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="id001743">
                <pb pagenum="96" xlink:href="015/01/115.jpg"/>
              erit diſcrimen ab attractione in plano. </s>
              <s id="id001744">Exempli gratia ſit, ut graue d
                <lb/>
              in plano ſit, ut quin que, & ſuſpenſum decem, ergo in medio angulo
                <lb/>
              erit penè ſeptem, ſed ſeptem minus longe
                <expan abbr="diſtãt">diſtant</expan>
              à quin que, quàm de­
                <lb/>
              cem ad ſeptem, ergo in ſecunda parte plus longè augebitur difficul
                <lb/>
              tas attractionis ſupra difficultatem in medio angulo accliui, quam
                <lb/>
              in prima parte à plano ad medium accliue, & quoniam planum in
                <lb/>
              plano deſcendit, tanto uehementius, quanto difficilius attrahitur,
                <lb/>
              ergo planum in decliui ſublimi longe maiore impetu feretur infrà
                <lb/>
              quam ſit proportio anguli ad angulum. </s>
              <s id="id001745">Exempli gratia, planum in
                <lb/>
              medio angulo, ſi incipiat deſcendere in dodrante multo lentius,
                <lb/>
              quàm pro dimidio uirium deſcenſus totius anguli, imò initium de­
                <lb/>
              ſcenſus eſt à medio recti ad unguem, ubi omnia plana ſint, & duriſ­
                <lb/>
              ſima, & cauſa huius eſt, quia omne graue tendit ad centrum, quòd
                <lb/>
              maior pars ipſius grauis eſt ultra medium grauitatis in decliui
                <lb/>
              humiliore.</s>
            </p>
            <p type="margin">
              <s id="id001746">
                <margin.target id="marg358"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id001747">
                <margin.target id="marg359"/>
              E
                <emph type="italics"/>
              x
                <emph.end type="italics"/>
              62. &
                <lb/>
              64. P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001748">Propoſitio centeſima quinta.</s>
            </p>
            <p type="main">
              <s id="id001749">Proportionem ferentium pondus in pertica inuenire.</s>
            </p>
            <figure id="id.015.01.115.1.jpg" xlink:href="015/01/115/1.jpg" number="109"/>
            <p type="main">
              <s id="id001750">Hæc proponitur etiam à Philoſo­
                <lb/>
                <arrow.to.target n="marg360"/>
                <lb/>
              pho, & ponatur ab, & ſi pondus ſit in
                <lb/>
                <arrow.to.target n="marg361"/>
                <lb/>
              medio d grauat æqualiter utrunque,
                <lb/>
              nam in hoc conſentit experimentum
                <lb/>
              cum ratione, at uerò ſi ponatur in cita,
                <lb/>
              ut b c ſit tripla b a uiderentur a & b, tanquam hypomochlia, & pon
                <lb/>
                <arrow.to.target n="marg362"/>
                <lb/>
              dus ipſum b, ut grauior eſſet cb, quam c a. </s>
              <s id="id001751">Ariſtoteles, ſeu author
                <lb/>
              ille hoc uidens bifariam reſpondet: primum quòd hoc eſt inuer­
                <lb/>
                <arrow.to.target n="marg363"/>
                <lb/>
              ſum inſtrumentum, cum in cæteris motor ſit ex aduerſo hypomo­
                <lb/>
              chlij, hic in ipſo, geſtans enim mouet & hypomochlij inſtar eſt hu­
                <lb/>
              merus. </s>
              <s id="id001752">At hoc uerum non eſt: quod mouet enim eſt pondus, & eſt
                <lb/>
              in c: nam a, & contingit moueri: quia ſi ſtarent, idem ſequeretur. </s>
              <s id="id001753">Se­
                <lb/>
              cunda reſponſio eſt, quod utrunque premit ſcilicet ferentes & pon­
                <lb/>
              dus, & quòd qui longior eſt ab hypomochlio facilius mouet, &
                <lb/>
              redit ad idem fermè: nam in c conſtituitur, quod moueri debet, ca­
                <lb/>
              pita uectium ſunt a, & b: motus autem eſt ipſum ſuſtinere pondus.
                <lb/>
              </s>
              <s id="id001754">At hoc non uidetur, quoniam ratio, qua uectis longior facilius mo
                <lb/>
              uet, eſt ambitus magnitudo, ob quam motus redditur tardior, &
                <lb/>
              ideo leuior: igitur non eſt hoc uerum de motu occulto, ſicut eſt gra
                <lb/>
              uis prementis, ſed circumducente, cum in occulto uelut in ſtatera
                <lb/>
              contrarium accidere docuerimus aliâs. </s>
              <s id="id001755">Quidam dixere b premere
                <lb/>
              c uerſus a, a contrà uerſus b, & ideò grauari magis a àb, quàm b ab
                <lb/>
              a, quia maiorem uim habet b e, quàm a c. </s>
              <s id="id001756">Iſtud falſum eſt bifariam.
                <lb/>
              </s>
              <s id="id001757">Primum, quia & ſi a, & b ſint in æquilibrio, ut nec unus in alterum </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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