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="6" xlink:href="015/01/025.jpg"/>
            <p type="main">
              <s id="id000151">Nam licet diuidere per ſeptimam petitionem quantitatem per
                <lb/>
              quantitatem proportionis: & quod exit, eſt proportio per quar­
                <lb/>
              tam petitionem, & per ſecundam animi communem ſententiam
                <lb/>
              illa proportio eſt numero æqualis: ergo diuiſa proportione, per ſi­
                <lb/>
              milem numerum ſtatuetur monas.</s>
            </p>
            <p type="main">
              <s id="id000152">Decima petitio.</s>
            </p>
            <p type="main">
              <s id="id000153">In quouis genere quantitatum ſumere poſſe quantitatem, quæ
                <lb/>
                <arrow.to.target n="marg2"/>
                <lb/>
              ſe habeat ad monadem in proportione data. </s>
              <s id="id000154">Similem huic propo­
                <lb/>
              nit Euclides in lineis generaliter: nos autem contrà generaliter in
                <lb/>
              omnibus quantitatibus, ſed de monade tantum.</s>
            </p>
            <p type="margin">
              <s id="id000155">
                <margin.target id="marg2"/>
              D
                <emph type="italics"/>
              uodecima
                <lb/>
              ſexti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              Vndecima petitio.</s>
            </p>
            <p type="main">
              <s id="id000156">Monadem in quancunque quantitatem ductam æquale ipſi pro­
                <lb/>
              ducere. </s>
              <s id="id000157">Similiter & proportionem æqualem.</s>
            </p>
            <p type="main">
              <s id="id000158">Nam cum aliqua quantitas augeat ducta aliqua minuat, neceſſe
                <lb/>
              eſt aliquam eſſe, quæ nec augeat, nec minuat, & hæc eſt monas.
                <lb/>
              </s>
              <s id="id000159">Idem dico de diuiſione. </s>
              <s id="id000160">Aequalitas etiam ducta, uel diuidens non
                <lb/>
                <arrow.to.target n="marg3"/>
                <lb/>
              mutat proportionem: nec quantitatem ipſam, igitur monas æqua­
                <lb/>
              litatem refert. </s>
              <s id="id000161">Quod etiam eſt perſpicuum ex ſupradictis.</s>
            </p>
            <p type="margin">
              <s id="id000162">
                <margin.target id="marg3"/>
              S
                <emph type="italics"/>
              ecunda ani
                <lb/>
              mi
                <expan abbr="cõmunis">communis</expan>
                <lb/>
              ſententia.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000163">Duodecima petitio.</s>
            </p>
            <p type="main">
              <s id="id000164">Cum fuerint quatuor quantitates & ad primam, & tertiam æquè
                <lb/>
              multiplicibus aſſumptis, item que ad ſecundam & quartam, & ſi mul­
                <lb/>
              tiplex primæ maius eſt multiplici ſecundæ, multiplex tertiæ ſit ma­
                <lb/>
              ius multiplici quartæ, & ſi minus minus, & ſi æquale æquale, idque
                <lb/>
              ſemper quouis modo aſſumptis his proportionibus ad primam &
                <lb/>
              tertiam, & ad ſecundam & quartam erit proportio primæ ad ſecun
                <lb/>
              dam, ut tertiæ ad quartam. </s>
              <s id="id000165">Hæc etiam aſſumitur ab Euclide. </s>
              <s id="id000166">Et per
                <lb/>
                <arrow.to.target n="marg4"/>
                <lb/>
              hanc intelligimus etiam conuerſam.</s>
            </p>
            <p type="margin">
              <s id="id000167">
                <margin.target id="marg4"/>
              Q
                <emph type="italics"/>
              uinto
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              le.
                <lb/>
              diff.
                <emph.end type="italics"/>
              6.</s>
            </p>
            <p type="main">
              <s id="id000168">Tertiadecima petitio.</s>
            </p>
            <p type="main">
              <s id="id000169">Quantitates æquales, atque proportiones in quaſuis quanti­
                <lb/>
              tates ductæ eandem ſeruant rationem. </s>
              <s id="id000170">Euclides hanc demonſtrat,
                <lb/>
              nos autem ad uitandum tædium petimus concedi, ſub qua in­
                <lb/>
                <arrow.to.target n="marg5"/>
                <lb/>
              cluduntur diuiſio etiam additio, detractio, laterum omnium in­
                <lb/>
              uentio.</s>
            </p>
            <p type="margin">
              <s id="id000171">
                <margin.target id="marg5"/>
              Q
                <emph type="italics"/>
              uarta quin
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000172">Quartadecima petitio.</s>
            </p>
            <p type="main">
              <s id="id000173">Cùm termini alicuius quantitatis eandem ſeruant rationem in
                <lb/>
              omnibus, & firmi ſunt ac ſtabiles eiuſdem rationis comparatione
                <lb/>
              contentæ partes æqualem ſeruant exceſſum, ſeu proportionem.</s>
            </p>
            <p type="main">
              <s id="id000174">PROPOSITIO prima.</s>
            </p>
            <p type="main">
              <s id="id000175">Proportionem in proportionem duci eſt ſuperiores nume­
                <lb/>
              ros atque inferiores inuicem ducere.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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