Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of contents

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[41.] COMMENTARIVS.
[42.] COMMENTARIVS.
[43.] COMMENTARIVS.
[44.] DIVISIO SPHÆRÆ MVNDI.
[45.] COMMENTARIVS.
[46.] COMMENTARIVS.
[47.] DE CIRCVLIS SPHAERAE.
[48.] COMMENTARIVS.
[49.] COMMENTARIVS.
[50.] DE NVMERO ET ORDINE ELEMENTORVM.
[51.] COMMENTARIVS.
[52.] COMMENTARIVS.
[53.] COMMENTARIVS,
[54.] DENVMERO ORBIVM CAELESTIVM.
[55.] DE MOTIBVS ORBIVM CÆLESTIVM.
[56.] DEPERIODIS MOTVVM CÆLESTIVM.
[57.] QVOMODO DEPREHENSVM SIT OMNES cælos ſimpliciter ab ortu in occaſum moueri.
[58.] QVA RATIONE COLLECTVS SIT MOTVS Cælorum ab occaſu in ortum.
[59.] QVA INDVSTRIA CAELOS INFERIORES ab Occaſu in Ortum ſuper diuerſos polos à polis mundi moueri obſeruatum ſit.
[60.] PROPTER QV AE PHAENOMENA ASTROMI motum trepidationis ſtellis fixis attribuerint.
[61.] DE ORDINE SPÆRARVM CÆLESTIVM.
[62.] COELVM MOVERI AB ORTV IN OCCASVM.
[63.] COMMENTARIVS.
[64.] COMMENTARIVS.
[65.] COELVM ESSE FIGVRÆ SPHÆRICÆ.
[66.] COMMENT ARIVS,
[67.] COMMENTARIVS.
[68.] DE FIGVRIS ISOPERIMETRIS. DEFINITIONES. I.
[70.] III.
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        <div xml:id="echoid-div128" type="section" level="1" n="50">
          <p>
            <s xml:id="echoid-s1671" xml:space="preserve">
              <pb o="35" file="071" n="72" rhead="Ioan. de Sacro Boſco."/>
            hoc eſt, unitates 127. </s>
            <s xml:id="echoid-s1672" xml:space="preserve">in illis continentur. </s>
            <s xml:id="echoid-s1673" xml:space="preserve">Sed hac de plura in noſtra Arithme-
              <lb/>
              <note position="right" xlink:label="note-071-01" xlink:href="note-071-01a" xml:space="preserve">Qũo ſcia-
                <lb/>
              tur ſumma
                <unsure/>
                <lb/>
              quorcũque
                <lb/>
              numerorũ
                <lb/>
              proportie
                <unsure/>
              -
                <lb/>
              nis duplæ
                <lb/>
              ab 1
                <unsure/>
              . incip@
                <lb/>
              entis.</note>
            tica Practica ſcripſimus. </s>
            <s xml:id="echoid-s1674" xml:space="preserve">Exemplum combinationum in ſupradictis quatuor
              <lb/>
            qualitatibus. </s>
            <s xml:id="echoid-s1675" xml:space="preserve">Numeri in dupla proportione iuxta nume rum rerum erunt 4. </s>
            <s xml:id="echoid-s1676" xml:space="preserve">ni
              <lb/>
            mirum 1. </s>
            <s xml:id="echoid-s1677" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1678" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1679" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1680" xml:space="preserve">quorum ſumma eſt 15. </s>
            <s xml:id="echoid-s1681" xml:space="preserve">abiectis ergo 4. </s>
            <s xml:id="echoid-s1682" xml:space="preserve">remanent 11. </s>
            <s xml:id="echoid-s1683" xml:space="preserve">Totigitur
              <lb/>
            modis diuerſis coniungi poterunt quatuor primæ qualitates, uidelicet hæ, ca-
              <lb/>
            liditas, frigiditas: </s>
            <s xml:id="echoid-s1684" xml:space="preserve">caliditas, ſiccitas caliditas, humiditas: </s>
            <s xml:id="echoid-s1685" xml:space="preserve">frigiditas, ſiccitas: </s>
            <s xml:id="echoid-s1686" xml:space="preserve">frigi-
