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="id000083">
                <pb pagenum="3" xlink:href="015/01/022.jpg"/>
              proportione a c ad d, relinquetur proportio a b ad d. </s>
              <s id="id000084">& probatur
                <lb/>
              ex conuerſione præcedentis.</s>
            </p>
            <p type="main">
              <s id="id000085">Sexta decima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000086">Extractio radicum alicuius proportionis fit per extractionem
                <lb/>
              radicum quantitatum illius iuxta unam, & eandem rationem.</s>
            </p>
            <p type="main">
              <s id="id000087">Velut quadratæ, uel cubæ, uel pronicæ, uel uninerſalis, uel alte­
                <lb/>
              rius modi.</s>
            </p>
            <p type="main">
              <s id="id000088">Decima ſeptima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000089">Cùm fuerint duæ proportiones ſimiles in tribus terminis con­
                <lb/>
              tinuatæ, dicetur proportio primæ quantitatis ad tertiam ueluti
                <lb/>
              primæ ad ſecundam duplicata. </s>
              <s id="id000090">Et ſi ſint tres proportiones ſimiles
                <lb/>
              in quatuor terminis, dicetur proportio primæ quantitatis ad quar­
                <lb/>
              tam triplicatà ei, quæ eſt primæ ad ſecundam,</s>
            </p>
            <p type="main">
              <s id="id000091">Decima octaua diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000092">Confuſa proportio dicitur ſimplicis, aut compoſitæ quantitatis
                <lb/>
              ad compoſitam in comparatione ad proportiones ad partes.</s>
            </p>
            <p type="main">
              <s id="id000093">Decimanona diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000094">Quantitates quę in continua ſunt proportione Analogæ
                <expan abbr="uocant̃">uocantur</expan>
              .</s>
            </p>
            <p type="main">
              <s id="id000095">Dictum eſt hoc ad fugiendum nomen barbarum, etiam ut bre­
                <lb/>
              uiter tamen poſſemus ſententiam explicare.</s>
            </p>
            <p type="main">
              <s id="id000096">Vigeſima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000097">Reflexa proportio dicitur cum trium quantitatum aggregatum
                <lb/>
              primæ, & tertiæ ſe habet ad ſecundam uelut ſecunda ad tertiam,</s>
            </p>
            <p type="main">
              <s id="id000098">Vigeſima prima diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000099">Trium quantitatum analogarum aliæ quidem Geometricæ,
                <lb/>
              cùm proportio ſimilis eſt: Aliæ Arithmeticæ, cum fuerit æqualis
                <lb/>
              exceſſus huc indè: Aliæ muſicæ cum fuerit proportio primæ ad ter
                <lb/>
              tiam multiplex, aut ſimplex, aut compoſita exceſſus quæ ſimplici
                <lb/>
              iuncta ſit ad multiplicis perfectionem: eadem autem ſit proportio
                <lb/>
              exceſſus primæ, & ſecundæ ad exceſſum ſecundæ ſupra tertiam.</s>
            </p>
            <p type="main">
              <s id="id000100">Velut proportio 6. 4. 3. dupla eſt utrinque, & 6. 3. 2 tripla. </s>
              <s id="id000101">& 28. 24.
                <lb/>
              21. & 45. 40. 36. Geometrica uerò & arithmetica facilius continuan­
                <lb/>
              tur in quotquot quantitatibus, ſed & muſica uelut 12. 8. 6. 4. 3. &
                <lb/>
              proportio 8 ad 5 muſica eſt: quia proportio 5 ad 4 muſica eſt, &
                <lb/>
              bene ſonans, igitur conſtitutis 8. 5. 4. cum 8 ad 4 benè ſonet, & 5
                <lb/>
              ad 4, & 4 ſit extrema non media inde 8. & 5 benè
                <expan abbr="ſonãt">ſonant</expan>
              . </s>
              <s id="id000102">nam in me­
                <lb/>
              dijs
                <expan abbr="nõ">non</expan>
              eſt
                <expan abbr="uerũ">uerum</expan>
              , ut in 9. 6. 4 bis diapente, & 16. 12. 9 bis diateſſaron.</s>
            </p>
            <p type="main">
              <s id="id000103">Vigeſima ſecunda diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000104">Quantitates quæ ſimilem habent proportionem non continua­
                <lb/>
              tam, omiologæ appellantur.</s>
            </p>
            <p type="main">
              <s id="id000105">Vigeſima tertia diffinitio.</s>
            </p>
            <p type="main">
              <s id="id000106">Prima operatione conſiſtere dicuntur proportiones, cùm inter
                <lb/>
              primo conflatas quantitates conſtiterint.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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