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">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div35" type="section" level="1" n="23">
          <p>
            <s xml:id="echoid-s1597" xml:space="preserve">
              <pb o="14" file="0030" n="30" rhead="De circulis Sphæræ."/>
            cos, qua parte ſupra horizontem exiſtunt à meridiano in æqualia ſecari: </s>
            <s xml:id="echoid-s1598" xml:space="preserve">& </s>
            <s xml:id="echoid-s1599" xml:space="preserve">ſimiliter infra horizontem. </s>
            <s xml:id="echoid-s1600" xml:space="preserve">ſune
              <lb/>
            autem hi tres circuli, tres Solis circulationes (vt poſtea explicabimus) ſiue tres diurnæ conuerſiones, & </s>
            <s xml:id="echoid-s1601" xml:space="preserve">ſi-
              <lb/>
            cuti eas meridianus diuidit, ſic etiam cæteras omnes, quas toto anno Sol ſingulis diebus peragit, & </s>
            <s xml:id="echoid-s1602" xml:space="preserve">quarum
              <lb/>
            circuli in Sphæra non ponuntur, idem meridianus partitur.</s>
            <s xml:id="echoid-s1603" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1604" xml:space="preserve">A meridiano circulò initium diei naturalis ſumunt Aſtronomi; </s>
            <s xml:id="echoid-s1605" xml:space="preserve">cum autem dies naturalis ſit integra So-
              <lb/>
            lis circa mundum reuolutio, dies Aſtronomicus Sole meridianum occupante incipiet, atq; </s>
            <s xml:id="echoid-s1606" xml:space="preserve">ad eundem Sole
              <lb/>
            iterum redeunte deſinet. </s>
            <s xml:id="echoid-s1607" xml:space="preserve">A meridie autem potius, quam ab horizonte diem inchoare maluerunt Aſtrono-
              <lb/>
            mi, quoniam in omni regione, atq; </s>
            <s xml:id="echoid-s1608" xml:space="preserve">habitatione Sol ſemper eodem modo ad meridianum ſe habet, ad hori-
              <lb/>
            zontem verò varietates ſubit; </s>
            <s xml:id="echoid-s1609" xml:space="preserve">quare dies ad meridiem relatus vbique vniformis, ac ſtabilis eſt, ad horizon-
              <lb/>
            tem verò relatus variationibus obnoxius eſt, quæ Aſtronomis negotium faceſſunt. </s>
            <s xml:id="echoid-s1610" xml:space="preserve">Quapropter ſapienter
              <lb/>
            faciunt pleræque nationes, Hiſpani, Galli, Belgæ, Germani, Poloni, qui hoc diei genere communiter
              <lb/>
            vtuntur.</s>
            <s xml:id="echoid-s1611" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1612" xml:space="preserve">5 Metitur maxima Aſtrorum altitudines ſupra horizontem; </s>
            <s xml:id="echoid-s1613" xml:space="preserve">cum enim eum Aſtra attingunt, tunc ma-
              <lb/>
            ximè ab horizote attoluntur, tantaq; </s>
            <s xml:id="echoid-s1614" xml:space="preserve">eſt eorum meridiana altitudo, quæ eſt omnium maxima, quantus eſt
              <lb/>
            meridiani arcus ab horizonte vſq; </s>
            <s xml:id="echoid-s1615" xml:space="preserve">ad Aſtrum interiectus. </s>
            <s xml:id="echoid-s1616" xml:space="preserve">Hanc portò, tum Solis, tum Aſtrorum meridianã
              <lb/>
            eleuationem reperies, primo per quadrantem Aſtronomicum propoſ. </s>
            <s xml:id="echoid-s1617" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1618" xml:space="preserve">apparatus hoc modo.</s>
            <s xml:id="echoid-s1619" xml:space="preserve"/>
          </p>
          <figure number="18">
            <image file="0030-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0030-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s1620" xml:space="preserve">Illud Aſtronomicè conſtitue, ideſt, in plano quopiam ho-
