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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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id003951">
                <pb pagenum="232" xlink:href="015/01/251.jpg"/>
              intercepta à linea ex centro longior eſt peripheria, ſimiliter in­
                <lb/>
              tercepta.</s>
            </p>
            <p type="main">
              <s id="id003952">
                <arrow.to.target n="marg773"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003953">
                <margin.target id="marg773"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003954">Sit portio circuli a e, & linea a b intercepta à linea c b ex centro,
                <lb/>
                <figure id="id.015.01.251.1.jpg" xlink:href="015/01/251/1.jpg" number="249"/>
                <lb/>
              dico ab eſſe longiorem a e, ducatur b e æqualis a b, ad </s>
            </p>
            <p type="main">
              <s id="id003955">
                <arrow.to.target n="marg774"/>
                <lb/>
              circumferentiam, quæ illi obuiabit, ducanturque c a, c e
                <lb/>
                <arrow.to.target n="marg775"/>
                <lb/>
              eritque angulus e c b æqualis a c b, igitur arcus a d, æ­
                <lb/>
              qualis d c, quare a d erit
                <expan abbr="dimidiũ">dimidium</expan>
              a e, & a b dimidium
                <lb/>
                <arrow.to.target n="marg776"/>
                <lb/>
              a b, b e, facta enim fuit b e æqualis a b, cum ergo per
                <lb/>
              præſentem duæ lineæ a b, b e, ſint maiores a e, igitur per commu­
                <lb/>
              nem animi ſententiam a b maior a d.</s>
            </p>
            <p type="margin">
              <s id="id003956">
                <margin.target id="marg774"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              tertij
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003957">
                <margin.target id="marg775"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              primi
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003958">
                <margin.target id="marg776"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              |26.
                <emph type="italics"/>
              ter­
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003959">Propoſitio ducenteſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id003960">Rationem ſtrepitus oſtendere.
                <lb/>
                <arrow.to.target n="marg777"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003961">
                <margin.target id="marg777"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003962">Fit ſtrepitus ob multitudinem aëris percuſsi, uelut cum tabulis
                <lb/>
              percutimus: & cauitatum cauſa, unde ligna & tabulæ leues magis
                <lb/>
              ſtrepunt, & illud Virgilij:</s>
            </p>
            <p type="main">
              <s id="id003963">—Sonitumque dedere cauernæ.</s>
            </p>
            <p type="main">
              <s id="id003964">Tum uerò ob ictus impetum, impetus
                <expan abbr="autẽ">autem</expan>
              partim uelocitatis cau­
                <lb/>
              ſa, partim anguſtiæ loci. </s>
              <s id="id003965">Fulmen edit tonitru in quo & caua nebula
                <lb/>
              excipit aërem, & multum impetuque maximo delatum,
                <expan abbr="obſtrepũt">obſtrepunt</expan>
              au
                <lb/>
              tem metalla magis quam ligna eo quòd magis ob
                <expan abbr="continuitatẽ">continuitatem</expan>
              par
                <lb/>
              tes moueantur. </s>
              <s id="id003966">Indicio eſt, quod intenta ut æs & tenuia
                <expan abbr="maiorẽ">maiorem</expan>
              ſtre
                <lb/>
              pitum edunt: & dum ſonant tremunt, aurum autem parum ſonat,
                <lb/>
              quoniam denſiſsimum eſt, et minus intentum
                <expan abbr="argẽtum">argentum</expan>
              , minus den
                <lb/>
              ſum, & magis intentum, quod autem intentum eſt totum ſimul mo
                <lb/>
              uetur, & ob id ſtridet: lignum
                <expan abbr="autẽ">autem</expan>
              & tabula ſonat, non quia ut me­
                <lb/>
              tallum percutiat aërem, ſed quia in eo aër percutitur. </s>
              <s id="id003967">Craſſum
                <expan abbr="autẽ">autem</expan>
                <lb/>
              metallum & lignum non adeò ſonant: metallum quoniam non mo
                <lb/>
              uet aërem, non enim mouetur: lignum quoniam non mouetur, nec
                <lb/>
              in eo qui eſt incluſus aër, aër autem facilè mouetur, & ob id in ligno
                <lb/>
              cauo, etiamſi craſſum ſit, ſtrepitus magnus editur. </s>
              <s id="id003968">Ergo etſi tenue
                <lb/>
              ſit metallum, quod infixum eſt tabulę, reſonat multum:
                <expan abbr="nõ">non</expan>
              quia mo
                <lb/>
              ueatur, ſed quoniam
                <expan abbr="aẽrem">aerrem</expan>
              in tabula
                <expan abbr="cõ">com</expan>
              cutit. </s>
              <s id="id003969">Neque enim tabula per
                <lb/>
              ſe ſola, quæ etiam nimis tunderetur ſonum edere magnum poteſt
                <lb/>
              quoniam cedit: Oportet
                <expan abbr="autẽ">autem</expan>
              non cedere quod reſonat, neque metal­
                <lb/>
              lum ſi craſſum, ſed hebetem
                <expan abbr="ſonũ">ſonum</expan>
              etiam tabulę infixum reddit, quo­
                <lb/>
              niam neque moueri poteſt infixum & craſſum, nec cauernoſum eſt, &
                <lb/>
              tamen excipit ictum, ne lignum reſonet. </s>
              <s id="id003970">Velox autem ictus
                <expan abbr="nõ">non</expan>
              acu­
                <lb/>
              tum
                <expan abbr="ſonũ">ſonum</expan>
              reddit, & ſi cum impetu ſit: indicio eſt tonitru & machinę
                <lb/>
              bellicæ igneę, contrà anguſta fiſtula
                <expan abbr="acutũ">acutum</expan>
              ſonum reddit,
                <expan abbr="etiã">etiam</expan>
              remiſ­
                <lb/>
              ſè inflata. </s>
              <s id="id003971">Igitur aër ſoni cauſa eſt ſecundum
                <expan abbr="motũ">motum</expan>
              , ubi ergo multus
                <lb/>
              aër & magnus motus ibi ſonus magnus. </s>
              <s id="id003972">Multus quidem aut in </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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