Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

Table of Notes

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        <div xml:id="echoid-div53" type="section" level="1" n="31">
          <p>
            <s xml:id="echoid-s1847" xml:space="preserve">
              <pb file="0041" n="41" rhead="TABVLARVM SINVVM."/>
            ♈eſt 35. </s>
            <s xml:id="echoid-s1848" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1849" xml:space="preserve">32. </s>
            <s xml:id="echoid-s1850" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1851" xml:space="preserve">iam ſi cupiam & </s>
            <s xml:id="echoid-s1852" xml:space="preserve">arcum eclypticæ ſibi reſpondentem inuenire in
              <lb/>
            ſphæra o bliqua, at adeo eleuato ibi polo ad 48. </s>
            <s xml:id="echoid-s1853" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1854" xml:space="preserve">ubi talis etiam intronizatio facta
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s1855" xml:space="preserve">Principio quæro per 8. </s>
            <s xml:id="echoid-s1856" xml:space="preserve">propoſitionem arcum eclypticæ in ſphæra recta cum arcu æ-
              <lb/>
            quatoris aſcendentem, in hunc modum: </s>
            <s xml:id="echoid-s1857" xml:space="preserve">Duco ſinum complementi huius aſcenſionis re-
              <lb/>
            ctæ, ſcilicet 35. </s>
            <s xml:id="echoid-s1858" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1859" xml:space="preserve">32. </s>
            <s xml:id="echoid-s1860" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1861" xml:space="preserve">qui gradus ſunt 54. </s>
            <s xml:id="echoid-s1862" xml:space="preserve">& </s>
            <s xml:id="echoid-s1863" xml:space="preserve">minut. </s>
            <s xml:id="echoid-s1864" xml:space="preserve">28. </s>
            <s xml:id="echoid-s1865" xml:space="preserve">ſinus autem 81377. </s>
            <s xml:id="echoid-s1866" xml:space="preserve">in ſinũ
              <lb/>
              <note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">
                <emph style="it">Illud deprc</emph>
                <lb/>
                <emph style="it">henditur la</emph>
                <lb/>
                <emph style="it">terali in-</emph>
                <lb/>
                <emph style="it">greſſu.</emph>
              </note>
            maximæ declinationis Solis 39874. </s>
            <s xml:id="echoid-s1867" xml:space="preserve">diuido, deinde quotientem in totum ſinum, qui erit
              <lb/>
            32448. </s>
            <s xml:id="echoid-s1868" xml:space="preserve">arcus illius 18. </s>
            <s xml:id="echoid-s1869" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1870" xml:space="preserve">56. </s>
            <s xml:id="echoid-s1871" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1872" xml:space="preserve">hoc ſanè ſubtraho à 90. </s>
            <s xml:id="echoid-s1873" xml:space="preserve">& </s>
            <s xml:id="echoid-s1874" xml:space="preserve">remanent adhuc 71. </s>
            <s xml:id="echoid-s1875" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1876" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s1877" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1878" xml:space="preserve">ſinum iſtius ſi mihi proponam ſimul cum ſinu aſcenſionis rectæ, ſcilicet 58117. </s>
            <s xml:id="echoid-s1879" xml:space="preserve">mino
              <lb/>
            rem quo ducam in ſinum totũ, productum uero diuidam in maiorem, proueniet inde
              <lb/>
              <note position="right" xlink:label="note-0041-02" xlink:href="note-0041-02a" xml:space="preserve">
                <emph style="it">Areali in-</emph>
                <lb/>
                <emph style="it">greſſu idẽ</emph>
                <lb/>
                <emph style="it">cõſequeris.</emph>
              </note>
            61441. </s>
            <s xml:id="echoid-s1880" xml:space="preserve">arcus eius erit 37. </s>
            <s xml:id="echoid-s1881" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1882" xml:space="preserve">55. </s>
            <s xml:id="echoid-s1883" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1884" xml:space="preserve">qui etiam arcus eſt eclypticæ à
              <unsure/>
            principio ♈, reſpon
              <lb/>
            dens arcui æquatoris in ſphæra recta in aſcenſu. </s>
            <s xml:id="echoid-s1885" xml:space="preserve">Ad hæc amplius inquiro per 5. </s>
            <s xml:id="echoid-s1886" xml:space="preserve">pronun-
              <lb/>
            ciatum iſtius arcus eclypticæ declinationem ab æquatore, & </s>
            <s xml:id="echoid-s1887" xml:space="preserve">quia arcus ille 37. </s>
            <s xml:id="echoid-s1888" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1889" xml:space="preserve">55.
