Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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        <div xml:id="echoid-div49" type="section" level="1" n="29">
          <p>
            <s xml:id="echoid-s1776" xml:space="preserve">
              <pb file="0040" n="40" rhead="GENVINVS VSVS"/>
            maior eſt ſinu maximæ declinationis Solis 39874. </s>
            <s xml:id="echoid-s1777" xml:space="preserve">tunc aũt ipſum maximæ decli-
              <lb/>
            nationis Solis multiplica cum toto ſinu, productũ diuide in diuiſorem, & </s>
            <s xml:id="echoid-s1778" xml:space="preserve">prouenſent in
              <lb/>
            quotiente 66904. </s>
            <s xml:id="echoid-s1779" xml:space="preserve">arcus iſtius erit 42. </s>
            <s xml:id="echoid-s1780" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1781" xml:space="preserve">quæ altitudo eſt æquatoris, eam ſi ſubtrahas
              <lb/>
            à 90. </s>
            <s xml:id="echoid-s1782" xml:space="preserve">remanebunt 48. </s>
            <s xml:id="echoid-s1783" xml:space="preserve">gradus, eleuatio ſcilicet polaris quam tantopere inquirebas.</s>
            <s xml:id="echoid-s1784" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div51" type="section" level="1" n="30">
          <head xml:id="echoid-head34" xml:space="preserve">PRONVNCIATVM XVIII.</head>
          <p>
            <s xml:id="echoid-s1785" xml:space="preserve">Cuiuslibet arcus eclypticæ, qui incipiat in ſectione uernali, aſcenſionem
              <lb/>
            obliquam in quacun ſiue ciuitate ſiue regione ſupputare.</s>
            <s xml:id="echoid-s1786" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1787" xml:space="preserve">Iam ſupra edoctus es pronunciato 15. </s>
            <s xml:id="echoid-s1788" xml:space="preserve">cognoſcere differentiã aſcenſionalem, ea res ti
              <lb/>
            bi hic plurimũ erit uſui. </s>
            <s xml:id="echoid-s1789" xml:space="preserve">Cæterum in pronunciato 7. </s>
            <s xml:id="echoid-s1790" xml:space="preserve">didiciſti inuentionem aſcenſionis re
              <lb/>
            ctæ. </s>
            <s xml:id="echoid-s1791" xml:space="preserve">Iam igitur ſi punctũ, ſuper quo differentia aſcenfionalis eſt quæſtia, declinationem
              <lb/>
            habet ſeptentrionalem, tũc tu differentiã illam ſubtrahe ab aſcenſiõe recta pũcti dati, ſin
              <lb/>
            aũt declinatio fuerit meridionalis, operæpreciũ erit te addere differentiã iſtã ad aſcenſio
              <lb/>
              <note position="left" xlink:label="note-0040-01" xlink:href="note-0040-01a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            nem rectã, & </s>
            <s xml:id="echoid-s1792" xml:space="preserve">tũc ſanè reliqua tibi manebit aſcenſio illius pũcti obliqua. </s>
            <s xml:id="echoid-s1793" xml:space="preserve">?</s>
            <s xml:id="echoid-s1794" xml:space="preserve">? Nunc ſi uis
              <lb/>
            cape eius rei tibi exemplũ huiuſmodi: </s>
            <s xml:id="echoid-s1795" xml:space="preserve">Sol in ipſo die intronizationis ornatiſsimi Præſu
              <lb/>
            lis Auguſtenſis fuit in 2. </s>
            <s xml:id="echoid-s1796" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1797" xml:space="preserve">26. </s>
            <s xml:id="echoid-s1798" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1799" xml:space="preserve">II, quapropter & </s>
            <s xml:id="echoid-s1800" xml:space="preserve">declinationem oportet habeat
              <lb/>
            ſeptentrionalem, porrò ex 7. </s>
            <s xml:id="echoid-s1801" xml:space="preserve">pronunciato inuentã habeo aſcenſionem eius rectã 60. </s>
            <s xml:id="echoid-s1802" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s1803" xml:space="preserve">21. </s>
