ad Occaſum.
              <lb/>
            </s>
            <s xml:id="echoid-s1320" xml:space="preserve">Nox autem artificialis eſt mora Solis infra Horizontem, ideſt tempus ab Occaſu ad Ortum. </s>
            <s xml:id="echoid-s1321" xml:space="preserve">Dicitur autem
              <lb/>
            dies artiſicialis, quod art@bus exercendis inſeruata qua ratione, nonnulii etiam appellant diem artificialem
              <lb/>
            totum illud tempus, quod ab initio crepuſculi matutini, vſque ad finem veſpertini intercipitur: </s>
            <s xml:id="echoid-s1322" xml:space="preserve">totum enim
              <lb/>
            illud temporis ſpacium artificibus, ac operibus aptum eſt. </s>
            <s xml:id="echoid-s1323" xml:space="preserve">Hinc ſequitur</s>
          </p>
          <p>
            <s xml:id="echoid-s1324" xml:space="preserve">6 Ipſum eſſe terminum diei, ac noctis, vt palam eſt ex dictis: </s>
            <s xml:id="echoid-s1325" xml:space="preserve">vnde nonnulli populi diem naturalem ab
              <lb/>
            Horizonte incipiunt, vt Itali, qui ab Occaſu Solis diem naturalem auſpicantur: </s>
            <s xml:id="echoid-s1326" xml:space="preserve">alij vero ab Ortu, vt </s>
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