              <lb/>
            </s>
            <s xml:id="echoid-s1890" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1891" xml:space="preserve">directe pertingit ad 7. </s>
            <s xml:id="echoid-s1892" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1893" xml:space="preserve">55. </s>
            <s xml:id="echoid-s1894" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1895" xml:space="preserve">♉. </s>
            <s xml:id="echoid-s1896" xml:space="preserve">quæro iam adhuc ipſum gradum & </s>
            <s xml:id="echoid-s1897" xml:space="preserve">minutũ ♉
              <lb/>
            declinationem hoc modo. </s>
            <s xml:id="echoid-s1898" xml:space="preserve">Duco ſinum arcus 37. </s>
            <s xml:id="echoid-s1899" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1900" xml:space="preserve">55. </s>
            <s xml:id="echoid-s1901" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1902" xml:space="preserve">in ſinũ maximæ declinatiõis
              <lb/>
            Solis, ſcilicet 39874. </s>
            <s xml:id="echoid-s1903" xml:space="preserve">productũ diuido in ſinum totum, & </s>
            <s xml:id="echoid-s1904" xml:space="preserve">prodibit 24499. </s>
            <s xml:id="echoid-s1905" xml:space="preserve">arcus illius eſt
              <lb/>
              <note position="right" xlink:label="note-0041-03" xlink:href="note-0041-03a" xml:space="preserve">
                <emph style="it">Lateralis.</emph>
              </note>
            14. </s>
            <s xml:id="echoid-s1906" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1907" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1908" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1909" xml:space="preserve">declinatio nimi℞ arcus eclypticæ quæſita. </s>
            <s xml:id="echoid-s1910" xml:space="preserve">Poſtea adhuc ſinũ arcus aſcenſi
              <lb/>
            onis rectæ æquatoris 58117. </s>
            <s xml:id="echoid-s1911" xml:space="preserve">duxi in ſinũ totũ, productũ diuiſi per ſinũ arcus eclypticæ ei
              <lb/>
              <note position="right" xlink:label="note-0041-04" xlink:href="note-0041-04a" xml:space="preserve">
                <emph style="it">Arealis.</emph>
              </note>
            in aſcenſione recta reſpondentẽ, & </s>
            <s xml:id="echoid-s1912" xml:space="preserve">prouenit in quotiente 94589. </s>
            <s xml:id="echoid-s1913" xml:space="preserve">arcus ipſius eſt 71. </s>
            <s xml:id="echoid-s1914" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s1915" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1916" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1917" xml:space="preserve">qui quia finitur in medietate eclypticæ aſcendente, ſubtraxi iam 71. </s>
            <s xml:id="echoid-s1918" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1919" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1920" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1921" xml:space="preserve">à ſe-
              <lb/>
              <note position="right" xlink:label="note-0041-05" xlink:href="note-0041-05a" xml:space="preserve">
                <emph style="it">Inucntunt</emph>
                <lb/>
                <emph style="it">primum.</emph>
              </note>
            micirculo, & </s>
            <s xml:id="echoid-s1922" xml:space="preserve">remanſerunt gra. </s>
            <s xml:id="echoid-s1923" xml:space="preserve">108. </s>
            <s xml:id="echoid-s1924" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1925" xml:space="preserve">56. </s>
            <s xml:id="echoid-s1926" xml:space="preserve">at hoc inuentũ dico primũ. </s>
            <s xml:id="echoid-s1927" xml:space="preserve">Deinde ſinum
              <lb/>
            altitudinis poli 48. </s>
            <s xml:id="echoid-s1928" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1929" xml:space="preserve">74314. </s>
            <s xml:id="echoid-s1930" xml:space="preserve">duxi in ſinũ declinationis extremitatis arcus eclypticæ, ſci
              <lb/>
            licet 14. </s>
            <s xml:id="echoid-s1931" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1932" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1933" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1934" xml:space="preserve">24499. </s>
            <s xml:id="echoid-s1935" xml:space="preserve">ꝓductũ diuiſi in ſinũ totum, & </s>
            <s xml:id="echoid-s1936" xml:space="preserve">quotiens eſt 18206. </s>
            <s xml:id="echoid-s1937" xml:space="preserve">arcus aũt
              <lb/>
              <note position="right" xlink:label="note-0041-06" xlink:href="note-0041-06a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">ingreſſus</emph>
                <lb/>
                <emph style="it">oſtendet in-</emph>
                <lb/>
                <emph style="it">uentum ſe-</emph>
                <lb/>
                <emph style="it">cundum.</emph>
              </note>
            illius 10. </s>
            <s xml:id="echoid-s1938" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1939" xml:space="preserve">29. </s>
            <s xml:id="echoid-s1940" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1941" xml:space="preserve">inuentum illud ſecũdũ. </s>
            <s xml:id="echoid-s1942" xml:space="preserve">Inſuper etiã ſinũ cõplementi altitudinis poli
              <lb/>
            66913. </s>
            <s xml:id="echoid-s1943" xml:space="preserve">tan̈ minorem in ſinũ totũ duxi, diuiſi eundẽ in ſinũ cõplementi ſecundi inuenti,
              <lb/>
            ſcilicet 79. </s>
            <s xml:id="echoid-s1944" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1945" xml:space="preserve">31. </s>
            <s xml:id="echoid-s1946" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1947" xml:space="preserve">98330. </s>
            <s xml:id="echoid-s1948" xml:space="preserve">& </s>
            <s xml:id="echoid-s1949" xml:space="preserve">prouenit in quotiente 68049. </s>
            <s xml:id="echoid-s1950" xml:space="preserve">arcus eius 42. </s>
            <s xml:id="echoid-s1951" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1952" xml:space="preserve">53. </s>
            <s xml:id="echoid-s1953" xml:space="preserve">min.
