Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div805" type="section" level="1" n="276">
          <pb o="281" file="311" n="311" rhead="LIBER SEXTVS."/>
          <p>
            <s xml:id="echoid-s13104" xml:space="preserve">
              <emph style="sc">Primvm</emph>
            expuncto 239. </s>
            <s xml:id="echoid-s13105" xml:space="preserve">ſubtraho cubum 216. </s>
            <s xml:id="echoid-s13106" xml:space="preserve">qui eſt maximus in eo con-
              <lb/>
              <note position="right" xlink:label="note-311-01" xlink:href="note-311-01a" xml:space="preserve">Cubicæ radi-
                <lb/>
              cis extractio.
                <lb/>
              radix 621.</note>
            tentus, cuius radicem 6. </s>
            <s xml:id="echoid-s13107" xml:space="preserve">ſcribo in Quotiente ad marginem. </s>
            <s xml:id="echoid-s13108" xml:space="preserve">Et quia relinquitur
              <lb/>
            numerus 23. </s>
            <s xml:id="echoid-s13109" xml:space="preserve">erit ſequens punctum 23483.</s>
            <s xml:id="echoid-s13110" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13111" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            paro diuiſorem hocmodo. </s>
            <s xml:id="echoid-s13112" xml:space="preserve">Supra radicem inuen-
              <lb/>
            tam 6. </s>
            <s xml:id="echoid-s13113" xml:space="preserve">pono eius quadratum 36. </s>
            <s xml:id="echoid-s13114" xml:space="preserve">Et ad dextram colloco duos nu-
              <lb/>
              <note position="right" xlink:label="note-311-02" xlink:href="note-311-02a" xml:space="preserve">
                <lb/>
              36--300
                <lb/>
              6-- 30
                <lb/>
              </note>
            meros peculiares radicis cubicæ, nimirum 300. </s>
            <s xml:id="echoid-s13115" xml:space="preserve">& </s>
            <s xml:id="echoid-s13116" xml:space="preserve">30. </s>
            <s xml:id="echoid-s13117" xml:space="preserve">vt hic vides.
              <lb/>
            </s>
            <s xml:id="echoid-s13118" xml:space="preserve">Multiplico ſuperiores duos numeros 36. </s>
            <s xml:id="echoid-s13119" xml:space="preserve">& </s>
            <s xml:id="echoid-s13120" xml:space="preserve">300. </s>
            <s xml:id="echoid-s13121" xml:space="preserve">inter ſe, & </s>
            <s xml:id="echoid-s13122" xml:space="preserve">pro-
              <lb/>
            ducto 10800. </s>
            <s xml:id="echoid-s13123" xml:space="preserve">addo productum 180. </s>
            <s xml:id="echoid-s13124" xml:space="preserve">ex multiplicatione numerorum inferiorũ
              <lb/>
            6. </s>
            <s xml:id="echoid-s13125" xml:space="preserve">& </s>
            <s xml:id="echoid-s13126" xml:space="preserve">30. </s>
            <s xml:id="echoid-s13127" xml:space="preserve">inter ſe. </s>
            <s xml:id="echoid-s13128" xml:space="preserve">Nam ſumma 10980. </s>
            <s xml:id="echoid-s13129" xml:space="preserve">erit Diuiſor. </s>
            <s xml:id="echoid-s13130" xml:space="preserve">Satis etiam eſſet productus
              <lb/>
            ex duobus ſuperioribus inter ſe multiplicatis, nimirum 10800. </s>
            <s xml:id="echoid-s13131" xml:space="preserve">pro Diuiſore. </s>
            <s xml:id="echoid-s13132" xml:space="preserve">
              <lb/>
            quodin alijs extractionibus intelligendum quoque eſt. </s>
            <s xml:id="echoid-s13133" xml:space="preserve">Diuido ergo punctum
              <lb/>
            meum 23483. </s>
            <s xml:id="echoid-s13134" xml:space="preserve">per diuiſoreminuentum 10980. </s>
            <s xml:id="echoid-s13135" xml:space="preserve">& </s>
            <s xml:id="echoid-s13136" xml:space="preserve">Quotientem 2. </s>
            <s xml:id="echoid-s13137" xml:space="preserve">ſcribo poſt fi-
              <lb/>
            guram 6. </s>
            <s xml:id="echoid-s13138" xml:space="preserve">prius inuentam. </s>
            <s xml:id="echoid-s13139" xml:space="preserve">Pingo poſt hæc figuram huiuſmodi. </s>
            <s xml:id="echoid-s13140" xml:space="preserve">Ad dextram
              <lb/>
            numerorum 36. </s>
            <s xml:id="echoid-s13141" xml:space="preserve">& </s>
            <s xml:id="echoid-s13142" xml:space="preserve">300. </s>
            <s xml:id="echoid-s13143" xml:space="preserve">colloco inuentam figuram 2. </s>
            <s xml:id="echoid-s13144" xml:space="preserve">& </s>
            <s xml:id="echoid-s13145" xml:space="preserve">infra
              <lb/>
            eam eius quadratum 4. </s>
            <s xml:id="echoid-s13146" xml:space="preserve">& </s>
            <s xml:id="echoid-s13147" xml:space="preserve">ſub hoc cubum eiuſdem 8. </s>
            <s xml:id="echoid-s13148" xml:space="preserve">Nam ſi
              <lb/>
              <note position="right" xlink:label="note-311-03" xlink:href="note-311-03a" xml:space="preserve">
                <lb/>
              36--300--2.
