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="39 [=29]" xlink:href="015/01/048.jpg"/>
            <p type="margin">
              <s id="id000553">
                <margin.target id="marg90"/>
              P
                <emph type="italics"/>
              rima ex
                <emph.end type="italics"/>
                <lb/>
              C
                <emph type="italics"/>
              ampano.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000554">Propoſitio trigeſima quinta.</s>
            </p>
            <p type="main">
              <s id="id000555">Vocum magnitudines excreſcunt in acumine non in grauitate,
                <lb/>
              finis autem eſt in utroque extremo, propter hoc minima facta uaria­
                <lb/>
              tione in hypate acutæ uix ferunt.
                <lb/>
                <arrow.to.target n="marg91"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000556">
                <margin.target id="marg91"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id000557">Quoniam facta uariatione in hypate, quæ eſt
                <lb/>
              in Diapaſon, uel bis Díapaſon maiore interual­
                <lb/>
                <figure id="id.015.01.048.1.jpg" xlink:href="015/01/048/1.jpg" number="42"/>
                <lb/>
              lo diſtat, uelut ex a in b in grauiore, maius eſt in­
                <lb/>
              teruallum ex c in d, igitur maior eſt b d, quàm a c
                <lb/>
              ergo ſingulæ uoces inter b & d magis diſtant,
                <lb/>
              quàm inter a & c, & quanto magis appropin­
                <lb/>
              quant ad d, igitur d maius eſt quàm b. </s>
              <s id="id000558">Ergo magnitudo eſt ratione
                <lb/>
              acuitatis, non grauitatis, cum ſuppoſuerimus d eſſe acutiorem b &
                <lb/>
              c ipſo a. </s>
              <s id="id000559">Oſtenditur etiam idem quia uox grauis fit ex priuatione
                <lb/>
              motus ſicut acuta ex uehementia. </s>
              <s id="id000560">Motus autem eſt res, quies,
                <lb/>
              priuatio.</s>
            </p>
            <p type="main">
              <s id="id000561">Secundum ſic: nam remiſsio mota non feriet aurem, ideò ſonum
                <lb/>
              non pariet ob nimiam tarditatem. </s>
              <s id="id000562">At in uelociſsimo motu oportet
                <lb/>
              uel fidem uel arteriam contrahi, & non contrahitur niſi per muſcu­
                <lb/>
              los, igitur contentio illa finem habet. </s>
              <s id="id000563">Si autem non ſit neceſſarium
                <lb/>
              habere, uel ualde procul poſsit extendi contentio, ut in machinis
                <lb/>
              igneis ſtrepitus fit maximus, nam motus, ut motus eſt etiam in aëre
                <lb/>
              nullum finem per ſe habet niſi ratione inſtrumenti, ergo ſtrepitus
                <lb/>
              tantus eſſe poteſt, ut fermè obſurdeſcant, qui audierint, ut ferunt de
                <lb/>
              Nili cataractis.</s>
            </p>
            <figure id="id.015.01.048.2.jpg" xlink:href="015/01/048/2.jpg" number="43"/>
            <p type="main">
              <s id="id000564">Tertium ſic ſit a b humi­
                <lb/>
              lior uox, quæ excreſcat ſe­
                <lb/>
              mitonio minore ſolum in
                <lb/>
              c, & ſit d e dupla ad ab ſe­
                <lb/>
              cundum naturam, ut in uo­
                <lb/>
              cibus medijs fiet, ut ſi e debeat excreſcere ſemitonio minore per de­
                <lb/>
              cimam nonam quinti
                <expan abbr="Elemẽtorum">Elementorum</expan>
              f e dupla c b, & in acutis ubi ex­
                <lb/>
              creuerit ad diapaſon quadrupla: pueri autem uox, quæ iam diapa­
                <lb/>
              ſon altior eſt d e, erit bis diapaſon, & ideò quadrupla b c, ſed in acu­
                <lb/>
              tioribus erit dupla, nullus enim puer eſt adeo fractæ uocis, quiſu­
                <lb/>
              pra humillimam non aſcendat per diapaſon, igitur interuallum uo­
                <lb/>
              cum erit octuplum a d, b c, ſed communiter aſcendunt ad bis diapa
                <lb/>
              ſon, igitur interuallum unius uocis etiam cum ſemitonio propor­
                <lb/>
              tionem habentis eſt æquale fermè toti a b, cum autem in diapaſon
                <lb/>
              ſint duodecim ſemitonia, & duo comata, manifeſtum eſt, quod ex­
                <lb/>
              tenſio illa erit maxima in
                <expan abbr="cõparatíone">comparatíone</expan>
              grauioris uo cis a b. </s>
              <s id="id000565">Et ideò
                <lb/>
              minimum in crementum in humilioribus uocibus, ubi quis </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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