              <lb/>
            </s>
            <s xml:id="echoid-s1954" xml:space="preserve">adpellabitur inuentũ tertiũ, hoc deinde ipſum à primo inuento ſubtraxi, hoc eſt 42. </s>
            <s xml:id="echoid-s1955" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1956" xml:space="preserve">
              <lb/>
            53. </s>
            <s xml:id="echoid-s1957" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1958" xml:space="preserve">à 180. </s>
            <s xml:id="echoid-s1959" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1960" xml:space="preserve">56. </s>
            <s xml:id="echoid-s1961" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1962" xml:space="preserve">reſiduũ eſt 66. </s>
            <s xml:id="echoid-s1963" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1964" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1965" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1966" xml:space="preserve">quo℞ ſinũ 91390. </s>
            <s xml:id="echoid-s1967" xml:space="preserve">duxi in ſinũ cõplemẽ
              <lb/>
              <note position="right" xlink:label="note-0041-07" xlink:href="note-0041-07a" xml:space="preserve">
                <emph style="it">Arealis</emph>
                <lb/>
                <emph style="it">operatio.</emph>
                <lb/>
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">tertium.</emph>
              </note>
            tiſecũdi inuẽti 79. </s>
            <s xml:id="echoid-s1968" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1969" xml:space="preserve">31. </s>
            <s xml:id="echoid-s1970" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1971" xml:space="preserve">hoc eſt 98330. </s>
            <s xml:id="echoid-s1972" xml:space="preserve">ꝓductũ diuiſi in ſinũ totũ, & </s>
            <s xml:id="echoid-s1973" xml:space="preserve">prodijt in quo
              <lb/>
            tienti 89864. </s>
            <s xml:id="echoid-s1974" xml:space="preserve">arcus illorum ſinuũ eſt 63. </s>
            <s xml:id="echoid-s1975" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1976" xml:space="preserve">59. </s>
            <s xml:id="echoid-s1977" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1978" xml:space="preserve">quibus ſubtractis à 90. </s>
            <s xml:id="echoid-s1979" xml:space="preserve">remanent 26.
              <lb/>
            </s>
            <s xml:id="echoid-s1980" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1981" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1982" xml:space="preserve">Poſtremò ꝓpono ſinũ iſtorum 26. </s>
            <s xml:id="echoid-s1983" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1984" xml:space="preserve">& </s>
            <s xml:id="echoid-s1985" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1986" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1987" xml:space="preserve">ſcilicet 43863. </s>
            <s xml:id="echoid-s1988" xml:space="preserve">& </s>
            <s xml:id="echoid-s1989" xml:space="preserve">ſinum ſecundi in-
              <lb/>
            uenti 18206. </s>
            <s xml:id="echoid-s1990" xml:space="preserve">hunc tan̈ minorem duco in totum, productum diuido in 43863. </s>
            <s xml:id="echoid-s1991" xml:space="preserve">& </s>
            <s xml:id="echoid-s1992" xml:space="preserve">prode
              <lb/>
              <note position="right" xlink:label="note-0041-08" xlink:href="note-0041-08a" xml:space="preserve">
                <emph style="it">Lateralis</emph>
                <lb/>
                <emph style="it">introitus.</emph>
              </note>
            unt in quotiente 41506. </s>
            <s xml:id="echoid-s1993" xml:space="preserve">arcum illius, puta 24. </s>
            <s xml:id="echoid-s1994" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1995" xml:space="preserve">31. </s>
            <s xml:id="echoid-s1996" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1997" xml:space="preserve">ſi iuxta regulã ſiue præſcriptũ
              <lb/>
            operationis, propter medietatem eclypticæ aſcendentem addidero ad arcũ eclypticæ 37.
