Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div478" type="section" level="1" n="160">
          <pb o="232" file="268" n="269" rhead="Comment. in II. Cap. Sphæræ"/>
        </div>
        <div xml:id="echoid-div479" type="section" level="1" n="161">
          <head xml:id="echoid-head167" xml:space="preserve">VSVS TABVLARVM PRÆCEDENTIVM.</head>
          <p>
            <s xml:id="echoid-s9401" xml:space="preserve">
              <emph style="sc">Si</emph>
            gradus in horas ſunt commutandi, accipiendi erunt gradus in priori ta-
              <lb/>
              <note position="left" xlink:label="note-268-01" xlink:href="note-268-01a" xml:space="preserve">Qua ratio-
                <lb/>
              ne ex præce
                <lb/>
              dentibus ta
                <lb/>
              bulis redu-
                <lb/>
              cantur gra
                <lb/>
              dus acminu
                <lb/>
              ta ad hora,
                <lb/>
              & co
                <unsure/>
              tra.</note>
            bella ſub titulo G. </s>
            <s xml:id="echoid-s9402" xml:space="preserve">& </s>
            <s xml:id="echoid-s9403" xml:space="preserve">mox duæ ſubſequentes columnę iudicabunt horas, minu
              <lb/>
            taq́; </s>
            <s xml:id="echoid-s9404" xml:space="preserve">horarum, quæ gradibus acceptis debentur. </s>
            <s xml:id="echoid-s9405" xml:space="preserve">Sic uides gradibus 4. </s>
            <s xml:id="echoid-s9406" xml:space="preserve">reſponde
              <lb/>
            re min. </s>
            <s xml:id="echoid-s9407" xml:space="preserve">16. </s>
            <s xml:id="echoid-s9408" xml:space="preserve">horæ. </s>
            <s xml:id="echoid-s9409" xml:space="preserve">Item gradib. </s>
            <s xml:id="echoid-s9410" xml:space="preserve">27. </s>
            <s xml:id="echoid-s9411" xml:space="preserve">horam 1. </s>
            <s xml:id="echoid-s9412" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9413" xml:space="preserve">48. </s>
            <s xml:id="echoid-s9414" xml:space="preserve">Item gradibus 45. </s>
            <s xml:id="echoid-s9415" xml:space="preserve">horas 3.
              <lb/>
            </s>
            <s xml:id="echoid-s9416" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9417" xml:space="preserve">0. </s>
            <s xml:id="echoid-s9418" xml:space="preserve">Item gradibus 250. </s>
            <s xml:id="echoid-s9419" xml:space="preserve">horas 86. </s>
            <s xml:id="echoid-s9420" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9421" xml:space="preserve">40. </s>
            <s xml:id="echoid-s9422" xml:space="preserve">&</s>
            <s xml:id="echoid-s9423" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9424" xml:space="preserve">Quod ſi numerus graduum
              <lb/>
            præciſe in prædicta tabella non reperiatur, accipiendus erit numerus proxi-
              <lb/>
            me minor, cum horis, ac minutis reſpondentibus: </s>
            <s xml:id="echoid-s9425" xml:space="preserve">Deinde reliqui gradus ite-
              <lb/>
            rum ſumendi cum horis & </s>
            <s xml:id="echoid-s9426" xml:space="preserve">minutis correſpondentibus: </s>
            <s xml:id="echoid-s9427" xml:space="preserve">Atque tandem poſte-
              <lb/>
            riores horæ, ac minuta cum prioribus coniungenda. </s>
            <s xml:id="echoid-s9428" xml:space="preserve">Vt ſi ſcire lubeat, quot
              <unsure/>
              <lb/>
            horæ reſpondeant gradibus 215. </s>
            <s xml:id="echoid-s9429" xml:space="preserve">Accipiendæ erunt hocæ 14. </s>
            <s xml:id="echoid-s9430" xml:space="preserve">reſpondentes gra
              <lb/>
            dibus 210. </s>
            <s xml:id="echoid-s9431" xml:space="preserve">Deinde ſumenda min. </s>
            <s xml:id="echoid-s9432" xml:space="preserve">20. </s>
            <s xml:id="echoid-s9433" xml:space="preserve">reſpondentia reliquis gradibus 5. </s>
            <s xml:id="echoid-s9434" xml:space="preserve">Atque
              <lb/>
            ita gradibus 215. </s>
            <s xml:id="echoid-s9435" xml:space="preserve">debentur horæ 14. </s>
            <s xml:id="echoid-s9436" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9437" xml:space="preserve">20. </s>
            <s xml:id="echoid-s9438" xml:space="preserve">& </s>
            <s xml:id="echoid-s9439" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s9440" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9441" xml:space="preserve">
              <emph style="sc">Si</emph>
            vero minuta, uel ſecunda graduum in horas ſunt conuertenda, accipien
              <lb/>
            da erunt minuta, uel ſecunda graduum, ſupra titulos M, vel S, & </s>
            <s xml:id="echoid-s9442" xml:space="preserve">illico ſequen
              <lb/>
            tes duæ c
              <unsure/>
            olumnæ oſtendent minuta, ſecunda, uel tertia horarum, vt literæ,
              <lb/>
            quæ ad pedem tabellæ ſunt poſitæ, indicant. </s>
            <s xml:id="echoid-s9443" xml:space="preserve">Hac ratione cernis, minutis 56.