                <lb/>
              6-- 30--4.
                <lb/>
              8.
                <lb/>
              </note>
            tam ſuperiores tres numeri 36. </s>
            <s xml:id="echoid-s13149" xml:space="preserve">300. </s>
            <s xml:id="echoid-s13150" xml:space="preserve">& </s>
            <s xml:id="echoid-s13151" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13152" xml:space="preserve">quam inferiores tres
              <lb/>
            6. </s>
            <s xml:id="echoid-s13153" xml:space="preserve">30. </s>
            <s xml:id="echoid-s13154" xml:space="preserve">& </s>
            <s xml:id="echoid-s13155" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13156" xml:space="preserve">inter ſe multiplicentur, & </s>
            <s xml:id="echoid-s13157" xml:space="preserve">productis 21600. </s>
            <s xml:id="echoid-s13158" xml:space="preserve">& </s>
            <s xml:id="echoid-s13159" xml:space="preserve">720.
              <lb/>
            </s>
            <s xml:id="echoid-s13160" xml:space="preserve">addatur cubus 8. </s>
            <s xml:id="echoid-s13161" xml:space="preserve">fiet numerus 22328. </s>
            <s xml:id="echoid-s13162" xml:space="preserve">quem ſi ex meo puncto
              <lb/>
            23483. </s>
            <s xml:id="echoid-s13163" xml:space="preserve">ſubtraham, remanent 1155. </s>
            <s xml:id="echoid-s13164" xml:space="preserve">atque adeo punctum ſequens erit 1155190.</s>
            <s xml:id="echoid-s13165" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13166" xml:space="preserve">
              <emph style="sc">Paro</emph>
            iam alium diuiſorem hocpacto. </s>
            <s xml:id="echoid-s13167" xml:space="preserve">Supra 62. </s>
            <s xml:id="echoid-s13168" xml:space="preserve">radicem hactenus inuen-
              <lb/>
            tam ſcribo eius quadratum 3844. </s>
            <s xml:id="echoid-s13169" xml:space="preserve">& </s>
            <s xml:id="echoid-s13170" xml:space="preserve">ad dextram eoſdem nu-
              <lb/>
            meros peculiares 300. </s>
            <s xml:id="echoid-s13171" xml:space="preserve">& </s>
            <s xml:id="echoid-s13172" xml:space="preserve">30. </s>
            <s xml:id="echoid-s13173" xml:space="preserve">Multiplicatio duorum ſuperio-
              <lb/>
              <note position="right" xlink:label="note-311-04" xlink:href="note-311-04a" xml:space="preserve">
                <lb/>
              3844--300.
                <lb/>
              62-- 30.
                <lb/>
              </note>
            rum inter ſefacit diuiſorem 1153200. </s>
            <s xml:id="echoid-s13174" xml:space="preserve">per quem ſi diuidatur pũ-
              <lb/>
            ctum 1155190. </s>
            <s xml:id="echoid-s13175" xml:space="preserve">fit Quotiens 1. </s>
            <s xml:id="echoid-s13176" xml:space="preserve">poſt alias duas figuras 62. </s>
            <s xml:id="echoid-s13177" xml:space="preserve">ſcri-
              <lb/>
            bendus. </s>
            <s xml:id="echoid-s13178" xml:space="preserve">Pingo iam figuram talem. </s>
            <s xml:id="echoid-s13179" xml:space="preserve">Ad dextram numero-
              <lb/>
            rum 3844. </s>
            <s xml:id="echoid-s13180" xml:space="preserve">& </s>
            <s xml:id="echoid-s13181" xml:space="preserve">300. </s>
            <s xml:id="echoid-s13182" xml:space="preserve">pono figuram 1. </s>
            <s xml:id="echoid-s13183" xml:space="preserve">proximè inuentam, & </s>
            <s xml:id="echoid-s13184" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-311-05" xlink:href="note-311-05a" xml:space="preserve">
                <lb/>
              3844--300--1.
                <lb/>
              62-- 30--1.
                <lb/>
              1.
