Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id002388">
                <pb pagenum="133" xlink:href="015/01/152.jpg"/>
              ne 216 & 10000, & 8 è regione 36 & 10000, & 16 è regione 6, & 50,
                <lb/>
              & duco 6 in 50 fit 300, duco in 16 fit 4800, duco 36 in 1000 fit
                <lb/>
              36000, duco 36 in 8 fit 288000, duco etiam 216 in 10000 & fit
                <lb/>
              2160000, & duco hos per 4 fit 86400000, duco rurſus 1296 in
                <lb/>
              50000 fit 64800000, duco in 2 fit 129600000. Demum addo 32 re­
                <lb/>
              latum primum 2, & fit ſumma omnium 138532832, & ita habemus
                <lb/>
              radicem relatam primam dicti numeri eſſe 62. Et ſi numerus produ
                <lb/>
              ctus fuiſſet maior oportuiſſet accipere proximo minorem. </s>
              <s id="id002389">Inde per
                <lb/>
              regulam ſequentem addere minutias.</s>
            </p>
            <p type="main">
              <s id="id002390">Propoſitio centeſima quadrageſima.</s>
            </p>
            <p type="main">
              <s id="id002391">Radices per numeros fractos determinare.</s>
            </p>
            <p type="main">
              <s id="id002392">Duplex eſt modus, ut etiam docui in arithmeticis, ſcilicet ut pro </s>
            </p>
            <p type="main">
              <s id="id002393">
                <arrow.to.target n="marg466"/>
                <lb/>
              radice quadrata addatur duo o, & pro cuba tria, & pro quadrata
                <lb/>
              quadrata quatuor, & pro relata prima quinque, & ita deinceps, &
                <lb/>
              prę decimis ſemel, pro centeſimis bis, pro milleſimis ter, pro millia­
                <lb/>
              ribus ſeu partibus earum quater, pro centeſimis milleſimis quin­
                <lb/>
              quies, pro milleſimis milleſimarum ſexies, & ita deinceps deinde
                <lb/>
              per præcedentem detrahere radicem, & erit ualde exacta. </s>
              <s id="id002394">Exemplo
                <lb/>
              non utar, niſi quòd ſi uelles radicem relatam 16 ad milleſimas, acci­
                <lb/>
              cipies radicem relatam numeri à latere propoſiti, & ita de alijs
                <lb/>
              1600000, 00000, 00000, & ſi uelles <02> cub. </s>
              <s id="id002395">5 1/5 per milleſimas, pri
                <lb/>
              mo addes ter 000, & fiet 3000000000, inde ſume 1/5 1000000000,
                <lb/>
              qui eſt 200000000, & adde ad 5000000000, fit 2500000000,
                <lb/>
              & hoc quia unum refert numerum 1000000000 ex ſuppoſito & 1/5
                <lb/>
              eſt 1/5 unius.</s>
            </p>
            <p type="margin">
              <s id="id002396">
                <margin.target id="marg466"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id002397">Secundus modus eſt, ut accipias proximè maiorem, & multipli­
                <lb/>
              ca in ſe, & detrahe numerum propoſitum, & reſiduum diuide per
                <lb/>
              duplum radicis primo inuentæ, ſi fuerit quadrata, & per triplum
                <lb/>
              quadrati eiuſdem ſi fuerit cubica, & per quadruplum cubi, ſi fuerit
                <lb/>
              quadrata quadrata, & per quincuplum quadrati quadrati, & quod
                <lb/>
              exit detrahes ex priore radice, & rurſus quod relinquitur, multipli­
                <lb/>
              ca in ſe, & eodem modo agendo quod ſupereſt à numero propoſi­
                <lb/>
              to, diuide per duplum radicis prioris, ſi ſit radix quadrata, uel per
                <lb/>
              triplum quadrati ſi ſit cubica, & quod exit rurſus detrahe, & ita a­
                <lb/>
              gendo, peruenies ad exactiſsimam radicem, exemplum uolo radi­
                <lb/>
              cem quadratam 5 proxima maior eſt 3, quadratum 9, differentia 4,
                <lb/>
              diuide per 6 duplum 3 exit 2/3, detrahe ex 3 fit 2 1/3, quadratum eſt 49/9
                <lb/>
              quod eſt 5 4/9, rurſus diuido 4/9 differentiam 5 4/9 & 5 per 4 2/3 duplum
                <lb/>
              radicis primæ exit 2/21, detrahe ex 2 1/3, relinquitur 2 5/21, radix ſatis pro­
                <lb/>
              pinqua, nam eius quadratum eſt 5 4/441, in cubica ſimiliter uolo <02>
                <lb/>
              cu. </s>
              <s id="id002398">5, proxima maior eſt 2, cubus 8, differentia 3, diuide per triplum </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>