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="176 [=182]" xlink:href="015/01/201.jpg"/>
            <p type="margin">
              <s id="id003155">
                <margin.target id="marg583"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id003156">
                <margin.target id="marg584"/>
              I
                <emph type="italics"/>
              n prima
                <emph.end type="italics"/>
                <lb/>
              D
                <emph type="italics"/>
              islcfficæ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003157">Propoſitio centeſima ſexageſima nona.</s>
            </p>
            <p type="main">
              <s id="id003158">Proportionem muſicam in inſtrumentis declarare iuxta compo
                <lb/>
              ſitionis rationem.
                <lb/>
                <arrow.to.target n="marg585"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003159">
                <margin.target id="marg585"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003160">Tria ſunt inſtrumentorum genera, in quibus maximè relucet ra­
                <lb/>
              tio compoſitionis muſicæ quæ à nobis nunc ſunt demonſtranda,
                <lb/>
              ſcilicet machinæ bellicę, ut catapultæ & baliſtę & ſcorpiones, & hy
                <lb/>
              draulica inſtrumenta ad modulationes parata, quæ antiquo tem­
                <lb/>
              pore maximè in uſu fuerunt nunc deſita, de quibus Vitruuius agit </s>
            </p>
            <p type="main">
              <s id="id003161">
                <arrow.to.target n="marg586"/>
                <lb/>
              in decimo libro. </s>
              <s id="id003162">Tertium eſt æneorum inſtrumentorum, quorum
                <lb/>
              etiam uſus deſijt in ſcœnicis theatris, ad intendendam uocem cum
                <lb/>
              modulatione, ut etiam clamor audientium & uulgi cum uoluptate
                <lb/>
                <arrow.to.target n="marg587"/>
                <lb/>
              excipiatur, de quo idem in quinto libro egit. </s>
              <s id="id003163">Sed nil melius quàm
                <lb/>
              uerba ipſius explicare de hoc tractantis, ſunt autem hæc. </s>
              <s id="id003164">“Muſicen
                <lb/>
              autem ſciat oportet, uti canonicam rationem & mathematicam no­
                <lb/>
              tam habeat: præterea baliſtarum, catapultarum, ſcorpionum tem­
                <lb/>
              peraturas poſsit rectè facere. </s>
              <s id="id003165">In capitulis enim dextra ac ſiniſtra
                <lb/>
              ſunt foramina homotonorum, per quę tenduntur ergatis aut ſucu­
                <lb/>
              lis & uectibus è neruo torti funes, qui non præcluduntur, nec præ­
                <lb/>
              ligantur niſi ſonitus ad artificis aures certos & ęquales fuerint. </s>
              <s id="id003166">Bra­
                <lb/>
              chia enim quæ in eas tentiones includuntur cum extenduntur æ­
                <lb/>
              qualiter & parter utraque plagam emittere debent. </s>
              <s id="id003167">Quod ſi non ho­
                <lb/>
              motona fuerint, impedient directam telorum miſsionem. </s>
              <s id="id003168">Item the­
                <lb/>
              atris uaſa ærea, quę in cellis ſub gradibus. </s>
              <s id="id003169">mathematica ratione
                <expan abbr="collo­cant̃">collo­
                  <lb/>
                cantur</expan>
              , &
                <expan abbr="ſonitũ">ſonitum</expan>
              diſcrimina, quę Gręci
                <foreign lang="grc">̓ηχ̂εια</foreign>
                <expan abbr="uocãt">uocant</expan>
              , ad ſymphonias mu
                <lb/>
              ſicas ſiue concentus
                <expan abbr="componunt̃">componuntur</expan>
              , diuiſa in circinatione diateſſaron
                <lb/>
              & diapente & diapaſon, uti uox ſcœnici ſonitus
                <expan abbr="cõueniens">conueniens</expan>
              in diſpo
                <lb/>
              ſitionibus, tactu
                <expan abbr="cũ">cum</expan>
              oſtenderit aucta
                <expan abbr="cũ">cum</expan>
                <expan abbr="incremẽto">incremento</expan>
              clarior et ſuauior
                <lb/>
              ad
                <expan abbr="ſpectatorũ">ſpectatorum</expan>
              perueniat aures. </s>
              <s id="id003170">Hydraulicas quo que machinas & cæ­
                <lb/>
              tera
                <expan abbr="q̃">quae</expan>
              ſunt ſimilia his organis ſine muſicis rationibus. </s>
              <s id="id003171">efficere nemo
                <lb/>
              poterit. </s>
              <s id="id003172">Capiamus ergo primum illud q̊d eſt manifeſtius, ſcilicet de
                <lb/>
              hydraulicis organis quorum meminit Suetonius in Nerone: Reli­
                <lb/>
              quam diei partem per organa hydraulica noui & ignoti generis cir
                <lb/>
              cunduxit, oſtendenſque ſingula de ratione ac difficultate cuiuſque diſ­
                <lb/>
              ſerens iam ſe prolaturum, ut conſtet illa fuiſſe magni opificij quæ
                <lb/>
              noſtra ętate deſiere.” Reſtat unicum & ualde leue
                <expan abbr="exemplũ">exemplum</expan>
              auiculæ
                <lb/>
              æneæ uelligneæ reſonantis. </s>
              <s id="id003173">Certum eſt
                <expan abbr="aẽre">aere</expan>
              effici ſonum, ſed ita mi
                <lb/>
              ſceri aquæ, ut dulcior & mollior non ſolum euadat, ſed etiam acuti­
                <lb/>
              or ac modulatior. </s>
              <s id="id003174">Eadem autem ratio maris: ſed cum aquæ corpus
                <lb/>
              moueatur, uidetur difficile ſeruare proportionem. </s>
              <s id="id003175">ea prima diffi­
                <lb/>
              cultas. </s>
              <s id="id003176">ſecunda eſt, quod cùm aqua moueatur, uix fieri poſſe uide­
                <lb/>
              tur ut totum ſeruet uocis integrum tenorem. </s>
              <s id="id003177">tertia ob illius </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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