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="13" xlink:href="015/01/032.jpg"/>
            <figure id="id.015.01.032.1.jpg" xlink:href="015/01/032/1.jpg" number="21"/>
            <p type="main">
              <s id="id000287">Quia ergo ex c in b fit f, ex c in d h, erit f ad h,
                <lb/>
              ut b ad d, igitur ut e ad c, ſed a ad c, ut g ad h igi
                <lb/>
                <arrow.to.target n="marg41"/>
                <lb/>
              tur a e ad c, ut k ad h, ſed k ad h cómponitur ex
                <lb/>
              proportionibus a ad c, & b ad d. </s>
              <s id="id000288">Ex octaua ha
                <lb/>
              rum igitur proportio a c ad c compoſita eſt ex
                <lb/>
              eiſdem. </s>
              <s id="id000289">Forſan quis dicat hanc eandem eſſe
                <lb/>
              octauæ ſed
                <expan abbr="nõ">non</expan>
              eſt, in illa enim proportio com­
                <lb/>
              paratur ad productum, in hac ad unam ex
                <lb/>
              quantitatibus.</s>
            </p>
            <p type="margin">
              <s id="id000290">
                <margin.target id="marg41"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              13. P
                <emph type="italics"/>
              et.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000291">Ex hoc ſequitur quòd: Quælibet duæ quantitates quarum ag­
                <lb/>
                <arrow.to.target n="marg42"/>
                <lb/>
              gregatum eſt idem ad eam quantitatem, componunt eandem pro­
                <lb/>
              portionem.</s>
            </p>
            <p type="margin">
              <s id="id000292">
                <margin.target id="marg42"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000293">Propoſitio tertia decima.</s>
            </p>
            <p type="main">
              <s id="id000294">Proportio confuſa aggregati primæ & tertiæ quatuor quantita­
                <lb/>
              tum omiologarum ad
                <expan abbr="aggregatũ">aggregatum</expan>
              ſecundæ & quartæ, eſt uelut com
                <lb/>
              poſita ex eiſdem diuiſa per duplam.
                <lb/>
                <arrow.to.target n="marg43"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000295">
                <margin.target id="marg43"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000296">Sint a ad b, ut c ad d, dico, quòd erit confuſa
                <lb/>
                <figure id="id.015.01.032.2.jpg" xlink:href="015/01/032/2.jpg" number="22"/>
                <arrow.to.target n="table11"/>
                <lb/>
              proportio a c aggregati ad
                <expan abbr="aggregatũ">aggregatum</expan>
              b d, com
                <lb/>
              poſitæ ex his proportionibus diuiſæ per du­
                <lb/>
              plam æqualis. </s>
              <s id="id000297">Erit enim aggregati ex a c ad aggregatum ex b d, ue­
                <lb/>
              lut a ad b per 18 quinti Elementorum. </s>
              <s id="id000298">Sed proportiones a ad b,
                <lb/>
              & c ad d componunt proportionem producti a in d, & c in b per
                <lb/>
              octauam harum, ad
                <expan abbr="productũ">productum</expan>
              ex b in d, productum uerò ex a in d
                <lb/>
              eſt æquale producto ex b in c per decimam ſextam ſexti Elemento­
                <lb/>
              rum, & proportio producti ex b in c ad productum ex b in d eſt ue
                <lb/>
              lut c ad d, quare ut aggregati a c ad aggregatum b d, igitur propor­
                <lb/>
              tio compoſita ex a ad b, & c ad d, eſt uelut confuſa bis ſumpta. </s>
              <s id="id000299">Igi­
                <lb/>
              tur confuſa eſt uelut compoſita diuiſa per duplam per modum un­
                <lb/>
              decimæ huius.</s>
            </p>
            <table>
              <table.target id="table11"/>
              <row>
                <cell>a</cell>
                <cell>c</cell>
              </row>
              <row>
                <cell>-----</cell>
                <cell>-----</cell>
              </row>
              <row>
                <cell>b</cell>
                <cell>d</cell>
              </row>
              <row>
                <cell>---</cell>
                <cell>---</cell>
              </row>
            </table>
            <p type="main">
              <s id="id000300">Propoſitio quarta decima.</s>
            </p>
            <p type="main">
              <s id="id000301">Proportiones confuſæ, & coniunctæ in tribus quantitatibus in­
                <lb/>
              uicem commutantur.</s>
            </p>
            <figure id="id.015.01.032.3.jpg" xlink:href="015/01/032/3.jpg" number="23"/>
            <p type="main">
              <s id="id000302">Sint tres quantitates, dico, quod proportio c </s>
            </p>
            <p type="main">
              <s id="id000303">
                <arrow.to.target n="marg44"/>
                <lb/>
              ad a b confuſa eſt, conuerſa coniunctæ a & b ad
                <lb/>
                <arrow.to.target n="marg45"/>
                <lb/>
              c. </s>
              <s id="id000304">Nam per dicta proportio a b ad c efficit con­
                <lb/>
              iunctam ex a b ad c: ſed c ad a b conuerſa eſt eius, quæ eſt a b ad c, &
                <lb/>
              proportio c ad a b eſt confuſa eius, quæ eſt c ad a & b. </s>
              <s id="id000305">Igitur pro­
                <lb/>
              portio confuſa in tribus quantitatibus eſt contraria coniunctæ in
                <lb/>
              eiſdem.</s>
            </p>
            <p type="margin">
              <s id="id000306">
                <margin.target id="marg44"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id000307">
                <margin.target id="marg45"/>
              14.
                <emph type="italics"/>
              diff.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000308">Ex quauis ergo illarum data, data erit & reliqua.
                <lb/>
                <arrow.to.target n="marg46"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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