            <s xml:id="echoid-s1804" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1805" xml:space="preserve">Ex pronũciato autem 15. </s>
            <s xml:id="echoid-s1806" xml:space="preserve">inueni ſuper eundem gradum Solis differentiam aſcen
              <lb/>
            ſionalem 24. </s>
            <s xml:id="echoid-s1807" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1808" xml:space="preserve">49. </s>
            <s xml:id="echoid-s1809" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1810" xml:space="preserve">Nunc ita ſibi differentiam illam aſcenſionalem ſubtrahã à 60. </s>
            <s xml:id="echoid-s1811" xml:space="preserve">
              <lb/>
            gra. </s>
            <s xml:id="echoid-s1812" xml:space="preserve">21. </s>
            <s xml:id="echoid-s1813" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1814" xml:space="preserve">ſiquidem declinatio ibi eſt ſeptentrionalis, remanent 35. </s>
            <s xml:id="echoid-s1815" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1816" xml:space="preserve">32. </s>
            <s xml:id="echoid-s1817" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1818" xml:space="preserve">æquato-
              <lb/>
            ris, & </s>
            <s xml:id="echoid-s1819" xml:space="preserve">exurgunt in horizonte exortiuo cum gradu Solis, quod ipſum erat optatum.</s>
            <s xml:id="echoid-s1820" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div53" type="section" level="1" n="31">
          <head xml:id="echoid-head35" xml:space="preserve">PRONVNCIATVM XIX.</head>
          <p>
            <s xml:id="echoid-s1821" xml:space="preserve">Quod ſi forte aſcenſio obliqua iam antea fuerit cum eleuatione poli cogni
              <lb/>
            ta, adhuc tamen gradum eclypticæ ſimul tunc aſcendentem ſuper horizon-
              <lb/>
            tem experiri & </s>
            <s xml:id="echoid-s1822" xml:space="preserve">indagare.</s>
            <s xml:id="echoid-s1823" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1824" xml:space="preserve">Hic principio admonendus es, ut ſemper aſcenſionem incipias cõputare à proxima in
              <lb/>
            terſectione æquino ctialis & </s>
            <s xml:id="echoid-s1825" xml:space="preserve">eclypticæ, ſiquidem ab utra  illa interſectiõe incipit aſcen-
              <lb/>
            ſio, operationem hãc ita ꝓponemus breuiſsime, nã in ſe admodũ operoſa eſt & </s>
            <s xml:id="echoid-s1826" xml:space="preserve">ꝓlixa. </s>
            <s xml:id="echoid-s1827" xml:space="preserve">Ha
              <lb/>
            bita iam aſcenſione obliqua, imaginare eam ſic quaſi eſſet aſcenſio recta, eius aſcenſionis
              <lb/>
            quære ex pronunciato 8. </s>
            <s xml:id="echoid-s1828" xml:space="preserve">arcũ eclypticæ, qui cũ illo arcu æquatoris in ſphæra recta aſcen
              <lb/>
            dit ſuper horizõtem, inuento illo, porrò cõquire per ꝓpoſitionem 5, declinationem eius
              <lb/>
            ab æquatore. </s>
            <s xml:id="echoid-s1829" xml:space="preserve">Mox arcus illius æquatoris, quem tibi per modũ aſcenſionis rectæ, propo-
              <lb/>
              <note position="left" xlink:label="note-0040-02" xlink:href="note-0040-02a" xml:space="preserve">
                <emph style="it">per aream</emph>
                <lb/>
                <emph style="it">aſſequcris.</emph>
              </note>
            ſuiſti ſinũ, duc in totũ illum ſinũ, productũ inde diuide cũ ſinu arcus eclypticæ, qui ſimul
              <lb/>
            aſcendit, arcũ quotientis ſubtrahe à ſemicirculo, ſi tamen arcus eclypticæ deſinat & </s>
            <s xml:id="echoid-s1830" xml:space="preserve">finia
              <lb/>
            tur in ſemicirculo aſcendente, hoc eſt inter principiũ ♑ ſecundũ ordinem ſigno℞ uſ ad
              <lb/>
            principiũ ♋. </s>
            <s xml:id="echoid-s1831" xml:space="preserve">ſin aũt finis arcus eclypticæ fuerit inter principiũ ♋ & </s>
