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="id003415">
                <pb pagenum="200" xlink:href="015/01/219.jpg"/>
              qualis relinquatur perfectionis, duc quadrantem in 10 fit 30, duc 12
                <lb/>
              in 7 fit 84, detrahe 30 ex 84, relinquitur 54, divide 54 per 9, reſidu­
                <lb/>
              um 12 & 3, exit 6 perfectio reſidui.</s>
              <lb/>
            </p>
            <p type="main">
              <s id="id003416">Si quis dicat propoſitis argenti pondo 50 & dodrante perfe­
                <lb/>
              ctionis 11/18, uolo partem aſſumere, & igne perficere, ita purum ar­
                <lb/>
              gentum, quod relinquitur additum reſiduo, efficiat ipſum perfe­
                <lb/>
              ctionis dextantis & beſsis unciæ pro libra, ſeu 8/9, divide 11/18 per 8/9 exit
                <lb/>
              11/16, duc in pondo 50 cum dodrante, fiunt pondo 34, unciæ 7 1/8, hoc
                <lb/>
              igitur erit aggregatum conflatum ex argento puro & reſiduo. </s>
              <s id="id003417">De­
                <lb/>
              trahe igitur 11/18 ex integro, relinquitur 7/18, detrahe pondo 34, uncia
                <lb/>
              7 1/8 ex pondo 50 cum dodrante, relinquuntur pondo 15 unciæ 6 7/8
                <lb/>
              (pondo enim uncias continet ſub hoc ſenſu, quia uſui ſeruimus o­
                <lb/>
              cto) divide per 7/8, exeunt pondo 40 unciæ 6 1/4, & tanta pars debuit
                <lb/>
              igne purgari. </s>
              <s id="id003418">In ea enim erunt puri argenti pondo 24, unciæ 7 /78,
                <lb/>
              quæ addita reſiduo, ſcilicet pondo 9, uncijs 7 3/4 conficiunt pondo
                <lb/>
              34 uncias 7 1/8 perfectionis dictæ.</s>
              <lb/>
            </p>
            <p type="main">
              <s id="id003419">Quidam miſcuit uncias decem auri perfectionis dextantis, &
                <lb/>
              partem perfectionis dextantis cum dimidio, & aliud perfectionis
                <lb/>
              beſsis concreuit maſſa perfectionis dodrantis unciarum octuagin
                <lb/>
              ta, quæruntur pondera reliquarum partium, ſubtrahe 10 pondus
                <lb/>
              ex 80 pondere, relinquuntur 70 perfectionis 17 5/7, inde detrahe per
                <lb/>
              modum ſuperiorem, & relinquuntur 3 2/7 & 1 5/7,
                <lb/>
                <figure id="id.015.01.219.1.jpg" xlink:href="015/01/219/1.jpg" number="212"/>
              iunge ſimul fiunt 5, dico ergo, ſi 6 producit
                <lb/>
              70, quid producet 3 2/7 & 1 5/7, & inuenies quod 1 5/7
                <lb/>
              producet 24 & 3 5/7 producet 46, qui iuncti faci­
                <lb/>
              unt 70. </s>
              <s id="id003420">Igitur aurum perfectionis dextantis
                <lb/>
              cum dimidio fuit unciarum 46 aurum perfe­
                <lb/>
              ctionis, beſsis unciarum 24. </s>
              <s id="id003421">Reliqua interro­
                <lb/>
              gata diſſolues per regulas Algebræ, horum
                <lb/>
              modo.</s>
            </p>
            <p type="main">
              <s id="id003422">Propoſitio centeſima ſeptuageſima nona.</s>
            </p>
            <p type="main">
              <s id="id003423">Si duobus totis duæ portiones ſimiles abſcindantur, ab eiſdem
                <lb/>
              denuo, & abſciſsis proportionibus partes eædem auferantur, denuo
                <expan abbr="q̀">que</expan>
                <lb/>
              ac denuo, quoties libuerit à portionibus, & à reſiduis ipſarum
                <lb/>
              quantitatum partes eædem auferantur, erit reſidui ad reſiduum, ue
                <lb/>
              luti totius ad totum.</s>
            </p>
            <p type="margin">
              <s id="id003424">
                <margin.target id="marg906"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003425">Sint duæ quanitates a b & k l, & abſciſſæ duæ partes ſimiles ex
                <lb/>
              utraque b c & l m, & ſit propoſita aliqua proportio, quæ ſit h, &
                <lb/>
              ſumatur portio b d ipſius b c, ſecundum proportionem h, & ſi­
                <lb/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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