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="id003623">
                <pb pagenum="215" xlink:href="015/01/234.jpg"/>
              dem proportionem, quam componunt proportiones a & h mo­
                <lb/>
              uendo d & a, & k mouendo e, & ſit maior diffe­
                <lb/>
                <figure id="id.015.01.234.1.jpg" xlink:href="015/01/234/1.jpg" number="225"/>
                <lb/>
              rentia ponderis e ad d quàm c ad b, dico quod
                <lb/>
              maiore
                <expan abbr="cũ">cum</expan>
              difficultate mouebuntur d & e quàm
                <lb/>
              b & e. </s>
              <s id="id003624">Nam
                <expan abbr="cũ">cum</expan>
              differentia e & d ſit maior quàm
                <lb/>
                <arrow.to.target n="marg664"/>
                <lb/>
              c & b, & d e & b c ſint æqualia, erit e maius c, igi­
                <lb/>
              tur e difficilius mouebitur ab a & k quàm c ab a
                <lb/>
              & g. </s>
              <s id="id003625">Itidem quia e tanto maius eſt c, quanto b
                <lb/>
              maius eſt d, & proportio a k ad e & a h ad d, conficiunt proportio­
                <lb/>
              nem a g ad c & a f ad b, erit ut motus d e ſint tardiores & difficilio­
                <lb/>
              res motibus b c, per regulam dialecticam, nam difficultas motus e
                <lb/>
              ſupra difficultatem motus c, eſt maior quam difficultas motus b
                <lb/>
              ſupra difficultatem motus d, igitur difficultas motus d & e, maior
                <lb/>
              eſt difficultate motus b & e, quod erat demonſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id003626">
                <margin.target id="marg663"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id003627">
                <margin.target id="marg664"/>
              P
                <emph type="italics"/>
              er præce­
                <lb/>
              dentem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003628">Propoſitio centeſima octuageſima nona.</s>
            </p>
            <p type="main">
              <s id="id003629">Si pondus minus ad longitudinem maiorem ſub æquali pro­
                <lb/>
              portione coaptetur, facilius deorſum trahetur quàm quod maius
                <lb/>
              eſt & propius.</s>
            </p>
            <p type="main">
              <s id="id003630">Sit ſitula aquæ f annexa tigno
                <lb/>
                <figure id="id.015.01.234.2.jpg" xlink:href="015/01/234/2.jpg" number="226"/>
                <lb/>
                <arrow.to.target n="marg665"/>
                <lb/>
              in e & ad minuendum pondus
                <lb/>
              ad datur ex aduerſo elongius ſeu
                <lb/>
              uincatur pondus a, dico quod
                <lb/>
                <expan abbr="cõmo">commo</expan>
              dius erit quàm ſi ęquale ad
                <lb/>
              grauitatem addatur b proprius
                <lb/>
              in e, nam quia b ęquiponderat in
                <lb/>
              d ut a in e, & homo trahens ex e
                <lb/>
              plus poteſt quàm ex d, igitur fa­
                <lb/>
              cilius trahet ex e quam d. </s>
              <s id="id003631">Et
                <expan abbr="quo­niã">quo­
                  <lb/>
                niam</expan>
              graue minus ponderat quan
                <lb/>
              to magis diſtat à medio, licet mo­
                <lb/>
              ueat magis, ergo inclinatum ad
                <lb/>
                <arrow.to.target n="marg666"/>
                <lb/>
              medium, cum ergo moueatur
                <lb/>
                <arrow.to.target n="marg667"/>
                <lb/>
              uelocius ex e quam d, & ſemper
                <lb/>
                <arrow.to.target n="marg668"/>
                <lb/>
              uelocius deſcendendo in com­
                <lb/>
              paratione a g h, igitur ſemper
                <lb/>
              magis & magis uelociter ex e
                <lb/>
              quàm d ut ſit duplex incrementum & comparatione c e ad c d &
                <lb/>
              deſcenſus ad deſcenſum in utroque & ſimiliter in reditu, quia facilius
                <lb/>
              impelletur ſurſum e quàm d per primam rationem.</s>
            </p>
            <p type="margin">
              <s id="id003632">
                <margin.target id="marg665"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id003633">
                <margin.target id="marg666"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              45.</s>
            </p>
            <p type="margin">
              <s id="id003634">
                <margin.target id="marg667"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003635">
                <margin.target id="marg668"/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              109.</s>
            </p>
            <p type="main">
              <s id="id003636">Propoſitio centeſima nonageſima.</s>
            </p>
            <p type="main">
              <s id="id003637">Si fuerit primum graue minus ſecundo, & ſecundum minus ter­
                <lb/>
              tio, proportio autem primi ad ſecundum multo maior quàm ſecun </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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