Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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        <div xml:id="echoid-div45" type="section" level="1" n="27">
          <pb file="0039" n="39" rhead="TABVLARVM SINVVM."/>
        </div>
        <div xml:id="echoid-div47" type="section" level="1" n="28">
          <head xml:id="echoid-head32" xml:space="preserve">PRONVNCIATVM XVI.</head>
          <p>
            <s xml:id="echoid-s1654" xml:space="preserve">Longitudinem diurnam ſuper quodcun punctum eclypticæ alia qua-
              <lb/>
            dam ratione addiſcere.</s>
            <s xml:id="echoid-s1655" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1656" xml:space="preserve">Quod ſi lõitudinẽ diurnã diuerſo modo cupis cognoſcere, quære principio ex 12. </s>
            <s xml:id="echoid-s1657" xml:space="preserve">ꝓ
              <lb/>
            nunciato amplitudinẽ ☉(sun), quãdo ille eſt in primo minuto ♑, deinde ex ſuperiori pronun
              <lb/>
              <note position="right" xlink:label="note-0039-01" xlink:href="note-0039-01a" xml:space="preserve">
                <emph style="it">Illud repe-</emph>
                <lb/>
                <emph style="it">rics ſi qua-</emph>
                <lb/>
                <emph style="it">drantem la</emph>
                <lb/>
                <emph style="it">teraliter in</emph>
                <lb/>
                <emph style="it">grediaris.</emph>
              </note>
            ciato inquire differentiã aſcẽſionalẽ, ex ſeptimo aũt aſcẽſionem rectã gradus Solis, ad eũ
              <lb/>
            diem cuius quantita tẽ ſcire deſideras, mox multiplica ſinũ rectũ eius aſcenſionis rectæ cũ
              <lb/>
            ſinu differentiæ aſcenſionalis principij ♑, productũ partire in totũ ſinũ, arcus quotien-
              <lb/>
            tis tibi cõmonſtrabit uerã differentiã aſcenſionalẽ, eam addes ad gra. </s>
            <s xml:id="echoid-s1658" xml:space="preserve">90. </s>
            <s xml:id="echoid-s1659" xml:space="preserve">in ſignis ſepten
              <lb/>
            trionalibus, ſubtrahes aũt in meridionalibus, & </s>
            <s xml:id="echoid-s1660" xml:space="preserve">remanebit arcus ſemidiurnus. </s>
            <s xml:id="echoid-s1661" xml:space="preserve">?</s>
            <s xml:id="echoid-s1662" xml:space="preserve">? Ex-
              <lb/>
              <note position="right" xlink:label="note-0039-02" xlink:href="note-0039-02a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi</emph>
              .</note>
            emplũ ſuꝑ ea re illuſtranda accipe huiuſmodi, ſicut in ſuperiori ꝓnunciato diem introni
              <lb/>
            zationis propoſuim us, ita eundem etiam hic ſeruabimus, at eius quantitatẽ inquiſitu
              <lb/>
            rus, primum omniũ eleuationem poli aſſumo 48. </s>
            <s xml:id="echoid-s1663" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1664" xml:space="preserve">complementũ eius eſt 42. </s>
            <s xml:id="echoid-s1665" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1666" xml:space="preserve">Iam
              <lb/>
            uero per pronũciatũ 12. </s>
            <s xml:id="echoid-s1667" xml:space="preserve">inuenio amplitudinẽ ☉(sun), qñ ille eſt in primo minuto ♑ 36. </s>
            <s xml:id="echoid-s1668" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s1669" xml:space="preserve">35. </s>
            <s xml:id="echoid-s1670" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1671" xml:space="preserve">ſinũ cõplemẽti illius amplitudinis 80299. </s>
            <s xml:id="echoid-s1672" xml:space="preserve">duco in ſinũ totũ, ꝓductũ in ſinũ cõple-
              <lb/>
            menti maximæ declinatiõis Solis diuide, & </s>
