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="id001001">
                <pb pagenum="55" xlink:href="015/01/074.jpg"/>
              rò proportio ratione deſcenſus aucta, declarata eſt paulo antè,
                <lb/>
              quare cum medium ſupponatur eiuſdem generis, & figura non
                <lb/>
              eiuſmodi, nec leuitas, ut prorſus non impellat, nedum ut moueat la
                <lb/>
              tus: figura quo que eadem ambobus relinquetur proportio motus
                <lb/>
              ad motum producta ex proportionibus incrementi in proportio­
                <lb/>
                <arrow.to.target n="marg185"/>
                <lb/>
              nem ponderum, & iam habuimus proportionem incrementi ex
                <lb/>
                <arrow.to.target n="marg186"/>
                <lb/>
              motu aëris, ergo proportio unius motus producti ad alteram no­
                <lb/>
              ta erit.</s>
            </p>
            <p type="margin">
              <s id="id001002">
                <margin.target id="marg182"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              30.</s>
            </p>
            <p type="margin">
              <s id="id001003">
                <margin.target id="marg183"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              59.</s>
            </p>
            <p type="margin">
              <s id="id001004">
                <margin.target id="marg184"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              62.</s>
            </p>
            <p type="margin">
              <s id="id001005">
                <margin.target id="marg185"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              42.
                <emph type="italics"/>
              ha­rum.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001006">
                <margin.target id="marg186"/>
              I
                <emph type="italics"/>
              n
                <emph.end type="italics"/>
              61.
                <emph type="italics"/>
              ha­rum.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001007">Propoſitio ſexageſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id001008">Proportionem laterum eptagoni, & ſubtenſarum conſiderare,
                <lb/>
              & quæ à reflexa proportione pendent.
                <lb/>
                <arrow.to.target n="marg187"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001009">
                <margin.target id="marg187"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id001010">Sit eptagonus a b d f g e c, & ſubtenſæ b
                <lb/>
                <figure id="id.015.01.074.1.jpg" xlink:href="015/01/074/1.jpg" number="70"/>
                <lb/>
              c, & f e duobus lateribus, tribus autem d c
                <lb/>
              d e, & erunt (quia intelligitur eptagono æ­
                <lb/>
              quilatero, & æquiangulo) b c & e f inuicem
                <lb/>
              æquales: & item d c, & d e æquales: & ſi du­
                <lb/>
              cerentur b e & c f inuicem æquales: & ad a c
                <lb/>
              & d g: quare cum angulus cb d conſiſtatin </s>
            </p>
            <p type="main">
              <s id="id001011">
                <arrow.to.target n="marg188"/>
                <lb/>
              arcu c e g f d, & angulus b d c in arcu b a c,
                <lb/>
              & angulus b c d in arcu b d; & ſit arcus c e g
                <lb/>
              f d duplus arcus b a c, quia c e g f d ſubtendit quatuor latera epta­
                <lb/>
              goni, & arcus b a c duo, & ita arcus etiam b a c duplus arcui b d
                <lb/>
              erit angulus d b e duplus angulo c d b, & angulus c d b duplus an­
                <lb/>
                <arrow.to.target n="marg189"/>
                <lb/>
              gulo b c d, quare per demonſtrata à nobis proportio laterum b d,
                <lb/>
              b c, c d, eſt reflexa, igitur proportio d b & b c, ad d c, ut d e ad b c, &
                <lb/>
                <arrow.to.target n="marg190"/>
                <lb/>
              rurſus proportio b d & d e ad b e, ut b e ad b d. </s>
              <s id="id001012">Quare ſuppoſita
                <lb/>
              d b 1, b c 1 poſitione, erit d c latus 1 quad. </s>
              <s id="id001013">p: 1 poſitione. </s>
              <s id="id001014">Proportio
                <lb/>
                <arrow.to.target n="marg191"/>
                <lb/>
              uerò, ut dictum eſt b d & d c ad b c, id eſt p: <02> 1 quad. </s>
              <s id="id001015">p: 1 pos, ad 1
                <lb/>
              pos eſt, ut b c ad b d, id eſt 1 pos ad 1, igitur 1 p: <02> v: 1 quad. </s>
              <s id="id001016">p: 1 pos
                <lb/>
              æquatur quadrato b c, quod eſt 1 quad. </s>
              <s id="id001017">igitur 1 quad. </s>
              <s id="id001018">m: 1 æquatur
                <lb/>
              <02> v: 1 quad. </s>
              <s id="id001019">p: 1 pos quare 1 quad. </s>
              <s id="id001020">quad. </s>
              <s id="id001021">m: 2, quad. </s>
              <s id="id001022">p: 1 æquatur 1
                <lb/>
              quad. </s>
              <s id="id001023">p: 1 pos. </s>
              <s id="id001024">Additis igitur communiter quatuor quadratis fient
                <lb/>
              1 quad. </s>
              <s id="id001025">quad. </s>
              <s id="id001026">p: 2 quad. </s>
              <s id="id001027">p: 1 æqualia 5 quad. </s>
              <s id="id001028">p: 1 pos. </s>
              <s id="id001029">Et reducitur ad
                <lb/>
              1 cu. </s>
              <s id="id001030">æqualem 1 3/4 pos p: 7/8.</s>
            </p>
            <p type="margin">
              <s id="id001031">
                <margin.target id="marg188"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              28. & 29.
                <emph type="italics"/>
              tertij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001032">
                <margin.target id="marg189"/>
              P
                <emph type="italics"/>
              er ult. </s>
              <s id="id001033">ſexti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001034">
                <margin.target id="marg190"/>
              D
                <emph type="italics"/>
              e
                <emph.end type="italics"/>
              S
                <emph type="italics"/>
              uh. lib.
                <emph.end type="italics"/>
              16.</s>
            </p>
            <p type="margin">
              <s id="id001035">
                <margin.target id="marg191"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              20.
                <emph type="italics"/>
              diff.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001036">Aliter ſtante ſuppoſitione ut Ludouicus Ferrarius ex demon­
                <lb/>
              ſtratis à Ptolemæo quadratum b c, & eſt 1 quad eſt æquale produ­
                <lb/>
              cto ex b d in c e, quod eſt 1, & a b in d c, igitur detracto 1, produ­
                <lb/>
              cto b d in c e ex 1 quad. </s>
              <s id="id001037">quadrato c b, relinquitur productum ex
                <lb/>
              a b in c d 1 quad. </s>
              <s id="id001038">m: 1, ergo diuiſo co per a b, quæ eſt 1, relinquitur
                <lb/>
              c d 1 quad. </s>
              <s id="id001039">m: 1 huius uerò quadratum per
                <expan abbr="eadẽ">eadem</expan>
              demonſtrata à </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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