Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

Table of contents

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[41.] COROLLARIVM.
Page: 60 (40)
[42.] SCHOLIVM.
Page: 60 (40)
[43.] THEOREMA 9. PROPOSITIO 11.
Page: 62 (42)
[44.] SCHOLIVM.
Page: 63 (43)
[45.] COROLLARIVM PRIMVM.
Page: 63 (43)
[46.] COROLLARIVM II.
Page: 63 (43)
[47.] THEOREMA 10. PROPOSITIO 12.
Page: 63 (43)
[48.] COROLLARIVM.
Page: 64 (44)
[49.] THEOREMA 11. PROPOSITIO 13.
Page: 64 (44)
[50.] THEOREMA 12. PROPOSITIO 14.
Page: 65 (45)
[51.] SCHOLIVM.
Page: 66 (46)
[52.] THEOREMA 13. PROPOSITIO 15.
Page: 66 (46)
[53.] LEMMA.
Page: 69 (49)
[54.] COROLLARIVM.
Page: 69 (49)
[55.] THEOREMA 14. PROPOSITIO 16.
Page: 69 (49)
[56.] COROLLARIVM.
Page: 70 (50)
[57.] THEOREMA 15. PROPOSITIO 17.
Page: 70 (50)
[58.] LEMMA.
Page: 72 (52)
[59.] SCHOLIVM.
Page: 72 (52)
[60.] THEOREMA 16. PROPOSITIO 18.
Page: 72 (52)
[61.] THEOREMA 17. PROPOSITIO 19.
Page: 73 (53)
[62.] SCHOLIVM.
Page: 74 (54)
[63.] THEOREMA 18. PROPOSITIO 20.
Page: 75 (55)
[64.] SCHOLIVM.
Page: 75 (55)
[65.] Linea horæ 24. ab ortu vel occaſu. Vel horizontalis linea.
Page: 76 (56)
[66.] Linea horæ 12. ab ortu vel occaſu.
Page: 76 (56)
[67.] Linea horæ ſextæ à meridie vel media nocte.
Page: 77 (57)
[68.] Linea horæ 12. à meridie vel media nocte.
Page: 77 (57)
[69.] Linea horæ 23. ab ortu vel occaſu.
Page: 81 (61)
[70.] Linea horæ 22. ab ortu vel occaſu.
Page: 81 (61)
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          <p>
            <s xml:id="echoid-s1784" xml:space="preserve">EODEM modo communis ſectio cuiuslibet horologii, & </s>
            <s xml:id="echoid-s1785" xml:space="preserve">coni, cuius baſis maiorem habet declina-
              <lb/>
              <note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">Quæ horologia
                <lb/>
              in ſuperficiebus
                <lb/>
              conicis, quarum
                <lb/>
              bales ſunt qui-
                <lb/>
              cunque paralle-
                <lb/>
              li Aequatoris,
                <lb/>
              t
                <unsure/>
              aciant Ellip@es.</note>
            tionem auſtralẽ quàm quantum eſt complementum altitudinis poli arctici ſupra circulum maximum, cui
              <lb/>
            planum horologii æquidiſtat, Ellipſis erit. </s>
            <s xml:id="echoid-s1786" xml:space="preserve">Talis erit ſectio coni baſim habentis parallelum ♑, & </s>
            <s xml:id="echoid-s1787" xml:space="preserve">horolo-
              <lb/>
            gij horizontalis ad latitudinem ſeptentrionalem, quæ excedit grad. </s>
            <s xml:id="echoid-s1788" xml:space="preserve">66. </s>
            <s xml:id="echoid-s1789" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1790" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1791" xml:space="preserve">quia hac ratione declinatio
              <lb/>
            ♑, nempe grad. </s>
            <s xml:id="echoid-s1792" xml:space="preserve">23. </s>
            <s xml:id="echoid-s1793" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1794" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1795" xml:space="preserve">maior erit complemento altitudinis poli. </s>
            <s xml:id="echoid-s1796" xml:space="preserve">Huiuſmodi quoque erit ſectio
              <lb/>
            coni baſim habentis parallelum ♐, & </s>
            <s xml:id="echoid-s1797" xml:space="preserve">♒, atque horologii horizontalis ad latitudinem Borealem, quę
              <lb/>
            excedit grad. </s>
            <s xml:id="echoid-s1798" xml:space="preserve">69. </s>
            <s xml:id="echoid-s1799" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1800" xml:space="preserve">48. </s>
            <s xml:id="echoid-s1801" xml:space="preserve">Nam huius paralleli declinatio continens grad. </s>
            <s xml:id="echoid-s1802" xml:space="preserve">20. </s>
            <s xml:id="echoid-s1803" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1804" xml:space="preserve">12. </s>
            <s xml:id="echoid-s1805" xml:space="preserve">maior eſt comple-
              <lb/>
            mento altitudinis poli. </s>
            <s xml:id="echoid-s1806" xml:space="preserve">Talis quoque erit ſectio coni baſim habentis parallelum ♏, & </s>
            <s xml:id="echoid-s1807" xml:space="preserve">♓, atque horo-
              <lb/>
            logii horizontalis ad latitudinem ſeptentrionalem maiorem, quàm grad. </s>
            <s xml:id="echoid-s1808" xml:space="preserve">78. </s>
            <s xml:id="echoid-s1809" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1810" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1811" xml:space="preserve">cum paralleli huius
              <lb/>
            declinatio, nimirum grad. </s>
            <s xml:id="echoid-s1812" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1813" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1814" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1815" xml:space="preserve">excedat hoc modo complementum altitudinis poli. </s>
            <s xml:id="echoid-s1816" xml:space="preserve">Idem dic de
              <lb/>