            <s xml:id="echoid-s1673" xml:space="preserve">ꝓueniũt in quotiente 87561. </s>
            <s xml:id="echoid-s1674" xml:space="preserve">arcus porro eſt
              <lb/>
            61. </s>
            <s xml:id="echoid-s1675" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1676" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1677" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1678" xml:space="preserve">id quũ ſubtraho à 90. </s>
            <s xml:id="echoid-s1679" xml:space="preserve">remanent 28. </s>
            <s xml:id="echoid-s1680" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1681" xml:space="preserve">53. </s>
            <s xml:id="echoid-s1682" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1683" xml:space="preserve">differentia aſcẽſionalis oĩm
              <lb/>
            maxima, eam ſi addo ad 90. </s>
            <s xml:id="echoid-s1684" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1685" xml:space="preserve">ꝓdit inde mihi tempus ſemidiurnũ lõgiſ simæ diei, ſi aũt
              <lb/>
            ſubtraho à 90. </s>
            <s xml:id="echoid-s1686" xml:space="preserve">reliquũ, manet tẽpus ſemidiurnũ breuiſsimæ diei totius anni. </s>
            <s xml:id="echoid-s1687" xml:space="preserve">Poſtea quæ
              <lb/>
            ro aſcenſionẽ rectã (ꝑ 7. </s>
            <s xml:id="echoid-s1688" xml:space="preserve">ꝓnunciatũ) gradus eclypticæ in q̊ Sol fuit die intronzationis,
              <lb/>
            & </s>
            <s xml:id="echoid-s1689" xml:space="preserve">ibi inuenio 60. </s>
            <s xml:id="echoid-s1690" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1691" xml:space="preserve">21. </s>
            <s xml:id="echoid-s1692" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1693" xml:space="preserve">iã ſinũ illius aſcenſiõis rectæ 86906. </s>
            <s xml:id="echoid-s1694" xml:space="preserve">duco in ſinũ differẽtiæ
              <lb/>
            aſcenſionalis 28. </s>
            <s xml:id="echoid-s1695" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1696" xml:space="preserve">53. </s>
            <s xml:id="echoid-s1697" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1698" xml:space="preserve">ſcilicet 48302. </s>
            <s xml:id="echoid-s1699" xml:space="preserve">ꝓductũ diuido in ſinũ ꝑfectũ, et ꝓueniũt in q̊
              <lb/>
            tiente 41977. </s>
            <s xml:id="echoid-s1700" xml:space="preserve">arcus erit 24. </s>
            <s xml:id="echoid-s1701" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1702" xml:space="preserve">49. </s>
            <s xml:id="echoid-s1703" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1704" xml:space="preserve">quæ differentia uera eſt aſcenſionalis, quam ex
              <lb/>
            proximo pronunciato non paulò diuerſo adinueni, illam ſi addas ad gra. </s>
            <s xml:id="echoid-s1705" xml:space="preserve">90. </s>
            <s xml:id="echoid-s1706" xml:space="preserve">(ſi quidẽ ☉(sun)
              <lb/>
            in ſigno eſt ſeptentrionali) ꝓueniet hinc arcus ſemidiurnus 114. </s>
            <s xml:id="echoid-s1707" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1708" xml:space="preserve">42. </s>
            <s xml:id="echoid-s1709" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1710" xml:space="preserve">ꝗbus horæ 7
              <lb/>
            conficiuntur & </s>
            <s xml:id="echoid-s1711" xml:space="preserve">48. </s>
            <s xml:id="echoid-s1712" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1713" xml:space="preserve">productũ diuerſæ huius operationis, conſimile tamen ſuperiori.</s>
            <s xml:id="echoid-s1714" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div49" type="section" level="1" n="29">
