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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            <p type="main">
              <s id="id002998">
                <pb pagenum="171" xlink:href="015/01/190.jpg"/>
              cet, ut 256 ad 243, 13 autem eſt paulo plus decimanona, ergo multo mi­
                <lb/>
              nus ſemitonio minore. </s>
              <s id="id002999">ſecundum
                <expan abbr="mẽtem">mentem</expan>
              ergo Ptolemæi, poſito tono
                <lb/>
              inter 135, & 120, & ſemitonio maiore inter 128 & 120 remanebit ſemito­
                <lb/>
              nium minus fermè inter 19 & 18, id eſt, 133 & 126, quę proportio differt
                <lb/>
              à 135 & 138. Si quis autem bene animaduertat, ſexquioctuageſima illa
                <lb/>
              adimitur, ex tono & additur ſemitonio minori, & hæc eſt cauſa quòd
                <lb/>
              ſemitonium maius Ptolemæi ſit concinnum, quia additur tonis imper
                <lb/>
              fectis. </s>
              <s id="id003000">Dimidium autem ſemitonij minoris eſt inter 36 & 35, & uocatur
                <lb/>
                <expan abbr="cõma">comma</expan>
              : & eſt minus & maius: maius eſt inter 35 & 34, rurſus
                <expan abbr="cõma">comma</expan>
              mi­
                <lb/>
              nus diuiditur in duas dieſes, minorem, quæ eſt inter 72 & 71, & maio­
                <lb/>
              rem, quę eſt inter 71 & 70, & ideò manet difficultas quomodo intenta
                <lb/>
              uoce per dieſim fiat melior conſonantia? </s>
              <s id="id003001">nam de remiſsione poſſemus
                <lb/>
              dicere quòd accipitur loco ſexquioctuageſimæ: ſed in ſexquioctuage­
                <lb/>
              ſima remittitur de tono ſecundum mentem Ptolemæi, in dieſi intendi­
                <lb/>
              tur ſemitonium minus, ſicut oſtendit experimentum, ſed forſan conue
                <lb/>
              niunt quia intentio ſemitonij minoris deducit ſemiditonum ad ſexqui
                <lb/>
              quintam: eſt enim differentia ſemitonij minoris intenti hoc modo ad
                <lb/>
              ſemitonium minus, ut 136 ad 135: ſed hoc eſt longè minus ſexquioctua
                <lb/>
              geſima, unum ſat eſt, hanc eſſe ultimam diuiſionem toni in octo par­
                <lb/>
              tes, & ut in diatonico toni dominantur, ita in chromatico ſemitonia in
                <lb/>
              enarmonico dieſes, ſed dieſes fugitando (ut ita dicam) ac aures uelli­
                <lb/>
              cando, mirum in modum oblectant audientes: uelut toni ſtando, un­
                <lb/>
              de etiam nomen, ſemitonia medium modum obtinent.</s>
            </p>
            <p type="main">
              <s id="id003002">Tertium genus proportionis (omitto modò
                <expan abbr="diuiſionẽ">diuiſionem</expan>
              temporum
                <lb/>
              binarij, ternarij, quinarij, qui ultimus eſt eorum quos ſenſus recipiat,
                <lb/>
              nam ſeptenarius propinquior eſt binarij diuiſioni ob octonarium, &
                <lb/>
              modos illos ſatis notos Doricum, Lydium & Phrigium, ac eiuſmodi)
                <lb/>
              eſt Ptolemæi: rurſus qui cum uideret deſpectam futuram muſicæ con­
                <lb/>
              templationem, conatus eſt illius aliquod ſingulare emolumentum
                <lb/>
              oſtendere, quemadmodum fecit & in libro de Prædictionibus, exiſti­
                <lb/>
              mans ni illos compoſuiſſet ueluti pręmium oſtendentes tanti laboris
                <lb/>
              quantus neceſſarius uideretur ad intellectum librorum Magnæ com­
                <lb/>
              poſitionis, futurum eſſe, ut hi negligerentur, ergo & hoc in muſicæ li­
                <lb/>
              bris oſtendere molitus eſt, ſcilicet, præclarum eſſe
                <expan abbr="aliquẽ">aliquem</expan>
              huius
                <expan abbr="cõtem­plationis">contem­
                  <lb/>
                plationis</expan>
              finem, quod
                <expan abbr="utinã">utinam</expan>
              non feciſſet, ne illud uerè de eo dici poſſet:</s>
            </p>
            <p type="main">
              <s id="id003003">—Non omnia poſſumus omnes.</s>
            </p>
            <p type="main">
              <s id="id003004">Virum enim hunc ſupra omnem humani ingenij
                <expan abbr="metã">metam</expan>
              fuiſſe
                <expan abbr="nõ">non</expan>
              nega­
                <lb/>
              mus: ſed hanc partem quam hic agit, adeò infeliciter tractat, ut malim
                <lb/>
              credere
                <expan abbr="totũ">totum</expan>
              illum tertium
                <expan abbr="librũ">librum</expan>
              fuiſſe ab aliquo alio
                <expan abbr="adiectũ">adiectum</expan>
              . </s>
              <s id="id003005">Etenim
                <lb/>
              quid turpius ſapienti homini <08> imitari uulgares illos? </s>
              <s id="id003006">
                <expan abbr="ſeptẽ">ſeptem</expan>
              planetæ,
                <lb/>
              ſeptem mundi miracula,
                <expan abbr="ſeptẽ">ſeptem</expan>
              artes liberales: quid enim ſimilitudo nu</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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