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="id001039">
                <pb pagenum="56" xlink:href="015/01/075.jpg"/>
              lemæo, ęquale eſt rectangulis ex b c in de, & b d in c e, igitur 1 quad.
                <lb/>
              </s>
              <s id="id001040">quad. </s>
              <s id="id001041">m: 2 quad. </s>
              <s id="id001042">p: 1 eſt æquale 1 producto b d in c e, & producto b
                <lb/>
              cin d e detracto 1 communi, relinquetur productum ex b c in d e 1
                <lb/>
              quad. </s>
              <s id="id001043">quad. </s>
              <s id="id001044">m: 2 quad. </s>
              <s id="id001045">igitur diuiſo 1 quad. </s>
              <s id="id001046">quad. </s>
              <s id="id001047">m: 2 quad. </s>
              <s id="id001048">per 1
                <lb/>
              pos, exit 1 cu. </s>
              <s id="id001049">m: 2 pos æqualia d e, & d e eſt æqualis d c, ut ab initio
                <lb/>
              demonſtrauimus, & d c fuit 1 quad. </s>
              <s id="id001050">m: 1, igitur 1 cu. </s>
              <s id="id001051">m: 2 æquantur 1
                <lb/>
              quad. </s>
              <s id="id001052">m: 1, igitur 1 cu. </s>
              <s id="id001053">p: 1 æquantur 1 quad. </s>
              <s id="id001054">p: 2 pos.</s>
            </p>
            <p type="main">
              <s id="id001055">Aliter ut Pacciolus, concurrant latera eptagoni b d, c e in a, & du
                <lb/>
              cantur perpendiculares a f, d g & c d, & ſit c e i ca 1 pos, & quia ut
                <lb/>
                <arrow.to.target n="marg192"/>
                <lb/>
              a e ad a c, ita d e ad b c, erit ergo b c (1 posp: 1)/(1 pos) quare b f (1/2 pos 1/2,)/(2 pos) &
                <lb/>
              quia d h eſt dimidium d e, erit d h, & g f
                <lb/>
                <figure id="id.015.01.075.1.jpg" xlink:href="015/01/075/1.jpg" number="71"/>
                <lb/>
              1/2, cum ergo b f ſit (1/2 pos p: 1/2)/pos erit ergo di­
                <lb/>
              uiſa 1/2 pos per 1 pos, & exit 1/2, b f 1/2p: 1/2/pos
                <lb/>
              igitur detracta g f relinquetur g b 1/2/(1 pos).
                <lb/>
              & eius quadratum 1/4/(1 quad). igitur cum qua­
                <lb/>
              dratum b d ſit 1, erit quadratum g d 1 m:
                <lb/>
              2/4/(2 quad)g c autem eſt compoſita ex e f, quæ
                <lb/>
              eſt 1/2p: 1/2/(1 pos) & f g quæ eſt 1/2, erit igitur c
                <lb/>
              g 1 p: 1/2/(1 pos), &
                <expan abbr="quadratũ">quadratum</expan>
              eius 1 p: 1/pos eſt 1/4/(1 quad.) quare
                <expan abbr="q̃dratũ">quadratum</expan>
              e d q̊d eſt
                <lb/>
                <arrow.to.target n="marg193"/>
                <lb/>
              compoſitum ex quadratis c g & g d erit 2 p: 1/pos c a uerò eſt æqua­
                <lb/>
              lis c d, quia, ut demonſtratum eſt angulus d c e eſt ſeptima pars
                <lb/>
              duorum rectorum, & angulus b c e ei duplus, quare cum c f a ſit re­
                <lb/>
              ctus erit ex trigeſima ſecunda primi Elementorum f a c tres ſepti­
                <lb/>
              mæ unius recti, ergo d a c 6/7 unius recti, d c a uerò 2/7 unius recti, quia
                <lb/>
                <arrow.to.target n="marg194"/>
                <lb/>
              eſt ſeptima pars duorum rectorum, ígitur a d c eſt 6/7 unius recti: igi­
                <lb/>
              tur c d eſt æqualis c a, ergo quadratum quadrato: igitur 1 quad. </s>
              <s id="id001056">p: 2
                <lb/>
              pos p: 1, æquatur 2 p: 1/(1 pos) igitur 1 quad. </s>
              <s id="id001057">p: 2 pos, æquantur 1 p: 1/(1 pos).
                <lb/>
              Quare 1 cub. </s>
              <s id="id001058">p: 2 quad. </s>
              <s id="id001059">æquatur 1 pos p: 1.
                <lb/>
                <figure id="id.015.01.075.2.jpg" xlink:href="015/01/075/2.jpg" number="72"/>
                <lb/>
              Sit etiam angulus a duplus b, & b c dupla
                <lb/>
              b a: & erit per eadem proportio a c, & a b
                <lb/>
              ad c b, ut c b ad c a. </s>
              <s id="id001060">Ponamus ergo ab 1, erit
                <lb/>
              b c 2, & a c 1 pos, & a c, a b 1 pos p: 1, & du­
                <lb/>
              cta in a c fit 1 quad. </s>
              <s id="id001061">p: 1 pos, & hoc eſt æquale 4 quadrato b c per re­
                <lb/>
              flexæ proportionis diffinitionem. </s>
              <s id="id001062">Igitur a c eſt <02> 4 1/4 m: 1/2, & ita
                <lb/>
              de alijs.</s>
            </p>
            <p type="margin">
              <s id="id001063">
                <margin.target id="marg192"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              42.
                <emph type="italics"/>
              pri mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001064">
                <margin.target id="marg193"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              32.
                <emph type="italics"/>
              pri mi
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              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001065">
                <margin.target id="marg194"/>
              P
                <emph type="italics"/>
              er ſextam eiuſdem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001066">Propoſitio ſexageſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id001067">Si fuerint aliquot quantitates ab una quantitate, aliæque totidem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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