          <head xml:id="echoid-head33" xml:space="preserve">PRONVNCIATVM XVII.</head>
          <p>
            <s xml:id="echoid-s1715" xml:space="preserve">Cognita regionis alicuius die longiſsima, aut alioqui propoſita, altitudi-
              <lb/>
            nem poli, in qua tanta eſt diei quantitas, ex ſphærica ſupputatione inuenire.</s>
            <s xml:id="echoid-s1716" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1717" xml:space="preserve">Non tantũ ꝑ diem lõgiſsimũ, ſed & </s>
            <s xml:id="echoid-s1718" xml:space="preserve">breuiſsimũ oꝑari hoc potes, at in hoc tibi ꝓpone
              <lb/>
            diẽ lõ giſsimũ, eũ diuide in duas ꝑtes, qua℞ q̃libet dicet̃ tẽpus ſemidiurnũ, inde ſubtrahe
              <lb/>
            horas 6. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">q̊d inde remanet, diciſolet differẽtia aſcẽſionalis maxima, eã cõuerte in gradus,
              <lb/>
            ita, ut ſemꝑ 15. </s>
            <s xml:id="echoid-s1720" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1721" xml:space="preserve">reſpõdeãt horæ, & </s>
            <s xml:id="echoid-s1722" xml:space="preserve">uni minuto tꝑis 15. </s>
            <s xml:id="echoid-s1723" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1724" xml:space="preserve">gradus. </s>
            <s xml:id="echoid-s1725" xml:space="preserve">Differentiã illam
              <lb/>
            aſcenſionalẽ iã in gradus & </s>
            <s xml:id="echoid-s1726" xml:space="preserve">minuta graduũ cõuerſam, diuides in duas partes æquales,
              <lb/>
              <note position="right" xlink:label="note-0039-03" xlink:href="note-0039-03a" xml:space="preserve">
                <emph style="it">Oſtẽdit hoc</emph>
                <lb/>
                <emph style="it">ingreſſum</emph>
                <lb/>
                <emph style="it">lateralem.</emph>
              </note>
            ea℞ alterutra ſufficiet tibi ad hãc oꝑationẽ. </s>
            <s xml:id="echoid-s1727" xml:space="preserve">Accipe deinde & </s>
            <s xml:id="echoid-s1728" xml:space="preserve">ſinũ cõplementi, eũ multi-
              <lb/>
            plica cũ ſinu cõplementi maximæ declinatiõis Solis. </s>
            <s xml:id="echoid-s1729" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s1730" xml:space="preserve">66. </s>
            <s xml:id="echoid-s1731" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1732" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1733" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1734" xml:space="preserve">ꝓductũ diuide in ſi
              <lb/>
            nũ totũ, & </s>
            <s xml:id="echoid-s1735" xml:space="preserve">arcus ille q̊tiẽtis ex 90. </s>
            <s xml:id="echoid-s1736" xml:space="preserve">relinquet tibi amplitudinẽ ortiuã principij ♋ uel ♑ in
              <lb/>
            regiõe ꝓpoſita, eius amplitudinis ſinũ tibi ꝓpone ſimul cũ ſinu maximæ declinatiõis So
              <lb/>
              <note position="right" xlink:label="note-0039-04" xlink:href="note-0039-04a" xml:space="preserve">
                <emph style="it">Hoc area-</emph>
                <lb/>
                <emph style="it">tim aſſeque</emph>
                <lb/>
                <emph style="it">ris.</emph>
              </note>
            lis, minorem duc in ſinũ totũ, ꝓductũ diuide in maiorẽ, arcus illius q̊tientis mõſtrabit al-
              <lb/>
            titudinẽ æquatoris, q̃ à 90. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">ſublata, relin ꝗt altitudinẽ poli q̃ſitã. </s>
            <s xml:id="echoid-s1738" xml:space="preserve">Eodẽ modo potes q̊cũ
              <lb/>
            tꝑe anni cognoſcere eleuationẽ poli, ſi tm̃ tibi ꝓponas ꝗ̃ntitatẽ diei et declinationẽ gra-
