Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1135" type="section" level="1" n="417">
          <p>
            <s xml:id="echoid-s18195" xml:space="preserve">
              <pb o="392" file="420" n="420" rhead="GEOME. PRACT. LIB. OCTAVVS."/>
            cando radicis inuentæ quadratum ex eadem tabula excerptum, nimirum 25921.
              <lb/>
            </s>
            <s xml:id="echoid-s18196" xml:space="preserve">per 300. </s>
            <s xml:id="echoid-s18197" xml:space="preserve">qui erit 7776300. </s>
            <s xml:id="echoid-s18198" xml:space="preserve">per quem ſi meum punctum diuido, reperio Quotiẽ-
              <lb/>
            tem 9. </s>
            <s xml:id="echoid-s18199" xml:space="preserve">& </s>
            <s xml:id="echoid-s18200" xml:space="preserve">facta operatione remanent 7295302. </s>
            <s xml:id="echoid-s18201" xml:space="preserve">adeo vt vltimum punctum ſit
              <lb/>
            7295302307</s>
          </p>
          <p>
            <s xml:id="echoid-s18202" xml:space="preserve">
              <emph style="sc">Deniqve</emph>
            paro nouum diuiſorem, multiplicando radicis 1619. </s>
            <s xml:id="echoid-s18203" xml:space="preserve">inuentæ
              <lb/>
            quadratum 2621161. </s>
            <s xml:id="echoid-s18204" xml:space="preserve">per 300. </s>
            <s xml:id="echoid-s18205" xml:space="preserve">qui erit 786348300. </s>
            <s xml:id="echoid-s18206" xml:space="preserve">per quem ſi vltimum meum
              <lb/>
            punctum diuido, inuenio Quotientem 9. </s>
            <s xml:id="echoid-s18207" xml:space="preserve">Facta autem operatione, remanent
              <lb/>
            214232708. </s>
            <s xml:id="echoid-s18208" xml:space="preserve">abſolutaque eſt extractio.</s>
            <s xml:id="echoid-s18209" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18210" xml:space="preserve">
              <emph style="sc">Neqve</emph>
            vero negligendum videtur non inutile compendium in extractio-
              <lb/>
            ne cubica. </s>
            <s xml:id="echoid-s18211" xml:space="preserve">quod eſt eiuſmodi. </s>
            <s xml:id="echoid-s18212" xml:space="preserve">Quando nouus diuiſor parandus eſt, ne coga-
              <lb/>
            mur totius radicis inuentæ quadratum ſupputare, diuidemus radicem inuentam
              <lb/>
            in duas partes, ita vt vna pars ſit vltima figura Quotientis inuenta, nimirum in-
              <lb/>
            uenta quarta figura 9. </s>
            <s xml:id="echoid-s18213" xml:space="preserve">in dato exemplo, partiemur radicem inuentam 1619. </s>
            <s xml:id="echoid-s18214" xml:space="preserve">in
              <lb/>
            1610. </s>
            <s xml:id="echoid-s18215" xml:space="preserve">& </s>
            <s xml:id="echoid-s18216" xml:space="preserve">9. </s>
            <s xml:id="echoid-s18217" xml:space="preserve">quas partes bis ſcribemus, vt in appoſita formula
              <lb/>
            vides. </s>
            <s xml:id="echoid-s18218" xml:space="preserve">Si igitur ſingulas partes in ſingulas partes ducemus,
              <lb/>
              <note position="right" xlink:label="note-420-01" xlink:href="note-420-01a" xml:space="preserve">
                <lb/>
              1610. # 9.
                <lb/>
              1610. # 9.
