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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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id001399">
                <pb pagenum="75" xlink:href="015/01/094.jpg"/>
              ſi fuiſſet pondus amborum libræ xxxix, manentibus reliquis, ſeque
                <lb/>
              retur quod pondus liquoris eſſet xxvij, & quia plenum uas ſuppo­
                <lb/>
              nitur eſſe librarum xxix, eſſet differentia libræ ij, at auri pondus eſt
                <lb/>
              libræ xij, igitur proportio ponderis auri ad liquorem eſſet ſexcu­
                <lb/>
              pla. </s>
              <s id="id001400">Nam ſi uas plenum liquore ex ſuppoſito eſt librarum xxix, &
                <lb/>
              cum auro xl, gratia exempli, & auri pondus eſt xij, igitur liquoris
                <lb/>
              pondus eſt xxviij librarum: ſed cum liquor ſit corpus ſimilium par­
                <lb/>
              tium, igitur loci ad lo cum, ut ponderis ad pondus, ergo dum adeſt
                <lb/>
              aurum, liquor occupat xxviij partes cxxxix, totius uaſis igitur au­
                <lb/>
              rum continet unam partem tantum, & cum aurum pondus habeat
                <lb/>
              librarum xij, & liquor unius: quia totum uas cxxxix librarum dum
                <lb/>
              eſt plenum, & eſt diuiſum in xxix partes, igitur pondus unius par­
                <lb/>
              tis liquoris eſt una libra, igitur pondus auri eſt duodecuplum ad
                <lb/>
              pondus liquoris quod fuit propoſitum.</s>
            </p>
            <p type="main">
              <s id="id001401">
                <arrow.to.target n="marg294"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001402">
                <margin.target id="marg294"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id001403">Ex quo ſequitur quòd ſi ducatur pondus illud partis per pon­
                <lb/>
              dus repleti uaſis ex alio graui, & productum diuidatur per differen
                <lb/>
              tiam illam, prodibit pondus uaſis repleti liquore graui.</s>
            </p>
            <p type="main">
              <s id="id001404">
                <arrow.to.target n="marg295"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001405">
                <margin.target id="marg295"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001406">Exemplum, ſi pondus auri fuerit librarum xij, pondus uaſis re­
                <lb/>
              pleti liquore xxix librarum, pondus auri & liquoris replentium
                <lb/>
              uas xxxix librarum, ducemus xij in xxix fit cccxlviij, diuido perij
                <lb/>
              differentiam xxvij ponderis uaſis, repleti ex ambobus detracto au­
                <lb/>
              ri pondere, & xxix ponderis uaſis repleti liquore exit clxxiiij, & tan
                <lb/>
              tum auri uas illud continebit, nam cum duæ partes quas occupa­
                <lb/>
              bat aurum eſſent ponderis librarum xij, totum quod erat partium
                <lb/>
              xxix, continebit decies & quater cum dimidio illud aurum xij, aut
                <lb/>
              ductum in xiiij cum dimidio, efficit cclxxiiij ut prius.</s>
            </p>
            <p type="head">
              <s id="id001407">EXEMPLVM.</s>
            </p>
            <p type="main">
              <s id="id001408">Quia ergo in ſuperiore propoſitione docui, quod ferrum eſt ue­
                <lb/>
              ra terra: uolui ſcire qualis eſſet proportio ferri ad aquam. </s>
              <s id="id001409">Accepi ur
                <lb/>
              ceum cuius aqua dum plenus eſſet ponderis, fuit unciarum ſex, &
                <lb/>
              ſeptuncis unciæ, & ſeptuncis duodecimæ partis unciæ & pondus
                <lb/>
              ferri unciæ ſeptem, & triens unciæ & triens duodecimæ partis un­
                <lb/>
              ciæ: & uaſis aquę & ferro eodem repleti unciæ tredecim, & duode­
                <lb/>
              cima & ſeptunx duodecimæ partis unciæ. </s>
              <s id="id001410">Detrahemus ergo vij &
                <lb/>
              trientem & trientem duodecimæ. </s>
              <s id="id001411">i. </s>
              <s id="id001412">7 & 64/144 pondus ferri ex 13 19/144, &
                <lb/>
              relinquentur 5 99/144, detrahe ex 6 81/144, pondere aquæ totius uaſis relin
                <lb/>
              quuntur 17/18, diuide 7 64/144 per 17/18 exit proportio ponderis ferri ad pon
                <lb/>
              dus aquæ 7 15/17. Et hoc eſt proximum ei quod dixit Philoſophus de
                <lb/>
              proportione ponderis terræ & aquæ.</s>
            </p>
            <p type="main">
              <s id="id001413">
                <arrow.to.target n="marg296"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001414">
                <margin.target id="marg296"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id001415">Ex hoc patet ſolutio problematis cuiuſdam propoſiti aliasque mi
                <lb/>
              nus bene ſoluti cùm cauſam habeat manifeſtiſsimam, ſcilicet quod </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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