              <lb/>
            rizontalis, vt latus A B. </s>
            <s xml:id="echoid-s1621" xml:space="preserve">Quadrantis ſit horizonti paralel-
              <lb/>
            lum, & </s>
            <s xml:id="echoid-s1622" xml:space="preserve">ſimul ſupra lineam mer@dianam inibi accuratè du-
              <lb/>
            ctam; </s>
            <s xml:id="echoid-s1623" xml:space="preserve">latus verò A D. </s>
            <s xml:id="echoid-s1624" xml:space="preserve">ſit perpendiculariter erectum, cu-
              <lb/>
            ius gratia perpendiculum D I. </s>
            <s xml:id="echoid-s1625" xml:space="preserve">debet propriè linea æqui-
              <lb/>
            diſtare, ac liberè iuxta latus A D. </s>
            <s xml:id="echoid-s1626" xml:space="preserve">radens deſcendere
              <unsure/>
            ; </s>
            <s xml:id="echoid-s1627" xml:space="preserve">La-
              <lb/>
            tus autem C B. </s>
            <s xml:id="echoid-s1628" xml:space="preserve">meridiem verſus aſpiciat. </s>
            <s xml:id="echoid-s1629" xml:space="preserve">Splendente iam
              <lb/>
            in meridie Sole, Dioptra quadranti adhærens ſuſque de-
              <lb/>
            que tollatur, donec Solis radius per vtrumq; </s>
            <s xml:id="echoid-s1630" xml:space="preserve">pinnularum
              <lb/>
            foramen æquè illabatur: </s>
            <s xml:id="echoid-s1631" xml:space="preserve">in quo Dioptræ ſitu, latus ipſius
              <lb/>
            C E. </s>
            <s xml:id="echoid-s1632" xml:space="preserve">indicabit in quadrante gradus altitudinis meridiane,
              <lb/>
            qui eſſent, v.</s>
            <s xml:id="echoid-s1633" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1634" xml:space="preserve">in arcu D E. </s>
            <s xml:id="echoid-s1635" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1636" xml:space="preserve">36. </s>
            <s xml:id="echoid-s1637" xml:space="preserve">tanta enim eſt eleuatio
              <lb/>
            ſupra horizontem, quantus eſt arcus quadrantis à puncto
              <lb/>
            D. </s>
            <s xml:id="echoid-s1638" xml:space="preserve">vſque ad Dioptram numeratus.</s>
            <s xml:id="echoid-s1639" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1640" xml:space="preserve">Quod ſi ſydus minus collucens obijciatur, tunc vice radij ip-
              <lb/>
            ſius, vtemur radio viſuali, ideſt, per vtrumque rimulam
              <lb/>
            in pinnularem ſumitatibus exciſam, in aſtrum collimabi-
              <lb/>
            mus, atq; </s>
            <s xml:id="echoid-s1641" xml:space="preserve">interim latus E C. </s>
            <s xml:id="echoid-s1642" xml:space="preserve">Dioptræ in quadrante me-
              <lb/>
            ridianæ gradus, ac graduum partes indigitabit.</s>
            <s xml:id="echoid-s1643" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1644" xml:space="preserve">Alio præterea modo, & </s>
            <s xml:id="echoid-s1645" xml:space="preserve">quidẽ ſubtiliori idem hoc pacto obſeruabimus: </s>
            <s xml:id="echoid-s1646" xml:space="preserve">inuenta (vti ſuperius docuimus)
              <lb/>
            in plano quopiam horizontali, linea meridiana, erigatur ex ea ſtylus plano perpendicularis; </s>
            <s xml:id="echoid-s1647" xml:space="preserve">cum enim ip-
              <lb/>
            ſius vmbra lineam meridianam occupauerit, habebit Sol meridianam latitudinem; </s>