              <lb/>
            ditas, humiditas: </s>
            <s xml:id="echoid-s1687" xml:space="preserve">ſiccitas, humiditas: </s>
            <s xml:id="echoid-s1688" xml:space="preserve">caliditas, ſrigiditas, ſiccitas: </s>
            <s xml:id="echoid-s1689" xml:space="preserve">caliditas, ſicci-
              <lb/>
            tas, humiditas: </s>
            <s xml:id="echoid-s1690" xml:space="preserve">frigiditas, ſiccitas, humiditas: </s>
            <s xml:id="echoid-s1691" xml:space="preserve">caliditas, frigiditas, humiditas: </s>
            <s xml:id="echoid-s1692" xml:space="preserve">& </s>
            <s xml:id="echoid-s1693" xml:space="preserve">
              <lb/>
            demum caliditas, frigiditas, ſiccitas, humiditas. </s>
            <s xml:id="echoid-s1694" xml:space="preserve">Neque fieri poteſt, ut alia com-
              <lb/>
            paratio efficiatur, quæ a omnibus iſtis differat. </s>
            <s xml:id="echoid-s1695" xml:space="preserve">Non. </s>
            <s xml:id="echoid-s1696" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1697" xml:space="preserve">hæ duæ, caliditas, frigidi-
              <lb/>
            tas: </s>
            <s xml:id="echoid-s1698" xml:space="preserve">frigiditas, caliditas, cum ordo tantum mutetur, & </s>
            <s xml:id="echoid-s1699" xml:space="preserve">non res, diſtinctæ eſſe cen
              <lb/>
            ſentur Hac rõne inter quinque res, ut inter quinque prædicabilia, 26. </s>
            <s xml:id="echoid-s1700" xml:space="preserve">poſſunt
              <lb/>
            fieri diuerſæ comparationes. </s>
            <s xml:id="echoid-s1701" xml:space="preserve">Nam ſumma horum numerorum 1. </s>
            <s xml:id="echoid-s1702" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1703" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1704" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1705" xml:space="preserve">16. </s>
            <s xml:id="echoid-s1706" xml:space="preserve">eſt 31.
              <lb/>
            </s>
            <s xml:id="echoid-s1707" xml:space="preserve">Ablatis aũt 5. </s>
            <s xml:id="echoid-s1708" xml:space="preserve">relinquuntur 26. </s>
            <s xml:id="echoid-s1709" xml:space="preserve">Hæc porro regula multum conducit Aſtrolo-
              <lb/>
            gis, ut ſciant oẽs cõiunctiones diuerſas, quæ fieri poſſunt inter ſeptem planetas. </s>
            <s xml:id="echoid-s1710" xml:space="preserve">
              <lb/>
            Iuxta. </s>
            <s xml:id="echoid-s1711" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1712" xml:space="preserve">artificium prædictum coniungi poſſunt, ſeu uariari modis 120. </s>
            <s xml:id="echoid-s1713" xml:space="preserve">quos lõ
              <lb/>
            gũ eſſet recenſere. </s>
            <s xml:id="echoid-s1714" xml:space="preserve">Pari rõne cognoſcetur, quot dictiones ſiue utiles, ſiue inuti
              <lb/>
            les, ex 23. </s>
            <s xml:id="echoid-s1715" xml:space="preserve">literis alphabeti poſſint conſtitui, hoc eſt, quot modis dictæ 13. </s>
            <s xml:id="echoid-s1716" xml:space="preserve">lite-
              <lb/>
            ræ inter ſe coniungi poſſint, ita ut ſemper ſint diuerſæ coniunctiones, ſiue pro-
              <lb/>
            @unciari poſſint, ſiue non. </s>
            <s xml:id="echoid-s1717" xml:space="preserve">Fient em̃ ex 23. </s>