              <lb/>
            dus eclypticæ, quẽ ꝑmeat Sol illo die. </s>
            <s xml:id="echoid-s1739" xml:space="preserve">?</s>
            <s xml:id="echoid-s1740" xml:space="preserve">? Habe in hoc tibi ſimilitudinẽ huiuſmodi. </s>
            <s xml:id="echoid-s1741" xml:space="preserve">Au
              <lb/>
              <note position="right" xlink:label="note-0039-05" xlink:href="note-0039-05a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            guſtæ, ubi talis intronizatio facta eſt, dies lõgiſsima horas habet 15. </s>
            <s xml:id="echoid-s1742" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1743" xml:space="preserve">50. </s>
            <s xml:id="echoid-s1744" xml:space="preserve">ſi uelim iã in-
              <lb/>
            de eleuationẽ poli eius loci colligere, à lõgitudine diurna, adimo horas 12. </s>
            <s xml:id="echoid-s1745" xml:space="preserve">& </s>
            <s xml:id="echoid-s1746" xml:space="preserve">remanẽt ho
              <lb/>
            ræ 3. </s>
            <s xml:id="echoid-s1747" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1748" xml:space="preserve">50. </s>
            <s xml:id="echoid-s1749" xml:space="preserve">ea ſi mediaro, habebo horã 1. </s>
            <s xml:id="echoid-s1750" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1751" xml:space="preserve">55. </s>
            <s xml:id="echoid-s1752" xml:space="preserve">Vel etiã diuido lõgitudinẽ diurnã totã in
              <lb/>
            duas ꝑtes, qua℞ q̃libet habebit horas 7. </s>
            <s xml:id="echoid-s1753" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1754" xml:space="preserve">55. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">inde ſi ſubtraxero 6. </s>
            <s xml:id="echoid-s1756" xml:space="preserve">horas, remanet hora
              <lb/>
            unica cũ 55. </s>
            <s xml:id="echoid-s1757" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1758" xml:space="preserve">ſicut prius. </s>
            <s xml:id="echoid-s1759" xml:space="preserve">Horas illas poſtea redigo in gradus, & </s>
            <s xml:id="echoid-s1760" xml:space="preserve">erunt 28. </s>
            <s xml:id="echoid-s1761" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1762" xml:space="preserve">53. </s>
            <s xml:id="echoid-s1763" xml:space="preserve">min.
              <lb/>
            </s>
            <s xml:id="echoid-s1764" xml:space="preserve">eos ſubtrahe tu deinde de quadrãte, manebit cõplementũ eius 61. </s>
            <s xml:id="echoid-s1765" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1766" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1767" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1768" xml:space="preserve">Sinũ illius
              <lb/>
            87561 multiplica cũ ſinu cõplemẽti maxĩæ declinatiõis 91706 ꝓductũ diuide ĩ totũ ſinũ
              <lb/>
            & </s>
            <s xml:id="echoid-s1769" xml:space="preserve">ĩ q̊tiẽte habebis 80299. </s>
            <s xml:id="echoid-s1770" xml:space="preserve">cui9 arc9 ẽ 53 gr. </s>
            <s xml:id="echoid-s1771" xml:space="preserve">25. </s>
            <s xml:id="echoid-s1772" xml:space="preserve">m̃. </s>
            <s xml:id="echoid-s1773" xml:space="preserve">cõplemẽtũ eius 36 g. </s>
            <s xml:id="echoid-s1774" xml:space="preserve">35 m̃. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">q̃ ☉(sun) ampli
              <lb/>
            plitudo maxĩa eſt in ea regiõe, ſinũ illius amplitudinis 59599. </s>
            <s xml:id="echoid-s1776" xml:space="preserve">adſume ꝓ diuiſore, </s>
          </p>
        </div>
      </text>
    </echo>
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