                <lb/>
              </note>
            producetur quadratus quæſitus radicis 1619. </s>
            <s xml:id="echoid-s18219" xml:space="preserve">vt ad propoſ. </s>
            <s xml:id="echoid-s18220" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s18221" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s18222" xml:space="preserve">2. </s>
            <s xml:id="echoid-s18223" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s18224" xml:space="preserve">demonſtrauimus. </s>
            <s xml:id="echoid-s18225" xml:space="preserve">Verbi gratia quia præcedens
              <lb/>
            quadratum numeri 161. </s>
            <s xml:id="echoid-s18226" xml:space="preserve">fuit 25921. </s>
            <s xml:id="echoid-s18227" xml:space="preserve">appoſitis duabus cifris, habebimus produ-
              <lb/>
            ctum 2592100. </s>
            <s xml:id="echoid-s18228" xml:space="preserve">ex 1610 in 1610. </s>
            <s xml:id="echoid-s18229" xml:space="preserve">cui ſi addemus 14490. </s>
            <s xml:id="echoid-s18230" xml:space="preserve">bis numerum videlicet
              <lb/>
            productum ex 1610. </s>
            <s xml:id="echoid-s18231" xml:space="preserve">in 9. </s>
            <s xml:id="echoid-s18232" xml:space="preserve">vel ex 9. </s>
            <s xml:id="echoid-s18233" xml:space="preserve">in 1610. </s>
            <s xml:id="echoid-s18234" xml:space="preserve">& </s>
            <s xml:id="echoid-s18235" xml:space="preserve">inſuper 81. </s>
            <s xml:id="echoid-s18236" xml:space="preserve">productum ex 9. </s>
            <s xml:id="echoid-s18237" xml:space="preserve">in 9. </s>
            <s xml:id="echoid-s18238" xml:space="preserve">
              <lb/>
            conficiemus 2621161. </s>
            <s xml:id="echoid-s18239" xml:space="preserve">quadratum radicis inuentæ 1619. </s>
            <s xml:id="echoid-s18240" xml:space="preserve">Eadem ratione ſi huius
              <lb/>
            numeri 16199. </s>
            <s xml:id="echoid-s18241" xml:space="preserve">quadratum deſideremus, diuidemus eum in 16190. </s>
            <s xml:id="echoid-s18242" xml:space="preserve">9. </s>
            <s xml:id="echoid-s18243" xml:space="preserve">bis, vt in
              <lb/>
            hac formula vides. </s>
            <s xml:id="echoid-s18244" xml:space="preserve">Deinde quia iam quadratum habuimus
              <lb/>
            2621161. </s>
            <s xml:id="echoid-s18245" xml:space="preserve">numeri 1619. </s>
            <s xml:id="echoid-s18246" xml:space="preserve">appoſitis duabus cifris, habebimus 26-
              <lb/>
              <note position="right" xlink:label="note-420-02" xlink:href="note-420-02a" xml:space="preserve">
                <lb/>
              16190. # 9.
                <lb/>
              16190. # 9.
                <lb/>
              </note>
            2116100. </s>
            <s xml:id="echoid-s18247" xml:space="preserve">quadratum numeri 16190. </s>
            <s xml:id="echoid-s18248" xml:space="preserve">cui ſi addemus 145710.
              <lb/>
            </s>
            <s xml:id="echoid-s18249" xml:space="preserve">bis, productum videlicet ex 16190. </s>
            <s xml:id="echoid-s18250" xml:space="preserve">in 9. </s>
            <s xml:id="echoid-s18251" xml:space="preserve">vel ex 9. </s>
            <s xml:id="echoid-s18252" xml:space="preserve">in 16190. </s>
            <s xml:id="echoid-s18253" xml:space="preserve">& </s>
            <s xml:id="echoid-s18254" xml:space="preserve">
              <lb/>
            inſuper 81 productum ex 9. </s>
            <s xml:id="echoid-s18255" xml:space="preserve">in 9. </s>
            <s xml:id="echoid-s18256" xml:space="preserve">efficiemus 262407601. </s>
            <s xml:id="echoid-s18257" xml:space="preserve">quadratum numeri 161-
              <lb/>
            99. </s>
            <s xml:id="echoid-s18258" xml:space="preserve">& </s>
            <s xml:id="echoid-s18259" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s18260" xml:space="preserve">Hoc ergo compendium reddet faciliorem cubicæ radicis
              <lb/>
            extractionem, cum ſemper præcedentis radicis inuentæ quadratum habeamus,
              <lb/>
            & </s>
            <s xml:id="echoid-s18261" xml:space="preserve">appoſitis duabus cifris, quadratum conficiamus eiuſdem radicis, appoſita ei
              <lb/>
            vna cifra, &</s>
            <s xml:id="echoid-s18262" xml:space="preserve">c.</s>
            <s xml:id="echoid-s18263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18264" xml:space="preserve">
              <emph style="sc">Bene</emph>
            autem vides, ſi tabula ſuperior extenderetur, vt haberentur quadra-
              <lb/>
            @i, & </s>
            <s xml:id="echoid-s18265" xml:space="preserve">cubiradicum 4. </s>
            <s xml:id="echoid-s18266" xml:space="preserve">aut 5. </s>
            <s xml:id="echoid-s18267" xml:space="preserve">figurarum, multo faciliorem effi ci extra ctionem ra-
              <lb/>
            dicum. </s>
            <s xml:id="echoid-s18268" xml:space="preserve">Sed quia tabula excreſceret hac ratione in immenſum, conten-
              <lb/>
            ti fuimus tabula, in quaradices habent 3. </s>
            <s xml:id="echoid-s18269" xml:space="preserve">figuras ad ſum-
              <lb/>
            mum, cum eã quilibet ex ijs, quæ diximus,
              <lb/>
            extendere poſsit, & </s>
            <s xml:id="echoid-s18270" xml:space="preserve">continuare.</s>
            <s xml:id="echoid-s18271" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1137" type="section" level="1" n="418">
          <head xml:id="echoid-head445" xml:space="preserve">FINIS LIBRI OCTAVI.</head>
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