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="id004017">
                <pb pagenum="235" xlink:href="015/01/254.jpg"/>
              tem habent rationem inuicem. </s>
              <s id="id004018">Hæc Ariſtoteles omittit, ut ad in­
                <lb/>
              troductionem, non rem pertinentia, uelut & finem tanquàm ex
                <lb/>
              præcedentibus notum. </s>
              <s id="id004019">Vnde uerba Ariſtotelis ſunt ad unguem
                <lb/>
              eadem uerbis Platonis, ſcilicet: “Quorum ſexquitertium funda­
                <lb/>
              mentum quinario iunctum duas efficit harmonias: loco autem ter
                <lb/>
              aucta quidem, ſcribit Ariſtoteles: efficiatur ſolidus, id eſt cubus, ut
                <lb/>
              in quadratum ſuum ducatur: loco autem uerborum æqualem æ­
                <lb/>
              qualiter centum centies, uſque illuc à diametris rationem habenti­
                <lb/>
              bus quinarij ponit numerum diagrammatis.” Eſt autem diagram­
                <lb/>
              ma, quod Plato uocat diametrum, cum numerus poteſt fermè du­
                <lb/>
              plum numeri alterius, ut 3 duplum 2, & 7 duplum 5, & 17 duplum
                <lb/>
              12, & ſemper numerus hic dimetiens, excedit duplum alterius uno,
                <lb/>
              quod ex his patet, quæ ab Euclide demonſtrata ſunt in decimo li­
                <lb/>
              bro. </s>
              <s id="id004020">Quare ſi debet eſſe quadratum eius monade maius duplo, al­
                <lb/>
              terius quadrati, & duplum | alterius quadrati eſt par, igitur addi­
                <lb/>
              ta monade erit impar, ergo latus eius dimetiens impar ſemper: la­
                <lb/>
              tera autem ipſa quadratorum, quæ duplicantur aliquando pa­
                <lb/>
              ria ſunt ut 2, & tunc quadratum dimetientis eſt unum plus duplo
                <lb/>
              ut 9 eſt maius 8 monade, ſi uerò latera imparia ſint, erit quadratum
                <lb/>
              dimetientis uno minus duplo, ut 49 quadratum 7 eſt minus uno
                <lb/>
              50, duplo 25, quadrati 5. Ex quo patet agnatio, ut ita dicam in­
                <lb/>
              ter 7 & 5.</s>
            </p>
            <p type="margin">
              <s id="id004021">
                <margin.target id="marg785"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <table>
              <table.target id="table29"/>
              <row>
                <cell>8</cell>
              </row>
              <row>
                <cell>12</cell>
              </row>
              <row>
                <cell>18</cell>
              </row>
              <row>
                <cell>27</cell>
              </row>
            </table>
            <p type="main">
              <s id="id004022">Cum ergo dicit, quorum ſexquitertia eſt, ac ſi diceret, ex horum
                <lb/>
              numerorum ſerie ſumemus ſeptenarium principium epitrite, & di­
                <lb/>
              metientem 5, quos ſimul iungemus.</s>
            </p>
            <p type="main">
              <s id="id004023">Propoſitio ducenteſima ſexta.</s>
            </p>
            <figure id="id.015.01.254.1.jpg" xlink:href="015/01/254/1.jpg" number="253"/>
            <p type="main">
              <s id="id004024">Rhombi paſsiones quaſdam declarare.</s>
            </p>
            <p type="main">
              <s id="id004025">Sit a d recta diuiſa in k per æqualia, cui ſu­
                <lb/>
                <arrow.to.target n="marg786"/>
                <lb/>
              perſtent k b & k c ad perpendiculum inter ſe
                <lb/>
              æquales, & ſingulæ
                <expan abbr="earũ">earum</expan>
              minores k a & k d,
                <lb/>
                <arrow.to.target n="marg787"/>
                <lb/>
              &
                <expan abbr="perficiat̃">perficiatur</expan>
              figura quadrilatera a b d c, cuius
                <lb/>
              latera erunt omnia æqualia inuicem, & angu
                <lb/>
              li a & d oppoſiti, & b & c oppoſiti etiam inui
                <lb/>
              cem ęquales. </s>
              <s id="id004026">Sed b & c maiores erunt a & d:
                <lb/>
                <arrow.to.target n="marg788"/>
                <lb/>
              & ideo talem figuram appellauit Ariſtoteles rhombum à piſcis ſi­
                <lb/>
              militudine in medio latioris
                <expan abbr="quã">quam</expan>
              in extremis, cuius
                <expan abbr="tamẽ">tamen</expan>
              longitudo
                <lb/>
              latitudine maior eſt. </s>
              <s id="id004027">Dicit ergo Ariſtoteles, q̊d ſi rhombus ipſe cir­
                <lb/>
                <arrow.to.target n="marg789"/>
                <lb/>
              cumuoluatur, ita ut b tranſiret per b a c, & a per a c d, a maius ſpa­
                <lb/>
              tium tranſiret ex recta, ſcilicet a k d quàm b, quod tranſiret b k c. </s>
              <s id="id004028">Et
                <lb/>
              ad hoc aſſumit, quòd cum angulus c ſit maior a, igitur duæ lineæ
                <lb/>
              a c d ſunt minus curuæ quam duæ b a c, igitur b a c habent </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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