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="id000062">
                <pb pagenum="2" xlink:href="015/01/021.jpg"/>
              pus. </s>
              <s id="id000063">Dicimus enim motum tardum, uel uelocem in comparatione
                <lb/>
              ad tempus.</s>
            </p>
            <p type="margin">
              <s id="id000064">
                <margin.target id="marg1"/>
              C
                <emph type="italics"/>
              ar
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000065">Nona diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000066">Proportionum aliæ dicuntur rhete, aliæ alogæ, rhetæ quæ ſunt
                <lb/>
              ut numeri ad numerum, alogæ quæ non ſunt numeri ad numerum.</s>
            </p>
            <p type="main">
              <s id="id000067">Decima diffinitio</s>
            </p>
            <p type="main">
              <s id="id000068">Proportio rhete alia æqualis, alia multiplex, uel ſubmultiplex:
                <lb/>
              alia unius partis exceſſus, aut defectus, alia plurium, quam ſuper­
                <lb/>
              partientem, aut ſupartientem uocant.</s>
            </p>
            <p type="main">
              <s id="id000069">Vndecima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000070">Cum diuiſo denominatore per numeratorem exit quantitas alo
                <lb/>
              ga, proportio dicitur aloga: ſi autem numerus integer, aut pars nu­
                <lb/>
              meri nota dicitur rhete.</s>
            </p>
            <p type="main">
              <s id="id000071">Duodecima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000072">Proportionem in proportionem duci eſt, quoties recto ordine
                <lb/>
              tres quantitates in eiſdem collo
                <expan abbr="cant̃">cantur</expan>
              : ut ſint tres quan
                <lb/>
                <figure id="id.015.01.021.1.jpg" xlink:href="015/01/021/1.jpg" number="2"/>
                <lb/>
              titates a b c dicetur proportio a ad c producta ex pro
                <lb/>
              portione a ad b & b ad c, & ſimiliter proportio c ad
                <lb/>
              a producitur ex proportione b ad a, & c ad b.</s>
            </p>
            <p type="main">
              <s id="id000073">Tertia decima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000074">Proportionem per proportionem diuidi eſt, quoties ad eandem
                <lb/>
              quantitatem duæ quantitates comparantur, tunc illarum propor­
                <lb/>
              tio eſt, quæ prodit una per alteram diuiſa.</s>
            </p>
            <p type="main">
              <s id="id000075">Sint proportiones a & b ad c & interponatur b inter a & c, dico
                <lb/>
              proportionem a ad c diuiſam per proportionem a ad b, & prodire
                <lb/>
              proportionem b ad c, conſtat ex conuerſa præcedentis.</s>
            </p>
            <p type="main">
              <s id="id000076">Quarta decima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000077">Additio proportionum intelligitur quotiens duarum quanti­
                <lb/>
              tatum ad unam tertiam, proportiones per aggregatum ipſarum
                <lb/>
              quantitatum ad eandem coniunguntur.</s>
            </p>
            <p type="main">
              <s id="id000078">Velut ſi comparentur a b & b c ad d, inde tota
                <lb/>
                <figure id="id.015.01.021.2.jpg" xlink:href="015/01/021/2.jpg" number="3"/>
                <lb/>
              a c ad d dicemus proportionem, ac ad d eſſe con
                <lb/>
                <expan abbr="iunctã">iunctam</expan>
              ex duabus proportionibus a b ad d & b c
                <lb/>
              ad
                <expan abbr="eandẽ">eandem</expan>
              d. </s>
              <s id="id000079">Hoc & duo ſequentes ſicut & duę
                <expan abbr="antecedẽtes">antecedentes</expan>
              demon­
                <lb/>
              ſtrabitur eſſe. </s>
              <s id="id000080">nunc ſolum quomodo
                <expan abbr="intelligendũ">intelligendum</expan>
              ſit proponimus.</s>
            </p>
            <p type="main">
              <s id="id000081">Quinta decima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000082">Detractionem proportionis à proportione intelligimus fieri
                <lb/>
              per
                <expan abbr="detractionẽ">detractionem</expan>
              minoris quantitatis à maiore, comparatam ad ean­
                <lb/>
              dem quantitatem.</s>
            </p>
            <p type="main">
              <s id="id000083">Velut in exemplo ſuperiore detracta proportione b c ad d ex </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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