              <lb/>
            </s>
            <s xml:id="echoid-s9444" xml:space="preserve">vnius gradus reſpondere min. </s>
            <s xml:id="echoid-s9445" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9446" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9447" xml:space="preserve">44. </s>
            <s xml:id="echoid-s9448" xml:space="preserve">unius horæ. </s>
            <s xml:id="echoid-s9449" xml:space="preserve">Item ſecundis 25. </s>
            <s xml:id="echoid-s9450" xml:space="preserve">unius
              <lb/>
            gradus deberi ſec. </s>
            <s xml:id="echoid-s9451" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9452" xml:space="preserve">ter. </s>
            <s xml:id="echoid-s9453" xml:space="preserve">40. </s>
            <s xml:id="echoid-s9454" xml:space="preserve">unius horæ.</s>
            <s xml:id="echoid-s9455" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9456" xml:space="preserve">
              <emph style="sc">Havd</emph>
            aliter ex poſſeriori tabella reducentur horæ, minuta, ſecunda, ac
              <lb/>
            terria horatum ad gradus, minuta ſecunda, & </s>
            <s xml:id="echoid-s9457" xml:space="preserve">tertia, &</s>
            <s xml:id="echoid-s9458" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9459" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9460" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi huiuſcemodi@ tabellis u ti quis noluerit, reducentur gradus, mi-
              <lb/>
              <note position="left" xlink:label="note-268-02" xlink:href="note-268-02a" xml:space="preserve">Quo pacto
                <lb/>
              ex grad &
                <lb/>
              min. fiant
                <lb/>
              horæ, &
                <lb/>
              min. & con
                <lb/>
              tra, qũo ex
                <lb/>
              hor. & min.
                <lb/>
              fiant grad.
                <lb/>
              & minu@a.</note>
            nuta, &</s>
            <s xml:id="echoid-s9461" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9462" xml:space="preserve">hoc modo. </s>
            <s xml:id="echoid-s9463" xml:space="preserve">Multiplicentur gradus, minuta, ſecunda, &</s>
            <s xml:id="echoid-s9464" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9465" xml:space="preserve">per 4. </s>
            <s xml:id="echoid-s9466" xml:space="preserve">Nam
              <lb/>
            producti numeri dabunt partes temporis proxime minores. </s>
            <s xml:id="echoid-s9467" xml:space="preserve">Vt productus nu-
              <lb/>
            merus ex gradibus dabit minuta hora@um, productus uero numerus ex minu-
              <lb/>
            tis graduum dabit ſecunda horarum, &</s>
            <s xml:id="echoid-s9468" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9469" xml:space="preserve">E X E M P L V M. </s>
            <s xml:id="echoid-s9470" xml:space="preserve">Si grad. </s>
            <s xml:id="echoid-s9471" xml:space="preserve">9. </s>
            <s xml:id="echoid-s9472" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9473" xml:space="preserve">40.
