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="id002969">
                <pb pagenum="169" xlink:href="015/01/188.jpg"/>
              uas producit 72 et 81,
                <expan abbr="nã">nam</expan>
              72 ad 64 eſt ſexquio
                <expan abbr="ctauũ">ctauum</expan>
              , ſicut 81 ad 72. uerùm
                <lb/>
              id accidebat in
                <expan abbr="cõmodi">commodi</expan>
              quae 81 ad 64
                <expan abbr="nullã">nullam</expan>
              habet
                <expan abbr="proportionẽ">proportionem</expan>
                <expan abbr="commodã">commodam</expan>
              ,
                <lb/>
              & multo minus 96 ad 81, quare uiſum eſt Ptolemęo ut ſubtracta mona
                <lb/>
              de
                <expan abbr="fierẽt">fierent</expan>
              termini 64, 72, 80, & 96, proportio
                <expan abbr="aũt">aut</expan>
              80 ad 64
                <expan abbr="cõſtituit">conſtituit</expan>
              ſexqui
                <lb/>
                <expan abbr="quartã">quartam</expan>
              atque
                <expan abbr="ditonũ">ditonum</expan>
              , proportio quoque 96 ad 72
                <expan abbr="ſexquitertiã">ſexquitertiam</expan>
                <expan abbr="ſemiditonũ">ſemiditonum</expan>
              que.
                <lb/>
              </s>
              <s id="id002970">Rurſus proportio 128 ad 64
                <expan abbr="cõponit̃">componitur</expan>
              ex proportionibus </s>
              <s id="id002971">80 ad 64,
                <expan abbr="q̃">quae</expan>
                <expan abbr="habet̃">habetur</expan>
                <lb/>
              pro ditono ut
                <expan abbr="dictũ">dictum</expan>
              eſt, & eſt ſexquiquarta proportio. </s>
              <s id="id002972">At 128 cum 80 eſt in
                <lb/>
              proportione ſuperpartiente tres quintas,
                <expan abbr="q̃">quae</expan>
                <expan abbr="iterũ">iterum</expan>
              eſt conſona. </s>
              <s id="id002973">Regula
                <expan abbr="em̃">emm</expan>
                <lb/>
              eſt quae ubi conſonantia uo
                <expan abbr="cũ">cum</expan>
                <expan abbr="diuidat̃">diuidatur</expan>
              in duas partes,
                <expan abbr="quarũ">quarum</expan>
              una ſit conſo
                <lb/>
              nans,
                <expan abbr="reliquã">reliquam</expan>
                <expan abbr="etiã">etiam</expan>
              eſſe
                <expan abbr="conſonantẽ">conſonantem</expan>
              , at
                <expan abbr="nõ">non</expan>
                <expan abbr="cõuertit̃">conuertitur</expan>
              . </s>
              <s id="id002974">Sępe. </s>
              <s id="id002975">n. </s>
              <s id="id002976">fit ut ex duabus
                <lb/>
              </s>
              <s id="id002977">conſonantibus diſſonans
                <expan abbr="cõpoſitio">compoſitio</expan>
                <expan abbr="oriat̃">oriatur</expan>
              , uelut ex duplici
                <expan abbr="diapẽte">diapente</expan>
              , aut
                <lb/>
                <expan abbr="diapẽte">diapente</expan>
                <expan abbr="cũ">cum</expan>
              ditono, ſed ut ad
                <expan abbr="propoſitũ">propoſitum</expan>
              reuertar, alia diapaſon eſt inter 80
                <lb/>
              & 40, at inter 48 & 40 eſt ſemiditonus ut
                <expan abbr="oſtẽſum">oſtenſum</expan>
              eſt, uelut inter 96 &
                <lb/>
              80, nam inter 45 & 40 eſt proportio ſexquioctaua, inter 48
                <expan abbr="aũt">aut</expan>
              & 45 ſex­
                <lb/>
              quiquinta decima,
                <expan abbr="igit̃">igitur</expan>
              ex regula data proportio 80 ad 48
                <expan abbr="q̃">quae</expan>
              eſt ſuperbi­
                <lb/>
              partiens tertias ſeu ſolida
                <expan abbr="cũ">cum</expan>
              beſſe ſeu ſexta maior erit
                <expan abbr="cõſonans">conſonans</expan>
              . </s>
              <s id="id002978">Iam er
                <lb/>
              go uidemus detractione aut additione ſexquioctuageſimæ, concinnas
                <lb/>
              reddi uulgatiores armonias:
                <expan abbr="tertiã">tertiam</expan>
              utran que
                <expan abbr="maiorẽ">maiorem</expan>
              ſcilicet &
                <expan abbr="minorẽ">minorem</expan>
              , ac
                <lb/>
              rurſus
                <expan abbr="ſextã">ſextam</expan>
                <expan abbr="maiorẽ">maiorem</expan>
              atque minore