            <s xml:id="echoid-s1648" xml:space="preserve">notetur igitur tunc tem
              <lb/>
            poris extremum vmbræ in ipſa meridiana exiſtens. </s>
            <s xml:id="echoid-s1649" xml:space="preserve">atque in eodem plano a pede ſtyli ducatur linea perpen
              <lb/>
            dicularis meridianæ lineæ, ſitque ipſi ſtylo æqualis, tandem ab extremo vmbræ prænotato, ducatur linea
              <lb/>
            vſque ad extremum lineæ ſtylo æqualis: </s>
            <s xml:id="echoid-s1650" xml:space="preserve">v.</s>
            <s xml:id="echoid-s1651" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1652" xml:space="preserve">ſit in plano meridiana A B. </s>
            <s xml:id="echoid-s1653" xml:space="preserve">ſtylus B C. </s>
            <s xml:id="echoid-s1654" xml:space="preserve">recta B E. </s>
            <s xml:id="echoid-s1655" xml:space="preserve">ſtylo æqua-
              <lb/>
            lis ad angulos rectos ipſi meridianæ; </s>
            <s xml:id="echoid-s1656" xml:space="preserve">vmbra ſtyli pertineat ad A. </s>
            <s xml:id="echoid-s1657" xml:space="preserve">& </s>
            <s xml:id="echoid-s1658" xml:space="preserve">ab A. </s>
            <s xml:id="echoid-s1659" xml:space="preserve">extremo vmbræ ducta ſit, A D. </s>
            <s xml:id="echoid-s1660" xml:space="preserve">erit
              <lb/>
            angulus D A B. </s>
            <s xml:id="echoid-s1661" xml:space="preserve">altitudo Solis meridiana. </s>
            <s xml:id="echoid-s1662" xml:space="preserve">& </s>
            <s xml:id="echoid-s1663" xml:space="preserve">quoniam vti propoſ. </s>
            <s xml:id="echoid-s1664" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1665" xml:space="preserve">appar. </s>
            <s xml:id="echoid-s1666" xml:space="preserve">quantitas angulorum deſumi-
              <lb/>
            tur ex arcu illi ſubtento: </s>
            <s xml:id="echoid-s1667" xml:space="preserve">facto centro in A. </s>
            <s xml:id="echoid-s1668" xml:space="preserve">deſcribatur arcus F E. </s>
            <s xml:id="echoid-s1669" xml:space="preserve">atque quot gradus contineat, expendatur
              <lb/>
            per eandem propoſitionem, tot enim gradibus Solis meridiana altitudo conſtabit. </s>
            <s xml:id="echoid-s1670" xml:space="preserve">Ratio eſt, quia ſi cogi-
              <lb/>
            temus triangulum A B D. </s>
            <s xml:id="echoid-s1671" xml:space="preserve">ex plano in quo iacet aſiurgere manente latere A B. </s>
            <s xml:id="echoid-s1672" xml:space="preserve">fixo tanquam axe huius mo-
              <lb/>
            tus, ita vt latus D B. </s>
            <s xml:id="echoid-s1673" xml:space="preserve">congruat ſtylo B C. </s>
            <s xml:id="echoid-s1674" xml:space="preserve">tranſibit latus A D. </s>
            <s xml:id="echoid-s1675" xml:space="preserve">per ſtyli verticem, quia punctum D. </s>
            <s xml:id="echoid-s1676" xml:space="preserve">congruet
              <lb/>
            mucroni C. </s>
            <s xml:id="echoid-s1677" xml:space="preserve">ſtyli; </s>
            <s xml:id="echoid-s1678" xml:space="preserve">& </s>
            <s xml:id="echoid-s1679" xml:space="preserve">proinde linea A D. </s>
            <s xml:id="echoid-s1680" xml:space="preserve">ragio Solis per eundem verticem, & </s>
            <s xml:id="echoid-s1681" xml:space="preserve">in A. </s>
            <s xml:id="echoid-s1682" xml:space="preserve">tandentem congruet; </s>
            <s xml:id="echoid-s1683" xml:space="preserve">vn-
              <lb/>
            de manifeſtè Solis altitudinem ſupra horizontale planum indicabit igitur quanta eſt inclinatio lineæ A D.