              <lb/>
            </s>
            <s xml:id="echoid-s9474" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9475" xml:space="preserve">20. </s>
            <s xml:id="echoid-s9476" xml:space="preserve">multiplicentur per 4. </s>
            <s xml:id="echoid-s9477" xml:space="preserve">producentur hor. </s>
            <s xml:id="echoid-s9478" xml:space="preserve">o minut. </s>
            <s xml:id="echoid-s9479" xml:space="preserve">36. </s>
            <s xml:id="echoid-s9480" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9481" xml:space="preserve">160. </s>
            <s xml:id="echoid-s9482" xml:space="preserve">ter. </s>
            <s xml:id="echoid-s9483" xml:space="preserve">80. </s>
            <s xml:id="echoid-s9484" xml:space="preserve">hoc
              <lb/>
            eſt, hor. </s>
            <s xml:id="echoid-s9485" xml:space="preserve">0. </s>
            <s xml:id="echoid-s9486" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9487" xml:space="preserve">38. </s>
            <s xml:id="echoid-s9488" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9489" xml:space="preserve">41. </s>
            <s xml:id="echoid-s9490" xml:space="preserve">ter. </s>
            <s xml:id="echoid-s9491" xml:space="preserve">20. </s>
            <s xml:id="echoid-s9492" xml:space="preserve">Rurſus ſi grad. </s>
            <s xml:id="echoid-s9493" xml:space="preserve">20. </s>
            <s xml:id="echoid-s9494" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9495" xml:space="preserve">40. </s>
            <s xml:id="echoid-s9496" xml:space="preserve">multiplicen-
              <lb/>
            tur per 4. </s>
            <s xml:id="echoid-s9497" xml:space="preserve">gig@entur hor. </s>
            <s xml:id="echoid-s9498" xml:space="preserve">0. </s>
            <s xml:id="echoid-s9499" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9500" xml:space="preserve">80. </s>
            <s xml:id="echoid-s9501" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9502" xml:space="preserve">160. </s>
            <s xml:id="echoid-s9503" xml:space="preserve">hoc eſt, hor. </s>
            <s xml:id="echoid-s9504" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9505" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9506" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9507" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9508" xml:space="preserve">40. </s>
            <s xml:id="echoid-s9509" xml:space="preserve">atque
              <lb/>
            ita de cæteris.</s>
            <s xml:id="echoid-s9510" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9511" xml:space="preserve">
              <emph style="sc">Iam</emph>
            uero, ſi horæ, minuta, &</s>
            <s xml:id="echoid-s9512" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9513" xml:space="preserve">diuidantur per 4. </s>
            <s xml:id="echoid-s9514" xml:space="preserve">producentur partes Ae-
              <lb/>
            quatoris proxime maior@@. </s>
            <s xml:id="echoid-s9515" xml:space="preserve">Vt ex tertijs horarum producentur ſecunda gra-
              <lb/>
            duum; </s>
            <s xml:id="echoid-s9516" xml:space="preserve">ex ſecundis horarum producentur minuta graduum; </s>
            <s xml:id="echoid-s9517" xml:space="preserve">ex minutis hora-
              <lb/>
            rum producentur gradus; </s>
            <s xml:id="echoid-s9518" xml:space="preserve">& </s>
            <s xml:id="echoid-s9519" xml:space="preserve">ex horis deniq; </s>
            <s xml:id="echoid-s9520" xml:space="preserve">producentur partes unius partis
              <lb/>
            Aequatoris, quæ comprehendat grad. </s>
            <s xml:id="echoid-s9521" xml:space="preserve">60. </s>
            <s xml:id="echoid-s9522" xml:space="preserve">quemadmodum, & </s>
            <s xml:id="echoid-s9523" xml:space="preserve">unus gradus com
              <lb/>
            plectitur min. </s>
            <s xml:id="echoid-s9524" xml:space="preserve">60. </s>
            <s xml:id="echoid-s9525" xml:space="preserve">E X E M P L V M. </s>
            <s xml:id="echoid-s9526" xml:space="preserve">Si hor. </s>
            <s xml:id="echoid-s9527" xml:space="preserve">0. </s>
            <s xml:id="echoid-s9528" xml:space="preserve">minu. </s>
            <s xml:id="echoid-s9529" xml:space="preserve">38. </s>
            <s xml:id="echoid-s9530" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9531" xml:space="preserve">41. </s>
            <s xml:id="echoid-s9532" xml:space="preserve">ter. </s>
            <s xml:id="echoid-s9533" xml:space="preserve">20. </s>
            <s xml:id="echoid-s9534" xml:space="preserve">diui-
              <lb/>
            dantur per 4. </s>
            <s xml:id="echoid-s9535" xml:space="preserve">producentur partes 0. </s>
            <s xml:id="echoid-s9536" xml:space="preserve">( quatum quælibet complectatur grad.
