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="id002941">
                <pb pagenum="168" xlink:href="015/01/187.jpg"/>
              tum pertinent. </s>
              <s id="id002942">Igitur ut ad rem redeam. </s>
              <s id="id002943">Solis cum octauo Orbe ea
                <lb/>
              ratio eſt, ut linea quam ille permeat eadem ſit quam quę fixę ſtellæ,
                <lb/>
              non. </s>
              <s id="id002944">n. </s>
              <s id="id002945">ad eandem diſtantiam & mente conceptam ab æquinoctijs
                <lb/>
              deſcendentem ac æquidiſtantem mouetur, ſed ad eam ſecundum
                <lb/>
              quam ſtellę fixę in octauo orbe mouentur in comparatione ad ecli­
                <lb/>
              pticam ſuperioris orbis. </s>
              <s id="id002946">Porrò de his atque huiuſmodi in Paralipo­
                <lb/>
              menis diximus, ubi etiam docuimus quomodo ſecundum duos cir
                <lb/>
                <arrow.to.target n="marg578"/>
                <lb/>
              culos, qui ſolum circa ſuum centrum mouentur, punctus datus per
                <lb/>
              petuò in recta linea feratur.</s>
            </p>
            <p type="margin">
              <s id="id002947">
                <margin.target id="marg577"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id002948">
                <margin.target id="marg578"/>
              L
                <emph type="italics"/>
              ib.
                <emph.end type="italics"/>
              14.
                <lb/>
                <emph type="italics"/>
              cap.
                <emph.end type="italics"/>
              7.</s>
            </p>
            <p type="main">
              <s id="id002949">Propoſitio centeſima ſexageſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id002950">Proportiones muſicas ſuperpartientes in eas quæ particula una
                <lb/>
              tantum abundant reducere.
                <lb/>
                <arrow.to.target n="marg579"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002951">
                <margin.target id="marg579"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="main">
              <s id="id002952">Ptolemęi hoc inuentum fuit, ut & multa alia pręclara: itaque ſta­
                <lb/>
              tuendum eſt, primum uoces ęquales non concentum efficere, quia
                <lb/>
              diuerſæ non ſunt, quę autem diuerſę ſunt, nihilominus proportio­
                <lb/>
              ne conſtant ſimpliciſsima & multiplici, tales optimam efficiunt ar­
                <lb/>
              moniam. </s>
              <s id="id002953">Eiuſmodi ſunt quæ in dupla ſunt proportione, uocatur
                <lb/>
              autem diapaſon. </s>
              <s id="id002954">1. quaſi omnia comprehendens non à numero uo­
                <lb/>
              cum uelut diapente & diateſſaron à quatuor & quin que uo cibus. </s>
              <s id="id002955">In
                <lb/>
              diapaſo. </s>
              <s id="id002956">n. </s>
              <s id="id002957">omnia
                <expan abbr="cõprehendi">comprehendi</expan>
              uidentur. </s>
              <s id="id002958">1. omnes uo
                <expan abbr="cũ">cum</expan>
              differentiæ,
                <lb/>
                <expan abbr="quanquã">quanquam</expan>
              ex octo
                <expan abbr="tantũ">tantum</expan>
              uo cibus conſtet. </s>
              <s id="id002959">Pòſt ſunt quæ in
                <expan abbr="q̃drupla">quadrupla</expan>
              ,
                <lb/>
              unde bis diapaſon, poſt quæ in tripla, nam propior eſt monadi ſeu ę­
                <lb/>
              qualitati: ſed non adeò ſimplex ut bis diapaſon. </s>
              <s id="id002960">Vocant
                <expan abbr="aũt">aut</expan>
              hanc
                <lb/>
              diapaſon diapente: inde
                <expan abbr="ſubſequit̃">ſubſequitur</expan>
              octupla quę uix in uocibus </s>
              <s id="id002961">huma­
                <lb/>
              nis habetur:
                <expan abbr="frequẽs">frequens</expan>
              in inſtrumentis, uo
                <expan abbr="cat̃que">caturque</expan>
              tris diapaſon inde ſex­
                <lb/>
              cupla, ſeu bis diapaſon diapente. </s>
              <s id="id002962">Quintupla
                <expan abbr="aũt">aut</expan>
              minus
                <expan abbr="cõcors">concors</expan>
              eſt:
                <lb/>
              ſed de hac inferius dicemus, atque de multiplicibus </s>
              <s id="id002963">dicta ſunto. </s>
              <s id="id002964">Sed de
                <lb/>
                <expan abbr="cõ">com</expan>
              centu ex particula ſuperaddita ſexquialtera ſexquitertia atque alijs
                <lb/>
              nunc agendum. </s>
              <s id="id002965">Clarum eſt. </s>
              <s id="id002966">n. </s>
              <s id="id002967">has eſſe ſimpliciſsimas. </s>
              <s id="id002968">Cum ergo du
                <lb/>
              pla proportio non magis poſsit diuidi æqualibus interuallis atque
                <lb/>
              ſimplicibus proportionibus quàm in ſexquialteram & ſexquiter­
                <lb/>
              tiam, uelut inter 4 & 2 interpoſito 3. nam proportio 3 ad 2 eſt ſex­
                <lb/>
              quialtera, & 4 ad 3 ſexquitertia: nec melius poteſt diuidi, at ſexqui­
                <lb/>
              alteram & ſexquitertiam quantumuis magnis numeris diuidere
                <lb/>
              non licebat melius aut commodius quam per ſexquioctauas: uelu­
                <lb/>
              ti ſumpto numero 64 cui duplus eſt 128, inter medius 96 qui cum
                <lb/>
              64 ſexquialteram facit proportionem, quæ ſuauiſsima eſt omni­
                <lb/>
              um deductis multiplicibus, uocaturque diapente. </s>
              <s id="id002969">At quæ eſt 128 ad
                <lb/>
              96 ſexquitertia eſt minuſque benè ſonat per ſe, ſed in acutioribus uo­
                <lb/>
              cibus ſolum cum alijs benè ſonat, uelut cum diapente, perficiens
                <lb/>
              diapaſon, interuallum, ergo inter 96 & 64 diuiſum per ſexquiocta­</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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