            <s xml:id="echoid-s1718" xml:space="preserve">literis dictiones, ſiue diuerſæ coniun
              <lb/>
            c
              <unsure/>
            tiones, numero 8388584. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">Nam ultimus numerus, uidelicet ui
              <unsure/>
            ceſimus tertius
              <lb/>
            proportionis duplæ eſt, 4194304. </s>
            <s xml:id="echoid-s1720" xml:space="preserve">& </s>
            <s xml:id="echoid-s1721" xml:space="preserve">ideo ſumma omnium numerorum erit
              <lb/>
            8388607. </s>
            <s xml:id="echoid-s1722" xml:space="preserve">Reiectis igitur 23. </s>
            <s xml:id="echoid-s1723" xml:space="preserve">remanent 8388584. </s>
            <s xml:id="echoid-s1724" xml:space="preserve">&</s>
            <s xml:id="echoid-s1725" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1726" xml:space="preserve">Verũ eſt, plures dictiones
              <lb/>
            fieri poſſe, ſiue literarum coniunctiones, ſi literæ in quauis coninctione permu
              <lb/>
            tentur inter ſeſe. </s>
            <s xml:id="echoid-s1727" xml:space="preserve">Vt hoc aggregatum, ſe coniunctio literarum,
              <emph style="sc">Ave</emph>
            , ſex modis
              <lb/>
            uariari põt, uidelicet,
              <emph style="sc">Ave</emph>
            ,
              <emph style="sc">Aev</emph>
            ,
              <emph style="sc">Vae</emph>
            ,
              <emph style="sc">Vea</emph>
            ,
              <emph style="sc">Eva</emph>
            ,
              <emph style="sc">Eav</emph>
            , qui quidem
              <lb/>
            modi ſumpti ſunt à nobis in regula pro una duntaxat coniunctione, quoniam
              <lb/>
            omnes hi modi eaſdem continent literas, quamuis inter ſe locum mutent.</s>
            <s xml:id="echoid-s1728" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1729" xml:space="preserve">
              <emph style="sc">Si</emph>
            vero propoſitus fuerit numerus rerũ, & </s>
            <s xml:id="echoid-s1730" xml:space="preserve">operæpretiũ ſit indagare, quotnã
              <lb/>
              <note position="right" xlink:label="note-071-02" xlink:href="note-071-02a" xml:space="preserve">Quot mo-
                <lb/>
              dis quotcũ
                <lb/>
              que res in-
                <lb/>
              ter ſe poſ
                <lb/>
              ſint cõmu
                <lb/>
              tari, manẽ
                <lb/>
              te ſemper
                <lb/>
              eodem nu
                <lb/>
              mero rerũ</note>
            modis illæ inter ſe poſſint cõmutari, manente tñ ſemper eodẽ numero rerum,
              <lb/>
            id hac conſequeris regula. </s>
            <s xml:id="echoid-s1731" xml:space="preserve">Cape tot numeros in ſerie naturali, quot ſunt res,
              <lb/>
            initio facto ab unitate, & </s>
            <s xml:id="echoid-s1732" xml:space="preserve">illos omnes inter ſe multiplica; </s>
            <s xml:id="echoid-s1733" xml:space="preserve">Procreatus em̃ nume
              <lb/>
            rus oſtendet propoſitum. </s>
            <s xml:id="echoid-s1734" xml:space="preserve">Vt duæ res, v. </s>
            <s xml:id="echoid-s1735" xml:space="preserve">g. </s>
            <s xml:id="echoid-s1736" xml:space="preserve">A, B, duobus modis uariari poſſunt.