            conis, quorum baſes ſunt paralleli Boreales prædictis oppoſiti, vt parallelus ♋; </s>
            <s xml:id="echoid-s1817" xml:space="preserve">♊, & </s>
            <s xml:id="echoid-s1818" xml:space="preserve">♌; </s>
            <s xml:id="echoid-s1819" xml:space="preserve">♉, & </s>
            <s xml:id="echoid-s1820" xml:space="preserve">♍,
              <lb/>
              <note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">10</note>
            vbi polus tamen antarcticus ſupra Horizontem extollitur.</s>
            <s xml:id="echoid-s1821" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1822" xml:space="preserve">HINC facile diſces, quęnam plana horologiorum Ellipſes faciant, Sole exiſtente in quouis paralle-
              <lb/>
            lo. </s>
            <s xml:id="echoid-s1823" xml:space="preserve">Etenim ſi Sol exiſtat in parallelo ſeptẽtrionali, cui circulus maximus plano horologii æquidiſtans ne-
              <lb/>
            que æquidiſtat, neque eum tangit, neque ſecat, erit communis ſectio horologii, & </s>
            <s xml:id="echoid-s1824" xml:space="preserve">coni vmbrę baſim ha-
              <lb/>
            bentis parallelum auſtralem oppoſitum, Ellipſis; </s>
            <s xml:id="echoid-s1825" xml:space="preserve">vbi nimirum polus arcticus ſupra horologii planum ele
              <lb/>
            uatur. </s>
            <s xml:id="echoid-s1826" xml:space="preserve">At uerò ſi antarcticus polus ſupra planum horologii extollatur, & </s>
            <s xml:id="echoid-s1827" xml:space="preserve">Sol ſit in parallelo auſtrali, cui
              <lb/>
            maximus circulus plano horologii æquidiſtans neque ęquidiſtat, neque eum tangit, neq; </s>
            <s xml:id="echoid-s1828" xml:space="preserve">ſecat, fiet Ellipſis
              <lb/>
            in cono vmbræ, cuius baſis parallelus eſt borealis oppoſitus, vt ex dictis perſpicuum eſt. </s>
            <s xml:id="echoid-s1829" xml:space="preserve">Tunc autem cir-
              <lb/>
            culus maximus parallelo cuiuis neque ęquidiſtat, neque eum tangit, neque ſecat, quando declinatio pa-
              <lb/>
            ralleli maior eſt complemento altitudinis poli ſupra circulum maximum: </s>
            <s xml:id="echoid-s1830" xml:space="preserve">Vel quando cõplementum de-
              <lb/>
            clinationis paralleli minus eſt altitudine poli ſupra maximum circulum, vt ex figura manifeſtum eſt.</s>
            <s xml:id="echoid-s1831" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
        </div>
        <div xml:id="echoid-div97" type="section" level="1" n="31">
          <head xml:id="echoid-head34" xml:space="preserve">PROBLEMA 2. PROPOSITIO 8.</head>
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            <s xml:id="echoid-s1832" xml:space="preserve">DATO cono, & </s>
            <s xml:id="echoid-s1833" xml:space="preserve">diametro conicæ ſectionis, ipſam conicam ſe-
              <lb/>
            ctionem in plano deſcribere.</s>
            <s xml:id="echoid-s1834" xml:space="preserve"/>
          </p>
          <figure number="24">
            <image file="0046-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-01"/>
          </figure>
          <note position="left" xml:space="preserve">30</note>
          <figure number="25">
            <image file="0046-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-02"/>
          </figure>
          <note position="left" xml:space="preserve">40</note>
          <figure number="26">
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          <note position="left" xml:space="preserve">50</note>
          <figure number="27">
            <image file="0046-04" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0046-04"/>
          </figure>
          <p>
            <s xml:id="echoid-s1835" xml:space="preserve">SIT datus conus A B C, qui ſecetur plano per axem faciente, per propoſ. </s>
            <s xml:id="echoid-s1836" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1837" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1838" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1839" xml:space="preserve">Apoll. </s>
            <s xml:id="echoid-s1840" xml:space="preserve">trian-
              <lb/>
              <note position="left" xlink:label="note-0046-07" xlink:href="note-0046-07a" xml:space="preserve">Qua ratione co
                <lb/>
              nica ſectio, cu-
                <lb/>
              ius diameter in
                <lb/>
              cono data ſit,
                <lb/>
              deſcribatur in
                <lb/>
              plano.</note>
            gulum per axem A B C; </s>
            <s xml:id="echoid-s1841" xml:space="preserve">ſecetur autem & </s>
            <s xml:id="echoid-s1842" xml:space="preserve">alio plano faciente vel Parabolen, vel Hyperbolen, vel
              <lb/>
            Ellipſim, cuius diameter D E, æquidiſtans quidem trianguli lateri A C, in Parabola, ſecans verò
              <lb/>
            idem latus A C, productum ſupra verticem A, in Hyperbola, vel intra conum, ſiue hoc fiat ſupra</s>
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