                <expan abbr="q̃">quae</expan>
              in minoribus numeris ſcilicet à mo­
                <lb/>
              nade ad octo poſitæ ſunt. </s>
              <s id="id002979">Vides præterea
                <expan abbr="ſemiditonũ">ſemiditonum</expan>
              in ſexquiquinta
                <lb/>
                <arrow.to.target n="table21"/>
                <lb/>
                <expan abbr="cõſtare">conſtare</expan>
              : adeò ut à ſenario infra nihil inutile
                <lb/>
                <figure id="id.015.01.188.1.jpg" xlink:href="015/01/188/1.jpg" number="195"/>
              reddatur. </s>
              <s id="id002980">Diateſſaron
                <expan abbr="aũt">aut</expan>
              cum primum di
                <lb/>
              uidi poteſt, ſi ſecus diuidatur <08> in
                <expan abbr="ditonũ">ditonum</expan>
                <lb/>
              &
                <expan abbr="ſemitoniũ">ſemitonium</expan>
              , aut in ſemiditonum &
                <expan abbr="tonũ">tonum</expan>
              ,
                <lb/>
              ſcilicet in duo
                <expan abbr="tantũ">tantum</expan>
              interualla, non
                <expan abbr="cõmo­dius">commo­
                  <lb/>
                dius</expan>
                <expan abbr="quã">quam</expan>
              inter octo & ſeptem & ſex diuidi
                <lb/>
              poteſt. </s>
              <s id="id002981">Cum ergo octo ad
                <expan abbr="ſeptẽ">ſeptem</expan>
              diſſona ſit,
                <lb/>
              quippe nimis remota eſt hęc proportio à ſen
                <lb/>
              ſu humano:
                <expan abbr="quamobrẽ">quamobrem</expan>
              ex regula data, ne­
                <lb/>
              que proportio
                <expan abbr="ſeptẽ">ſeptem</expan>
              ad ſex. </s>
              <s id="id002982">Sed dubitabis
                <lb/>
              meritò, quia
                <expan abbr="cũ">cum</expan>
              diateſſaron diuidatur
                <expan abbr="bifa­riã">bifa­
                  <lb/>
                riam</expan>
              , in
                <expan abbr="ditonũ">ditonum</expan>
              &
                <expan abbr="ſemitoniũ">ſemitonium</expan>
              , ac rurſus in
                <expan abbr="ſe­miditonũ">ſe­
                  <lb/>
                miditonum</expan>
              &
                <expan abbr="tonũ">tonum</expan>
              , quarum altera
                <expan abbr="cõſonans">conſonans</expan>
              eſt, reliqua
                <expan abbr="nõ">non</expan>
              . </s>
              <s id="id002983">
                <expan abbr="Videt̃">Videtur</expan>
              ergo
                <lb/>
              infirmari regula illa, quae conſonantia diuiſa ſi una pars
                <expan abbr="cõſonet">conſonet</expan>
              , alia non
                <lb/>
              poſsit eſſe diſſonans,
                <expan abbr="nã">nam</expan>
              conſtat
                <expan abbr="coniũ">conium</expan>
              &
                <expan abbr="ſemitoniũ">ſemitonium</expan>
              tam per ſe quam in
                <lb/>
                <expan abbr="cõpoſitione">compoſitione</expan>
              diſſonare: &
                <expan abbr="nõ">non</expan>
                <expan abbr="parũ">parum</expan>
              ſed acerbè. </s>
              <s id="id002984">
                <expan abbr="Verũ">Verum</expan>
              reſpondeo diateſſa
                <lb/>
              ron, ut dixi, numerari inter ambiguas coniugationes, quatenus
                <expan abbr="em̃">emm</expan>
              per
                <lb/>
              ſe eſt, diſſonans eſt: at que ſic in
                <expan abbr="conſonantẽ">conſonantem</expan>
              & diſſonantem diuidi poteſt:
                <lb/>
              quatenus
                <expan abbr="aũt">aut</expan>
              pars eſt diapaſon
                <expan abbr="cõſonans">conſonans</expan>
              in acutis: quan <08>
                <expan abbr="etiã">etiam</expan>
              adiecta
                <lb/>
              ditono aut ſemiditono ſuprà efficiat
                <expan abbr="ſextã">ſextam</expan>
              maiorem aut
                <expan abbr="minorẽ">minorem</expan>
              parum
                <lb/>
              benè ſonantes. </s>
              <s id="id002985">At quintupla proportio ut ab initio propoſitum eſt,
                <expan abbr="cõſtat">conſtat</expan>
                <lb/>
              bis diapaſon, & ſexquiquarta, ut planè
                <expan abbr="manifeſtũ">manifeſtum</expan>
              eſt: ſexquiquarta
                <expan abbr="aũt">aut</expan>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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