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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              <s id="id003451">
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              C
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              o
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              ^{m}.</s>
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              <s id="id003452">Quarto ſequitur, quod ſi detractio fuerit facta eodem modo, &
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              fuerit proportio totius ad totum, ut reſidui ad reſiduum, erunt par
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              tes aſſumptæ ſimiles.</s>
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              <s id="id003453">
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              C
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              or
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              ^{m}. 4.</s>
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              <s id="id003454">Velut ſi fuerit facta detractio iuxta propoſitionem, aut primum
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              uel ſecundum corrolarium, & fuerit proportio a g ad k g, ut a b ad
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              k l, erit a b ad b c, ut k l ad l m.</s>
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              C
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              o
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              ^{m}.</s>
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              <s id="id003456">Sequitur etiam, quod ſi fuerit aſſumpta proportio
                <expan abbr="primarũ">primarum</expan>
              par­
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              tium eadem, & facta fuerit detractio in omnibus præter unam iux­
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              ta dicta, & fuerit totius ad totum, ut reſidui ad reſiduum, erit ut illa
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              etiam reliqua detractio, ſeu ad tota, ſeu ad partes ſit facta, ſecundum
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              eandem proportionem.</s>
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              <s id="id003457">
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              C
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              or
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              ^{m}. 5.</s>
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            <p type="main">
              <s id="id003458">Velut ſi ſit proportio a b ad k l, ut a g ad k g, & rurſus ut b c ad
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              l m, & aſſumptæ ſint proportiones eædem ſemper totius, & totius
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              ad partes, & reſiduorum ad partes, etiam & b c & l m ad partes, eti­
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              am excepta una ſeu quantitatum a b & k l, ſeu reſiduorum ut a c &
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              k o, ſeu partium ut b c & l m ad partes, dico quod hæ partes etiam
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              erunt aſſumptæ ſecundum eandem proportionem ad ipſas magni­
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              tudines, uel partes primas uel reſidua.</s>
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              <s id="id003459">
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              C
                <emph type="italics"/>
              o
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              ^{m}.</s>
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            <p type="main">
              <s id="id003460">Sed & id ſequitur ex his, quod cuiuſcunque ſeu totius ſeu partis
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              ſeu utriuſque pars maior aſſumetur, erit maior proportio totius ad
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              totum quàm reſidui ad reſiduum.</s>
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              <s id="id003461">
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              C
                <emph type="italics"/>
              or
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              ^{m}. 6.</s>
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              <s id="id003462">Hæc demonſtrantur à Campano, nam ſi ſit maior proportio a b
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              ad a g, quam k l ad k g, erit maior a b ad k l quàm a g ad k g.
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                <arrow.to.target n="marg646"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003463">
                <margin.target id="marg645"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id003464">
                <margin.target id="marg646"/>
              R
                <emph type="italics"/>
              up.
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              16.
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                <emph type="italics"/>
              quinti
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              E
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              lem.
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              </s>
            </p>
            <p type="main">
              <s id="id003465">Sequitur rurſus, quod in eadem conſtitutione cuiuſcunque ma­</s>
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              ior pars abſumetur, ea quantitas minori numero, uel numeri parte
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              abſumetur.</s>
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              <s id="id003467">
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              C
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              or
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              ^{m}. 7.</s>
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              <s id="id003468">Nam ſi minor erit continuo proportio a b ad a e, quàm k l ad k
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              o, & a e ad e g, quàm k o ad o g, erit longe minor a b ad b g quàm k l
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              ad l g, igitur longe maior a b ad a g quam k l ad k g. </s>
              <s id="id003469">Igitur a g citius
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              abſumetur quam k g.</s>
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              C
                <emph type="italics"/>
              o
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              ^{m}.</s>
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            <p type="main">
              <s id="id003471">Propoſitio centeſima octuageſima.</s>
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            <p type="main">
              <s id="id003472">Si aliqua quantitas in duas partes diuidatur, fueritque alicuius,
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              quantitatis ad partes illas compoſita proportio eiuſdem quan­
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              titatis ad partes alias quantitatis diuiſa aliter proportio eadem
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              componi.
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              </s>
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              C
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              o
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              ^{m}.</s>
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              <s id="id003474">Sit a b proportio ad partes c d quæ ſint c e, & c d componens f,
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              dico quod non poterit c d aliàs diuidi, ut proportio a b ad illas
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              componat eandem proportionem f. </s>
              <s id="id003475">Aliter ſit diuiſa in g, & erit </s>
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          </chap>
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