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>
            <pb pagenum="220" xlink:href="015/01/239.jpg"/>
            <p type="main">
              <s id="id003719">Propoſitio centeſima nonageſima quinta.</s>
            </p>
            <p type="main">
              <s id="id003720">Si lectus fiat dupla longitudine ad latitudinem melius ſuffulcie­
                <lb/>
              tur reſtibus ex medio ad angulos, & eis æquidiſtantibus quam ſe­
                <lb/>
              cundum longitudinem & latitudinem.
                <lb/>
                <arrow.to.target n="marg697"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003721">
                <margin.target id="marg697"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003722">Hęc proponitur à Philoſopho in mechanicis, & dico quod ſi a b </s>
            </p>
            <p type="main">
              <s id="id003723">
                <arrow.to.target n="marg698"/>
                <lb/>
              ſit dupla a c, &
                <foreign lang="grc">α β α γ</foreign>
              dupla, & diuidantur a b a c &
                <foreign lang="grc">α β α γ</foreign>
              in quotuis
                <lb/>
              partes ęquales inuicem, nam ſupponitur a b ęqualis
                <foreign lang="grc">α β</foreign>
              & a c æqua­
                <lb/>
              lis
                <foreign lang="grc">α γ</foreign>
              , & ducantur rectæ lineæ decuſſatim & ad rectos angulos, &
                <lb/>
                <expan abbr="ſecundũ">ſecundum</expan>
              id ſtatuantur reſtes, quod decuſſa­
                <lb/>
                <figure id="id.015.01.239.1.jpg" xlink:href="015/01/239/1.jpg" number="234"/>
                <lb/>
              tim poſitæ utiliores
                <expan abbr="erũt">erunt</expan>
              , omitto quod de­
                <lb/>
              centius ob ſpatiorum minorem differenti­
                <lb/>
              am. </s>
              <s id="id003724">Adducam ſolùm tres Philoſophi ratio­
                <lb/>
              nes: prima, quoniam ligna non adeò facilè
                <lb/>
              finduntur nec incuruantur tranſuerſim tra­
                <lb/>
              cta, ut recta & ſecundum longitudinem, Et
                <lb/>
              ideò longè plus durabit
                <foreign lang="grc">α β γ δ</foreign>
                <expan abbr="quã">quam</expan>
              a b c d,
                <lb/>
              & cum ſpondis rectoribus, & ideò etiam
                <lb/>
              cum reſtibus magis intentis: & erit firmior
                <lb/>
              & pulchrior. </s>
              <s id="id003725">Secunda ratio eſt, quod cum
                <lb/>
              reſtes in ſecunda conſtitutione æquales inuicem ſint, in prima quæ
                <lb/>
              ſecundum latitudinem duplę, quę longiores erunt magis laxabun­
                <lb/>
              tur tranſuerſalibus, & ita turpiores & incommodæ breui redden­
                <lb/>
              tur, & in ſecunda conſtitutione ęqualiter ſuſtinebunt pondus & re­
                <lb/>
              uolutionem cubantis, tum ob æqualitatem longitudinis inter ſe,
                <lb/>
              tum ob ſitum ſimilem inter ſe, tum ad humanum decubitum
                <expan abbr="diſsi­milẽ">diſsi­
                  <lb/>
                milem</expan>
              , nam (ut oſtenſum eſt) in præcedenti magis grauat pondus in
                <lb/>
              extremis quam in medio, & magis laxantur ob id quæ ſunt ſecun­
                <lb/>
              dum eundem situm. </s>
              <s id="id003726">Et hanc cauſſam expoſitores non intellexe­
                <lb/>
              runt multi, multo minus tertiam, in qua faciunt demonſtrationem
                <lb/>
              Geometricam & computantem numeris. </s>
              <s id="id003727">Deinde non animaduer
                <lb/>
              tunt quod in ſecunda figura aſſumunt quinque lineas, cum in prima
                <lb/>
              tantum aſſumpſiſſent quatuor. </s>
              <s id="id003728">Peius omnibus eſt quod demon­
                <lb/>
              ſtratio hæc cum de tranſuerſis ad magis tranſuerſas lineas ſit non
                <lb/>
              eſt ad propoſitum Ariſtotelis, qui in duabus primis rationibus
                <lb/>
              tranſuerſas comparauit his, quæ à latere ad latus & à capite ad ca­
                <lb/>
              put deducuntur, ita ubi trifariam decepti ſunt, ibi maximè glori­
                <lb/>
              antur. </s>
              <s id="id003729">Miſerum nunc philoſophandi genus: uoluntque ſupercilium
                <lb/>
              eſſe loco doctrinæ. </s>
              <s id="id003730">Sint igitur lineæ ductæ ut uides, dico omnes
                <lb/>
              pariter acceptas in prima figura, eſſe longiores omnibus pariter ac­
                <lb/>
                <arrow.to.target n="marg699"/>
                <lb/>
              ceptis in ſecunda figura, quod intendit
                <expan abbr="demõ">demon</expan>
              ſtrare Ariſtoteles. </s>
              <s id="id003731">O­
                <lb/>
              ſtenſo ergo de duabus, idem ſuppoſito numero equali de omnibus </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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