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="64" xlink:href="015/01/083.jpg"/>
            <p type="margin">
              <s id="id001212">
                <margin.target id="marg254"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="margin">
              <s id="id001213">
                <margin.target id="marg255"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              40. 7</s>
            </p>
            <p type="main">
              <s id="id001214">Propoſitio ſeptuageſima tertia.</s>
            </p>
            <p type="main">
              <s id="id001215">Proportionem ponderum attractorum penes figuram in pla­
                <lb/>
              no inuenire.
                <lb/>
                <arrow.to.target n="marg256"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001216">
                <margin.target id="marg256"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001217">Sint duo pondera æqualia in plano a & b, & ſit
                <lb/>
                <figure id="id.015.01.083.1.jpg" xlink:href="015/01/083/1.jpg" number="80"/>
                <lb/>
              a ſuperficies qua planum tangit dupla b ſuperfi­
                <lb/>
              ciei, qua planum tangit: dico quod ſi trahantur ab
                <lb/>
              imo, quod erunt æqualia: ſuſpendantur, & erunt
                <lb/>
              æqualia ex ſuppoſito, ſed a quieſcens in plano eſt
                <lb/>
              dimidium a ſuſpenſi, & b quieſcens in plano eſt di
                <lb/>
              midium b ſuſpenſi ex demonſtratis ſuperius, igi­
                <lb/>
              tur per communem animi ſententiam a & b in pla­
                <lb/>
              no ſunt æqualia.</s>
            </p>
            <p type="main">
              <s id="id001218">
                <arrow.to.target n="marg257"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001219">
                <margin.target id="marg257"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001220">Ex hoc manifeſtum eſt, quod proportio uirium trahentium pon
                <lb/>
              dera in plano eadem eſt, quæ ipſorum ponderum dum ſuſpendun­
                <lb/>
              tur. </s>
              <s id="id001221">Vbi planum æquale ſit, & ſolidum.</s>
            </p>
            <p type="main">
              <s id="id001222">
                <arrow.to.target n="marg258"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001223">
                <margin.target id="marg258"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              62.</s>
            </p>
            <p type="main">
              <s id="id001224">Propoſitio ſeptuageſima quarta.</s>
            </p>
            <p type="main">
              <s id="id001225">Proportionem concutientis ad concuſſum ſtabili inuenire.</s>
            </p>
            <p type="main">
              <s id="id001226">
                <arrow.to.target n="marg259"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001227">
                <margin.target id="marg259"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001228">Intelligo concutiens eſſe ſolidum, quod non frangitur, idque gra­
                <lb/>
              uitate, & impetu concutere, nam de duritie ſupponitur, & grauitas,
                <lb/>
              ut demonſtrabitur in corrolario eſt iuxta ſuperficiem inferiorem
                <lb/>
              ponderi comparatam. </s>
              <s id="id001229">Cum ergo motus concuſsionis magnitudo
                <lb/>
              conſtet ex grauitate, impetu & figura, concuſsi autem ex pondere
                <lb/>
              & connexione: multiplicatis inuicem partibus productorum pro­
                <lb/>
              portio, erit proportio concuſsionis: ut ſit grauitas decem, impetus
                <lb/>
              quadraginta: pondus icti centum connexio ut duo, ducemus qua­
                <lb/>
              draginta in decem, & fient quadringenta, et duo in centum, fient du
                <lb/>
              centa, igitur concuſsio erit dupla.</s>
            </p>
            <p type="main">
              <s id="id001230">
                <arrow.to.target n="marg260"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001231">
                <margin.target id="marg260"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id001232">Cum fuerit figura rotunda, concuſsio erit integra in puncto:
                <lb/>
              quia ſphæra iacens in plano totum pondus in punctum cogit.</s>
            </p>
            <p type="main">
              <s id="id001233">
                <arrow.to.target n="marg261"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001234">
                <margin.target id="marg261"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id001235">Si autem planum eſt, quod ijcitur, proportio totius ad totum eſt
                <lb/>
              minor, quàm partis ad partem pro ratione quantitatis latitudinis. </s>
            </p>
            <p type="main">
              <s id="id001236">
                <arrow.to.target n="marg262"/>
                <lb/>
              ſed maior ratione aëris comprehenſi, de quo infrà.
                <lb/>
                <arrow.to.target n="marg263"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001237">
                <margin.target id="marg262"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              84.</s>
            </p>
            <p type="margin">
              <s id="id001238">
                <margin.target id="marg263"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 3.</s>
            </p>
            <p type="main">
              <s id="id001239">Cum proportio minor fuerit ſtabile, non poterit in ſolido plano
                <lb/>
              moueri: aliter fieret motus à debiliore, & per præcedentem etiam
                <lb/>
              poſſet pari ratione eleuari.</s>
            </p>
            <p type="main">
              <s id="id001240">
                <arrow.to.target n="marg264"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001241">
                <margin.target id="marg264"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 4.</s>
            </p>
            <p type="main">
              <s id="id001242">Cumque ſtabile non mouetur, & omne agens agat aliquid neceſſe
                <lb/>
              eſt, ut ſtabilis partes cedant, aut diſſoluantur. </s>
              <s id="id001243">Quanto ergo magis
                <lb/>
              cedit, tanto minus diſſoluitur.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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