              <lb/>
            </s>
            <s xml:id="echoid-s1684" xml:space="preserve">ſiue quantus eſt angulus ad A. </s>
            <s xml:id="echoid-s1685" xml:space="preserve">ſiue arcus F E. </s>
            <s xml:id="echoid-s1686" xml:space="preserve">tanta erit meridiana altitudo Solis: </s>
            <s xml:id="echoid-s1687" xml:space="preserve">nam in hac trianguli ele-
              <lb/>
            uatione angulus ad A. </s>
            <s xml:id="echoid-s1688" xml:space="preserve">nihil eſt variatus; </s>
            <s xml:id="echoid-s1689" xml:space="preserve">quare etiamſi triangulum non aſſurgat, nihi@ominus angulus ad A. </s>
            <s xml:id="echoid-s1690" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0030-02" xlink:href="fig-0030-02a" number="19">
                <image file="0030-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0030-02"/>
              </figure>
            ſiue arcus eius F E, quantitatem quæſitã pateſaciet. </s>
            <s xml:id="echoid-s1691" xml:space="preserve">poſſumus
              <lb/>
            autem expeditè prædictum arcum cognoſcere, hoc modo ac-
              <lb/>
            cipiatur circino linea A E. </s>
            <s xml:id="echoid-s1692" xml:space="preserve">inſtrumenti propoſ. </s>
            <s xml:id="echoid-s1693" xml:space="preserve">5. </s>
            <s xml:id="echoid-s1694" xml:space="preserve">appar. </s>
            <s xml:id="echoid-s1695" xml:space="preserve">& </s>
            <s xml:id="echoid-s1696" xml:space="preserve">ei
              <lb/>
            æqualis in latere A D. </s>
            <s xml:id="echoid-s1697" xml:space="preserve">huius triãguli ſumatur, quæ ſit v.</s>
            <s xml:id="echoid-s1698" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1699" xml:space="preserve">A F.
              <lb/>
            </s>
            <s xml:id="echoid-s1700" xml:space="preserve">deinde circino accipiatur arcus F E. </s>
            <s xml:id="echoid-s1701" xml:space="preserve">appliceturque arcui qua-
              <lb/>
            drantis inſtrumẽti, facto initio ab E. </s>
            <s xml:id="echoid-s1702" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s1703" xml:space="preserve">v.</s>
            <s xml:id="echoid-s1704" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1705" xml:space="preserve">arcus illi æqua-
              <lb/>
            lis E K. </s>
            <s xml:id="echoid-s1706" xml:space="preserve">qui gr. </s>
            <s xml:id="echoid-s1707" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1708" xml:space="preserve">continet: </s>
            <s xml:id="echoid-s1709" xml:space="preserve">altitudo igitur quæſita meridia-
              <lb/>
            na totidem gr. </s>
            <s xml:id="echoid-s1710" xml:space="preserve">erit: </s>
            <s xml:id="echoid-s1711" xml:space="preserve">ſicque in quadrante, aut etiam in ſemicir-
              <lb/>
            culo eiuſdẽ inſtrumenti, fi angulus eſſet obtuſus, ſemper abſq; </s>
            <s xml:id="echoid-s1712" xml:space="preserve">
              <lb/>
            nouæ diuiſionis labore, apparebit in grad. </s>
            <s xml:id="echoid-s1713" xml:space="preserve">& </s>
            <s xml:id="echoid-s1714" xml:space="preserve">minutis quanti-
              <lb/>
            tas cuiuſuis arcus, ſeu anguli. </s>
            <s xml:id="echoid-s1715" xml:space="preserve">Hiſce duobus prædictis modis,
              <lb/>
            ideſt, per quadrantem, & </s>
            <s xml:id="echoid-s1716" xml:space="preserve">per vmbram ſtyli in plano horizontali, cæteræ quoq; </s>
            <s xml:id="echoid-s1717" xml:space="preserve">altitudines non </s>
          </p>
        </div>
      </text>
    </echo>
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