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="id003425">
                <pb pagenum="201" xlink:href="015/01/220.jpg"/>
              militer l n ipſius l m, iuxta pro­
                <lb/>
                <figure id="id.015.01.220.1.jpg" xlink:href="015/01/220/1.jpg" number="213"/>
                <lb/>
              portionem h, ſumatur rurſus
                <lb/>
                <arrow.to.target n="marg626"/>
                <lb/>
              de ipſius a b pars ſecundum h,
                <lb/>
                <arrow.to.target n="marg627"/>
                <lb/>
              & n o ipſius k l, ſecundum ean
                <lb/>
              dem proportionem. </s>
              <s id="id003426">Et rurſus
                <lb/>
                <arrow.to.target n="marg628"/>
                <lb/>
              ſumatur e f æqualis d b, & o p
                <lb/>
                <arrow.to.target n="marg629"/>
                <lb/>
              æqualis n l, ut ſint portiones
                <lb/>
              b c & l m ſecundum proportionem h, & ſumatur f g ipſius a c, ſecun
                <lb/>
                <arrow.to.target n="marg630"/>
                <lb/>
              dum proportionem h, & p q ipſius k o, ſecundum eandum propor­
                <lb/>
                <arrow.to.target n="marg631"/>
                <lb/>
              tionem, & ita procedendo ſemper, dico quod erit a g reſidui ad k q
                <lb/>
                <arrow.to.target n="marg632"/>
                <lb/>
              reſiduum, ut a b ad k l. </s>
              <s id="id003427">Quia enim a b ad b c, ut k l ad l m ex ſuppoſi­
                <lb/>
                <arrow.to.target n="marg633"/>
                <lb/>
              to, erit a b ad b d, ut k l ad l n: eſt etiam a b ad d e, ut k l ad n o ex ſup­
                <lb/>
              poſito, igitur a b ad b c, ut k l ad l o. </s>
              <s id="id003428">Igitur a b ad a c, ut k l ad k o. </s>
              <s id="id003429">Rur
                <lb/>
                <arrow.to.target n="marg634"/>
                <lb/>
              ſus quia b c ad e f, ut l m ad o p, erit a b ad e f, ut k l ad o p, at fuit a b
                <lb/>
              ad a e, ut k l ad k o & a e ad g f, ut k o ad p q, igitur a b ad' g f, ut k l ad
                <lb/>
              q p. </s>
              <s id="id003430">Quare a b ad g e, ut k l ad q o. </s>
              <s id="id003431">Iterum ergo a b ad b g, ut k l ad
                <lb/>
              l
                <expan abbr="q.">que</expan>
              Ergo a b ad a g, ut k l ad k
                <expan abbr="q.">que</expan>
              Igitur a b ad k l, ut a g ad k q, quod
                <lb/>
              erat demonſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id003432">
                <margin.target id="marg626"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              22.
                <lb/>
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003433">
                <margin.target id="marg627"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              18.
                <lb/>
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003434">
                <margin.target id="marg628"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              19.
                <emph type="italics"/>
              &
                <emph.end type="italics"/>
                <lb/>
              22.
                <emph type="italics"/>
              eiuſdem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003435">
                <margin.target id="marg629"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              22.
                <emph type="italics"/>
              eiuſ­
                <lb/>
              dem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003436">
                <margin.target id="marg630"/>
              P
                <emph type="italics"/>
              er eandem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003437">
                <margin.target id="marg631"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              19.
                <emph type="italics"/>
              &
                <emph.end type="italics"/>
                <lb/>
              22
                <emph type="italics"/>
              eiuſdem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003438">
                <margin.target id="marg632"/>
              P
                <emph type="italics"/>
              er eaſdem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003439">
                <margin.target id="marg633"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              19
                <emph type="italics"/>
              quin­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003440">
                <margin.target id="marg634"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              16.
                <emph type="italics"/>
              eiuſ­
                <lb/>
              dem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003441">Ex hoc patet, quod etſi proportio non maneat eadem in parti­
                <lb/>
                <arrow.to.target n="marg635"/>
                <lb/>
              bus totius, & partis modo ſit eadem in totis ad partes aſſumptas, et
                <lb/>
              in partibus ad partes aſſumptas, nihilominus ſequitur idem.</s>
            </p>
            <p type="margin">
              <s id="id003442">
                <margin.target id="marg635"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id003443">Sequitur rurſus, quod etſi proportio eadem non maneat quan­
                <lb/>
                <arrow.to.target n="marg636"/>
                <lb/>
              titatum aſſumptarum ad partes quæ ſumuntur, nec etiam partium
                <lb/>
              modo ſemper pars, quæ aſſumitur ſit totius pars, & alia partis idem
                <lb/>
              ueratur.</s>
            </p>
            <p type="margin">
              <s id="id003444">
                <margin.target id="marg636"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id003445">Velut ſi prima uice capiam b d partem b c, ut l n partem l m ſe­
                <lb/>
                <arrow.to.target n="marg637"/>
                <lb/>
              cundum h proportionem, & deinde capiam d e partem a b & n o
                <lb/>
              partem k l ſecundum proportionem r, quæ ſit alia ab h, & ſecunda
                <lb/>
              uice capiam e f partem b c, & o p partem l m ſecundum proportio­
                <lb/>
              nem h, quæ ſit alia ab h & r. </s>
              <s id="id003446">Et capiam f g partem a e & p q partem
                <lb/>
              k o, ſecundum eandem proportionem, ſed tamen quæ non ſit ali­
                <lb/>
              qua prædictarum, ſcilicet h r s, ſed diuerſa ab eis, & uocetur t, dico
                <lb/>
              quod nihilominus erit proportio a g ad k q, ut a b ad k l, quæ pa­
                <lb/>
              tent ex ui demonſtrationum, in quibus nil plus aſſumitur ad de­
                <lb/>
              monſtrandum, quàm id quod proponitur in corrolarijs.</s>
            </p>
            <p type="margin">
              <s id="id003447">
                <margin.target id="marg637"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id003448">Ex hoc etiam ſequitur, quod ſecundum quem numerum prima
                <lb/>
                <arrow.to.target n="marg638"/>
                <lb/>
              quantitas abſumetur, ſecundum eundem abſumetur & ſecunda.</s>
            </p>
            <p type="margin">
              <s id="id003449">
                <margin.target id="marg638"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. .3.</s>
            </p>
            <p type="main">
              <s id="id003450">Velut ſi prima quantitas abſumatur ad unguem in quinta detra­
                <lb/>
                <arrow.to.target n="marg639"/>
                <lb/>
              ctione, etiam ſecunda k l in quinta detractione ad unguem abſume
                <lb/>
              tur, quod patet per demonſtrata, nam reſidua ſemper ſunt eædem
                <lb/>
              partes ipſarum quantitatum.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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