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="4" xlink:href="015/01/023.jpg"/>
            <p type="main">
              <s id="id000107">PRIMA Animi communis ſententia.</s>
            </p>
            <p type="main">
              <s id="id000108">Omnis Proportio eſt, aut æqualitatis, aut maior inæqualis,
                <lb/>
              aut minor.</s>
            </p>
            <p type="main">
              <s id="id000109">Secunda animi communis ſententia.</s>
            </p>
            <p type="main">
              <s id="id000110">Quilibet numerus tantus dicitur, quanta eſt illius proportio ad
                <lb/>
              monadem.</s>
            </p>
            <p type="main">
              <s id="id000111">Dicimus enim quatuor, quod monadem quater contineat. </s>
              <s id="id000112">Et
                <lb/>
              duo cum dimidio cùm monadem bis & ſemis contineat.</s>
            </p>
            <p type="main">
              <s id="id000113">Tertia animi communis ſententia.</s>
            </p>
            <p type="main">
              <s id="id000114">Proportionem defectus, ſeu detractæ quantitatis ad defectum
                <lb/>
              eſſe poſſe, ut quantitatis ad quantitatem dicuntur communes ani­
                <lb/>
              mi ſententiæ, quæ ex intellectu ſolo terminorum, quod ueræ ſint,
                <lb/>
              cognoſcuntur. </s>
              <s id="id000115">Si ergo defectus eſt quantitas, & quantitas eiuſdem
                <lb/>
              ſpeciei, quia detrahitur, & defectus non eſt ſimplicitur, ſed detra­
                <lb/>
              cto ergo per quartam petitionem: uel primam diffinitionem erit
                <lb/>
              proportio inter illas. </s>
              <s id="id000116">Sunt enim ambæ detractæ.</s>
            </p>
            <p type="main">
              <s id="id000117">Quarta animi communis ſententia.</s>
            </p>
            <p type="main">
              <s id="id000118">Inter quantitatem, & defectum minorem quantitate, cuius eſt de
                <lb/>
              fectus, eſt proportio, quatenus eſt quantitas. </s>
              <s id="id000119">Sit a b linea, & detra­
                <lb/>
              cta quantitas b c, non maior a b & d ſit alia quæuis quantitas eiuſ­
                <lb/>
                <figure id="id.015.01.023.1.jpg" xlink:href="015/01/023/1.jpg" number="4"/>
                <lb/>
                <expan abbr="dẽ">dem</expan>
              generis, dico quòd inter d & b c eſt propor­
                <lb/>
              tio quatenus b c eſt quantitas, quia ſunt eiuſ­
                <lb/>
              dem generis ideo ſunt in aliqua proportione
                <lb/>
              per primam diffinitionem. </s>
              <s id="id000120">Sed ut b c eſt defectus, nulla eſt propor­
                <lb/>
              tio: quia quanto b c augetur, tanto augetur proportio d ad b c, &
                <lb/>
              hoc eſt contra demonſtrata ab Euclide.</s>
            </p>
            <p type="main">
              <s id="id000121">Quinta animi communis ſententia.</s>
            </p>
            <p type="main">
              <s id="id000122">Cum proportio producitur ex proportionibus quælibet illa­
                <lb/>
              rum dicetur producta diuiſa per alteram.</s>
            </p>
            <p type="main">
              <s id="id000123">Sexta animi communis ſententia.</s>
            </p>
            <p type="main">
              <s id="id000124">Æqualium quantitatum ſeu proportionum ad tertiam compa­
                <lb/>
              rabilium eadem eſt proportio atque uiciſsim. </s>
              <s id="id000125">Hæc etſi demonſtre­
                <lb/>
              tur ab Euclide, eſt tamen hic generalior: & ſatis per ſe nota. </s>
              <s id="id000126">Vt ſit
                <lb/>
              propior animi communi ſententiæ, quàm rei demonſtrandæ.</s>
            </p>
            <p type="main">
              <s id="id000127">Septima animi communis ſententia.</s>
            </p>
            <p type="main">
              <s id="id000128">Ad quod quantitas proportionem habet infinitam, id in genere
                <lb/>
              illius quantitatis non comprehenditur.</s>
            </p>
            <p type="main">
              <s id="id000129">Nam proportio eſt duarum quantitatum eiuſdem generis com­
                <lb/>
              paratio certa: at hæc comparatio certa non eſt: non igitur quantita­
                <lb/>
              tes ambæ ſunt, aut non eiuſdem generis.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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