              <lb/>
            </s>
            <s xml:id="echoid-s1998" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1999" xml:space="preserve">55. </s>
            <s xml:id="echoid-s2000" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2001" xml:space="preserve">prouenient uti 62. </s>
            <s xml:id="echoid-s2002" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2003" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2004" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2005" xml:space="preserve">eclypticæ, quæ cũ illa aſcenſione ſiue arcu æ-
              <lb/>
              <note position="right" xlink:label="note-0041-09" xlink:href="note-0041-09a" xml:space="preserve">
                <emph style="it">Arealis in-</emph>
                <lb/>
                <emph style="it">greſſus.</emph>
              </note>
            quatoris 35. </s>
            <s xml:id="echoid-s2006" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2007" xml:space="preserve">32. </s>
            <s xml:id="echoid-s2008" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2009" xml:space="preserve">in eleuatione poli 48. </s>
            <s xml:id="echoid-s2010" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2011" xml:space="preserve">aſcendũt, ſiue horizontem attingunt
              <lb/>
            planè in 2. </s>
            <s xml:id="echoid-s2012" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2013" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2014" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2015" xml:space="preserve">II, ubi tunc Solerat in ipſo die intronizationis ornatiſsimi Præ-
              <lb/>
              <note position="right" xlink:label="note-0041-10" xlink:href="note-0041-10a" xml:space="preserve">
                <emph style="it">Locus So-</emph>
                <lb/>
                <emph style="it">lis die intro</emph>
                <lb/>
                <emph style="it">nizationis</emph>
                <lb/>
                <emph style="it">præſulis</emph>
                <lb/>
                <emph style="it">Auguſtani.</emph>
              </note>
            ſulis Auguſtani. </s>
            <s xml:id="echoid-s2016" xml:space="preserve">Ecce quàm operoſa & </s>
            <s xml:id="echoid-s2017" xml:space="preserve">prolixa operatione hacidẽ illud adinueni, cuius
              <lb/>
            contrarium ſuperior propoſitio facili & </s>
            <s xml:id="echoid-s2018" xml:space="preserve">compendiaria uia monſtrauit, quamuis in
              <lb/>
            reliquis tribus quartis zodia ci à ♋ uſ ad ♎, & </s>
            <s xml:id="echoid-s2019" xml:space="preserve">inde à ♎ ad ♑, at à ♑ ad ♈, aliquan-
              <lb/>
            do alia operatio eſt, attamen mihi conſultum uiſum eſt, illas nullis peculiaribus exem-
              <lb/>
            plis indicare: </s>
            <s xml:id="echoid-s2020" xml:space="preserve">quiſquis em̃ operationem hanc cũ exemplo adiuncto recte intellexrit, is
              <lb/>
            etiam in reliquis illis nõ aberrabit, ſedubi facile ſe extricabit, nos igitur aliò iam prope
              <lb/>
            rabimus, animum & </s>
            <s xml:id="echoid-s2021" xml:space="preserve">cogitationem eleuaturi ad altitudinem Solis ſuper horizontem.</s>
            <s xml:id="echoid-s2022" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div55" type="section" level="1" n="32">
          <head xml:id="echoid-head36" xml:space="preserve">PRONVNCIATVM XX.</head>
          <p>
            <s xml:id="echoid-s2023" xml:space="preserve">Altitudinem Solis in circulo uerticali (dummodo ſit in ſigno aliquo ſe-
              <lb/>
            ptentrionali) inueſtigare.</s>
            <s xml:id="echoid-s2024" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2025" xml:space="preserve">Iam ſupra pronunciato 12. </s>
            <s xml:id="echoid-s2026" xml:space="preserve">edoctus es, quidnã ſit ortus æquinoctialis, quamobrẽ ſuꝑ-
              <lb/>
            uacuũ ſuerit idẽ hic denuo cõmemorare, tm̃ ne ignores, quid hic nomine circuli uertica-
              <lb/>
            lis intelligamus, illũ tibi breuiter deſcribemus. </s>
            <s xml:id="echoid-s2027" xml:space="preserve">Vertex igit̃ ſiue pũctus uerticalis, eſt pun
              <lb/>
              <note position="right" xlink:label="note-0041-11" xlink:href="note-0041-11a" xml:space="preserve">
                <emph style="it">Vertex ſiue</emph>
                <lb/>
                <emph style="it">zenith ꝗd.</emph>
              </note>
            ctus cœli capiti tuo directe imminens, ſi modo tu ſtes erectus, monſtrat punctũ illũ tibi
              <lb/>
            filũ ſuſpenſum, ex quo plumbimaſſa, aut aliud quiddã graue dependeat, quẽ igitur ſuperi
              <lb/>
            or ſili pars in cœlo locum demonſtrat, ibi ſcias eſſe punctum uerticalem, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum