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>
            <pb pagenum="199" xlink:href="015/01/218.jpg"/>
            <p type="margin">
              <s id="id003401">
                <margin.target id="marg623"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003402">Ex demonſtratione ſequitur, quod qualis eſt proportio e ad a b,
                <lb/>
                <arrow.to.target n="marg624"/>
                <lb/>
              talis eſt producti d in e, ad aggregatum eorum. </s>
              <s id="id003403">Si quis ergo dicat,
                <lb/>
              habeo 10, & uolo inuenire duas quantitates, quarum differentia ſit
                <lb/>
              1, & proportio 10, ad eas componat quintuplam, dices quintupla
                <lb/>
              eſt dimidium 10, igitur in uenias duas quantitates, quarum differen
                <lb/>
              tia ſit 1, & proportio producti unius in alteram ad aggregatum ſit
                <lb/>
              dupla. </s>
              <s id="id003404">Et hoc eſt manifeſtum.</s>
            </p>
            <p type="margin">
              <s id="id003405">
                <margin.target id="marg624"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id003406">Propoſitio centeſima ſeptuageſima octaua.</s>
            </p>
            <p type="main">
              <s id="id003407">Proportionem miſtionis metallorum, maximè auri & argenti
                <lb/>
              declarare.</s>
            </p>
            <p type="main">
              <s id="id003408">Dubium non eſt, quod miſtio non cognoſcatur ducto ponde­
                <lb/>
                <arrow.to.target n="marg625"/>
                <lb/>
              re totius in partem auri uel argenti, & productis collectis diuiſo
                <lb/>
              aggregato per aggregatum ponderis, idqúe eſt per ſe manife­
                <lb/>
              ſtum, nam qualis eſt proportio partis ad partem, talis eſt totius ad
                <lb/>
              totum.</s>
            </p>
            <p type="margin">
              <s id="id003409">
                <margin.target id="marg625"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003410">Sed eſt genus miſtionis, quod uocant conſolationem. </s>
              <s id="id003411">Veluti,
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              uolo ex argento perfectionis decem & ſeptem, & quinque, confla­
                <lb/>
              re argenti maſſam centum librarum perfectionis nouem, ita agen­
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              dum eſt. </s>
              <s id="id003412">Detrahe 9 à 10, & omni maiori 10, relinqui­
                <lb/>
              tur 1, hoc ſuppone 7 & 5, item detrahe 7 & 5, & omne
                <lb/>
                <figure id="id.015.01.218.1.jpg" xlink:href="015/01/218/1.jpg" number="210"/>
                <lb/>
              minus 9 à 9, relinquitur 2 & 4, iunge omnia reſidua
                <lb/>
              fient 8, nam 4. 2. 11. Dicemus ergo quod 8 uncię per­
                <lb/>
              fectionis nouem componentur ex 6 uncijs perfe­
                <lb/>
              ctionis decem & una ſeptem alia quinque. </s>
              <s id="id003413">Poſt di­
                <lb/>
              ces, ſi unciæ octo fiant 100, ſex & una, & una, quot fient, eruntque un­
                <lb/>
              ciæ aut libræ, aut ut uocant marchæ perfectionis decem, & duo de­
                <lb/>
              cim cum dimidia, ac duodecim cum dimidia perfectionis, ut ſe­
                <lb/>
              ptem & ut quinque: licebit etiam propoſitis terminis pluribus ex
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              repetita operatione idem facere, ueluti ſint maſſæ perfectionis 10.
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              7. 5. & 2. uolo maſſam perfectionis ut 8. Tu ſcis quod ex 10. 7 & 5.
                <lb/>
              fit maſſa perfectionis nouem data lege ſub 6. 1 & 1. nunc habeo iam
                <lb/>
              perfectam ut 9, aliam ut 2, detraho 2 ex 8, relinquitur 6 & 8, x 9 re­
                <lb/>
              linquitur 1, iunge fient 7, erunt ergo ſeptem unciæ, in
                <lb/>
                <figure id="id.015.01.218.2.jpg" xlink:href="015/01/218/2.jpg" number="211"/>
                <lb/>
              quibus ſex erunt perfectionis, ut 9 & 1 perfectionis ut
                <lb/>
              2, & totum erit perfectionis ut octo. </s>
              <s id="id003414">Duc ergo, ut ex­
                <lb/>
              plores ueritatem, 6 in 9 fit 54, duc 2 in 1 fit 2, iunge fit 56
                <lb/>
              diuide per 7 exit 8 perfectio quæſita.</s>
            </p>
            <p type="main">
              <s id="id003415">Per idem intelliges detractionem ex maſſa argenti perfectionis
                <lb/>
              7, detraxi quartam partem perfectionis 10, uolo ſcire dodrantem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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