            <s xml:id="echoid-s1832" xml:space="preserve">♑. </s>
            <s xml:id="echoid-s1833" xml:space="preserve">relinques ita ar
              <lb/>
            cum illũ quotientis, q̊d aũt iſto primo modo uel altero tibi per operationem prouenit, id
              <lb/>
            inuentum primũ dicetur. </s>
            <s xml:id="echoid-s1834" xml:space="preserve">Deinde multiplica ſinũ altitudinis poli cũ ſinu declinationis ꝓ
              <lb/>
            poſiti arcus eclypticæ, & </s>
            <s xml:id="echoid-s1835" xml:space="preserve">productũ diuide in ſinũ totũ, at is arcus quotientis uocabitur
              <lb/>
              <note position="left" xlink:label="note-0040-03" xlink:href="note-0040-03a" xml:space="preserve">
                <emph style="it">per latera.</emph>
              </note>
            inuentum ſecundũ. </s>
            <s xml:id="echoid-s1836" xml:space="preserve">Præterea propone tibi ſinũ cõplementi huius ſecundi inuenti, & </s>
            <s xml:id="echoid-s1837" xml:space="preserve">ſi-
              <lb/>
            mul etiã ſinũ cõplemẽti altitudinis poli, ſinũ ex ijs minorem duc in integrũ ſiue perfectũ,
              <lb/>
            productũ diuide in maiorem, & </s>
            <s xml:id="echoid-s1838" xml:space="preserve">arcus quotientis appellabitur inuentũ tertiũ. </s>
            <s xml:id="echoid-s1839" xml:space="preserve">hoc ipſum
              <lb/>
              <note position="left" xlink:label="note-0040-04" xlink:href="note-0040-04a" xml:space="preserve">
                <emph style="it">Per aream</emph>
              </note>
            ſi ſubtrahas ab inuento primo, & </s>
            <s xml:id="echoid-s1840" xml:space="preserve">finũ reſidui ducas in ſinũ cõplementi ſecũdi inuenti, at
              <lb/>
            diuidas in totũ, deinde arcũ quotientis ſubtra has à 90. </s>
            <s xml:id="echoid-s1841" xml:space="preserve">ſinũ quo reſidui tibi ꝓponas cũ
              <lb/>
              <note position="left" xlink:label="note-0040-05" xlink:href="note-0040-05a" xml:space="preserve">
                <emph style="it">per latera.</emph>
              </note>
            ſinu ſecundi inuenti, minorem ex ijs ducas in ſinũ totũ, productũ in maiorem diuidas: </s>
            <s xml:id="echoid-s1842" xml:space="preserve">tũc
              <lb/>
            tandem arcus quotientis tibi monſtrabit optatũ, dummodo addideris eũ ad arcũ eclypti
              <lb/>
              <note position="left" xlink:label="note-0040-06" xlink:href="note-0040-06a" xml:space="preserve">
                <emph style="it">Per aream</emph>
              </note>
            cæ, qui propoſitæ aſcenſioni in ſphæra recta reſpõdet, arcu etiã eclypticæ deſinẽte in me
              <lb/>
            dietate aſcenſionali, ſi inter ♑ & </s>
            <s xml:id="echoid-s1843" xml:space="preserve">♋, uel ſubtraxeris, ſi finiatur ille in medietate zodiaci,
              <lb/>
            deſcendente à principio nimirũ ♋ uſ ad principiũ ♑, ſecundũ ordinem ſigno℞ nume-
              <lb/>
            rando: </s>
            <s xml:id="echoid-s1844" xml:space="preserve">ſic iam habebis arcũ eclypticæ quæſitum. </s>
            <s xml:id="echoid-s1845" xml:space="preserve">?</s>
            <s xml:id="echoid-s1846" xml:space="preserve">? Adſume quo in hãcrem exem-
              <lb/>
              <note position="left" xlink:label="note-0040-07" xlink:href="note-0040-07a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            plum tibi huiuſcemodi, niſi forte moleſtũ eſt, nõ erit aũt ſi pleniorem intelligentiã habe-
              <lb/>
            re deſideras. </s>
            <s xml:id="echoid-s1847" xml:space="preserve">Propoſito ipſo intronizationis die, ecce aſcenſio recta æ quatoris à </s>
          </p>
        </div>
      </text>
    </echo>
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