                <lb/>
              </note>
            infra eam eius quadratum 1. </s>
            <s xml:id="echoid-s13185" xml:space="preserve">& </s>
            <s xml:id="echoid-s13186" xml:space="preserve">ſub hoc eiuſdem cubum. </s>
            <s xml:id="echoid-s13187" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s13188" xml:space="preserve">Nam ſi tam tres ſuperiores numeri 3844.</s>
            <s xml:id="echoid-s13189" xml:space="preserve">300. </s>
            <s xml:id="echoid-s13190" xml:space="preserve">& </s>
            <s xml:id="echoid-s13191" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13192" xml:space="preserve">quam
              <lb/>
            inferiores tres 62. </s>
            <s xml:id="echoid-s13193" xml:space="preserve">30. </s>
            <s xml:id="echoid-s13194" xml:space="preserve">& </s>
            <s xml:id="echoid-s13195" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13196" xml:space="preserve">inter ſe multiplicentur, & </s>
            <s xml:id="echoid-s13197" xml:space="preserve">pro-
              <lb/>
            ductis 1153200. </s>
            <s xml:id="echoid-s13198" xml:space="preserve">& </s>
            <s xml:id="echoid-s13199" xml:space="preserve">1860. </s>
            <s xml:id="echoid-s13200" xml:space="preserve">addatur cubus 1. </s>
            <s xml:id="echoid-s13201" xml:space="preserve">fiet numerus 1155061. </s>
            <s xml:id="echoid-s13202" xml:space="preserve">quem ſi ex meo
              <lb/>
            puncto 1155190. </s>
            <s xml:id="echoid-s13203" xml:space="preserve">demam, remanent 129. </s>
            <s xml:id="echoid-s13204" xml:space="preserve">Eſt ergo abſoluta extractio, radixque
              <lb/>
            inuenta eſt 621. </s>
            <s xml:id="echoid-s13205" xml:space="preserve">quæ in ſe cubice multiplicata procreatnumerum 239483061. </s>
            <s xml:id="echoid-s13206" xml:space="preserve">cui
              <lb/>
            ſi adijciatur reſiduum 129. </s>
            <s xml:id="echoid-s13207" xml:space="preserve">coflabitur numerus propoſitus 239483190.</s>
            <s xml:id="echoid-s13208" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div809" type="section" level="1" n="277">
          <head xml:id="echoid-head303" xml:space="preserve">EXTRACTIO RADICIS
            <lb/>
          Surdeſolidæ.</head>
          <p>
            <s xml:id="echoid-s13209" xml:space="preserve">
              <emph style="sc">Sit</emph>
            numerus 1039589621. </s>
            <s xml:id="echoid-s13210" xml:space="preserve">cuius radix ſurdeſolida quæritur.</s>
            <s xml:id="echoid-s13211" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13212" xml:space="preserve">. </s>
            <s xml:id="echoid-s13213" xml:space="preserve">.</s>
            <s xml:id="echoid-s13214" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Surdeſolidæ
            <lb/>
          ràdicis extra-
            <lb/>
          ctio
            <lb/>
          radix 63.</note>
          <p>
            <s xml:id="echoid-s13215" xml:space="preserve">
              <emph style="sc">Primvm</emph>
            à puncto 10395. </s>
            <s xml:id="echoid-s13216" xml:space="preserve">ſubtraho maximum ſurdeſolidum 7776. </s>
            <s xml:id="echoid-s13217" xml:space="preserve">in eo in-
              <lb/>
            cluſum, cuius radicem 6. </s>
            <s xml:id="echoid-s13218" xml:space="preserve">ſcribo in margine ꝓ Quotiente: </s>
            <s xml:id="echoid-s13219" xml:space="preserve">& </s>
            <s xml:id="echoid-s13220" xml:space="preserve">quia numerus relin-
              <lb/>
            quitur 2619. </s>
            <s xml:id="echoid-s13221" xml:space="preserve">ideo punctum ſequens erit 261989621.</s>
            <s xml:id="echoid-s13222" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13223" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            paro diuiſorem hoc modo. </s>
            <s xml:id="echoid-s13224" xml:space="preserve">Supra radicem inuentam 6. </s>
            <s xml:id="echoid-s13225" xml:space="preserve">ſcribo e-
              <lb/>
            ius quadratum 36. </s>
            <s xml:id="echoid-s13226" xml:space="preserve">& </s>
            <s xml:id="echoid-s13227" xml:space="preserve">ſupra hunc eiuſdem cubum 216. </s>
            <s xml:id="echoid-s13228" xml:space="preserve">& </s>
            <s xml:id="echoid-s13229" xml:space="preserve">ſupra hunc eiuſdem
              <lb/>
            Zenſizenſum, vel quadrati quadratum 1296: </s>
            <s xml:id="echoid-s13230" xml:space="preserve">ita vt conſtituatur </s>
          </p>
        </div>
      </text>
    </echo>
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