              <lb/>
            </s>
            <s xml:id="echoid-s9537" xml:space="preserve">60.) </s>
            <s xml:id="echoid-s9538" xml:space="preserve">g@ad. </s>
            <s xml:id="echoid-s9539" xml:space="preserve">9 {1/2}. </s>
            <s xml:id="echoid-s9540" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9541" xml:space="preserve">10 {1/4}. </s>
            <s xml:id="echoid-s9542" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9543" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9544" xml:space="preserve">hoc eſt, part. </s>
            <s xml:id="echoid-s9545" xml:space="preserve">0. </s>
            <s xml:id="echoid-s9546" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s9547" xml:space="preserve">9. </s>
            <s xml:id="echoid-s9548" xml:space="preserve">minu. </s>
            <s xml:id="echoid-s9549" xml:space="preserve">40. </s>
            <s xml:id="echoid-s9550" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9551" xml:space="preserve">20. </s>
            <s xml:id="echoid-s9552" xml:space="preserve">Nam
              <lb/>
            grad. </s>
            <s xml:id="echoid-s9553" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s9554" xml:space="preserve">facit min. </s>
            <s xml:id="echoid-s9555" xml:space="preserve">30. </s>
            <s xml:id="echoid-s9556" xml:space="preserve">quæ cum min. </s>
            <s xml:id="echoid-s9557" xml:space="preserve">10. </s>
            <s xml:id="echoid-s9558" xml:space="preserve">faciunt min. </s>
            <s xml:id="echoid-s9559" xml:space="preserve">40. </s>
            <s xml:id="echoid-s9560" xml:space="preserve">Item min. </s>
            <s xml:id="echoid-s9561" xml:space="preserve">{1/4}. </s>
            <s xml:id="echoid-s9562" xml:space="preserve">facit ſec. </s>
            <s xml:id="echoid-s9563" xml:space="preserve">
              <lb/>
            15. </s>
            <s xml:id="echoid-s9564" xml:space="preserve">quæ cum ſec. </s>
            <s xml:id="echoid-s9565" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9566" xml:space="preserve">faciunt ſec. </s>
            <s xml:id="echoid-s9567" xml:space="preserve">20. </s>
            <s xml:id="echoid-s9568" xml:space="preserve">Rurſus ſi hor. </s>
            <s xml:id="echoid-s9569" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9570" xml:space="preserve">minu. </s>
            <s xml:id="echoid-s9571" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9572" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s9573" xml:space="preserve">40. </s>
            <s xml:id="echoid-s9574" xml:space="preserve">diuidantur
              <lb/>
            per 4. </s>
            <s xml:id="echoid-s9575" xml:space="preserve">prouenient par. </s>
            <s xml:id="echoid-s9576" xml:space="preserve">{1/4}. </s>
            <s xml:id="echoid-s9577" xml:space="preserve">(ex illis, quarum quælibet complectitur grad. </s>
            <s xml:id="echoid-s9578" xml:space="preserve">60.) </s>
            <s xml:id="echoid-s9579" xml:space="preserve">
              <lb/>
            grad. </s>
            <s xml:id="echoid-s9580" xml:space="preserve">5 {1/2}. </s>
            <s xml:id="echoid-s9581" xml:space="preserve">min. </s>
            <s xml:id="echoid-s9582" xml:space="preserve">10. </s>
            <s xml:id="echoid-s9583" xml:space="preserve">hoc eſt, grad. </s>
            <s xml:id="echoid-s9584" xml:space="preserve">20. </s>
            <s xml:id="echoid-s9585" xml:space="preserve">minu. </s>
            <s xml:id="echoid-s9586" xml:space="preserve">40. </s>
            <s xml:id="echoid-s9587" xml:space="preserve">propterea quòd part. </s>
            <s xml:id="echoid-s9588" xml:space="preserve">{1/4}. </s>
            <s xml:id="echoid-s9589" xml:space="preserve">(ex illis,
              <lb/>
            quarum quælibet grad. </s>
            <s xml:id="echoid-s9590" xml:space="preserve">60. </s>
            <s xml:id="echoid-s9591" xml:space="preserve">continer) facir grad. </s>
            <s xml:id="echoid-s9592" xml:space="preserve">15. </s>
            <s xml:id="echoid-s9593" xml:space="preserve">quæ cum grad. </s>
            <s xml:id="echoid-s9594" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9595" xml:space="preserve">faciunt gr. </s>
            <s xml:id="echoid-s9596" xml:space="preserve">
              <lb/>
            20. </s>
            <s xml:id="echoid-s9597" xml:space="preserve">Item grad. </s>
            <s xml:id="echoid-s9598" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s9599" xml:space="preserve">facit mi@u. </s>
            <s xml:id="echoid-s9600" xml:space="preserve">30. </s>
            <s xml:id="echoid-s9601" xml:space="preserve">quæ cum min. </s>
            <s xml:id="echoid-s9602" xml:space="preserve">10. </s>
            <s xml:id="echoid-s9603" xml:space="preserve">faciunt min. </s>
            <s xml:id="echoid-s9604" xml:space="preserve">40. </s>
            <s xml:id="echoid-s9605" xml:space="preserve">atque ita
              <lb/>
            de cæteris.</s>
            <s xml:id="echoid-s9606" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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