              <lb/>
            </s>
            <s xml:id="echoid-s1737" xml:space="preserve">Nam quæuis primũ occupabit locũ, hoc modo, A B, B A, qm̃ hi numeri 1. </s>
            <s xml:id="echoid-s1738" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1739" xml:space="preserve">in-
              <lb/>
            rer ſe multiplicati efficiunt 1. </s>
            <s xml:id="echoid-s1740" xml:space="preserve">Attres res poſsũt ſex modis uariari. </s>
            <s xml:id="echoid-s1741" xml:space="preserve">Nã hi nume
              <lb/>
            ri 1. </s>
            <s xml:id="echoid-s1742" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1743" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1744" xml:space="preserve">multiplicati inter ſe faciũt 6. </s>
            <s xml:id="echoid-s1745" xml:space="preserve">Ratio huius eſt, qm̃ unaquæq; </s>
            <s xml:id="echoid-s1746" xml:space="preserve">res primũ
              <lb/>
            tenebit locũ ſemel, & </s>
            <s xml:id="echoid-s1747" xml:space="preserve">reliquæ duæ bis poſsũt, ut dixi
              <unsure/>
            mus, mutari inter ſeſe. </s>
            <s xml:id="echoid-s1748" xml:space="preserve">Ita
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s1749" xml:space="preserve">quatuor res uigintiquatuor modis uariari poſsũt; </s>
            <s xml:id="echoid-s1750" xml:space="preserve">cũ hi numeri 1. </s>
            <s xml:id="echoid-s1751" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1752" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1753" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1754" xml:space="preserve">
              <lb/>
            inter ſe multiplicati faciãt 24. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">Ratio eſt, quia unaquęq; </s>
            <s xml:id="echoid-s1756" xml:space="preserve">res ſemel primũ occu-
              <lb/>
            pabit locũ, & </s>
            <s xml:id="echoid-s1757" xml:space="preserve">reliquæ tres ſexies, ut diximus, inter ſe uariari poſſunt, Eadem uia
              <lb/>
            colliges 10. </s>
            <s xml:id="echoid-s1758" xml:space="preserve">res poſſe ordinẽ inter ſe uariare modis 36.</s>
            <s xml:id="echoid-s1759" xml:space="preserve">8800. </s>
            <s xml:id="echoid-s1760" xml:space="preserve">ꝙ hi numeri 1. </s>
            <s xml:id="echoid-s1761" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1762" xml:space="preserve">
              <lb/>
            3. </s>
            <s xml:id="echoid-s1763" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1764" xml:space="preserve">5. </s>
            <s xml:id="echoid-s1765" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1766" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1767" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1768" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1769" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1770" xml:space="preserve">inter ſe multiplicati gignant hunc numerũ 3628800. </s>
            <s xml:id="echoid-s1771" xml:space="preserve">Res ue-
              <lb/>
            ro undecim, modis 39916800. </s>
            <s xml:id="echoid-s1772" xml:space="preserve">inter ſe; </s>
            <s xml:id="echoid-s1773" xml:space="preserve">qm̃ hi numeri 1. </s>
            <s xml:id="echoid-s1774" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1776" xml:space="preserve">4. </s>
            <s xml:id="echoid-s1777" xml:space="preserve">5. </s>
            <s xml:id="echoid-s1778" xml:space="preserve">6. </s>
            <s xml:id="echoid-s1779" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1780" xml:space="preserve">8. </s>
            <s xml:id="echoid-s1781" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1782" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1783" xml:space="preserve">11. </s>
            <s xml:id="echoid-s1784" xml:space="preserve">
              <lb/>
            multiplicati inter ſe procreant numerũ prædictũ. </s>
            <s xml:id="echoid-s1785" xml:space="preserve">Poſtquam igitur per docu-
              <lb/>
            mentũ præcedens omnes coniunctiones uigintitriũ literarum alphabeti cogi-
              <lb/>
            tæ fuerint, ſi inquiratur per hanc regulã, quot modis literæ uniuſcuiuſq; </s>
            <s xml:id="echoid-s1786" xml:space="preserve">con-
              <lb/>
            iunctionis inter ſe cõmutari poſſint, habebitur numerus omniũ dictionum uti
              <lb/>
            liũ & </s>
            <s xml:id="echoid-s1787" xml:space="preserve">inutilium, dummodo in una dictione nulla litera bis, uel ter, &</s>
            <s xml:id="echoid-s1788" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1789" xml:space="preserve"/>
          </p>
        </div>
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