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="id003995">
                <pb pagenum="234" xlink:href="015/01/253.jpg"/>
              ſeu uectes, quare tanto facilius mouebuntur quanto maiores
                <expan abbr="erũt">erunt</expan>
              ,
                <lb/>
                <figure id="id.015.01.253.1.jpg" xlink:href="015/01/253/1.jpg" number="251"/>
                <lb/>
              & ut plures. </s>
              <s id="id003996">Vna enim alterius loco fungitur uectis. </s>
              <s id="id003997">Trochlea qui­
                <lb/>
              dem eſt, ut uides, inſtrumentum longum ſuprà anguſtius, ſed non,
                <lb/>
              craſſum, in quo plures orbiculi ſolent collo cari, unde ſæpe numero
                <lb/>
              trochleæ nomine intelligimus orbiculos ei incluſos, circa quos fu­
                <lb/>
              nis uocatur, ut in trochleis & orbiculi & funes includuntur. </s>
              <s id="id003998">Succu­
                <lb/>
              lis etiam ſolent capita funium trahi: ut uectis auxilio imò nonnum­
                <lb/>
              quàm rotarum facilius pondera eleuantur.
                <lb/>
                <arrow.to.target n="marg783"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003999">
                <margin.target id="marg781"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id004000">
                <margin.target id="marg782"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              71.</s>
            </p>
            <p type="margin">
              <s id="id004001">
                <margin.target id="marg783"/>
              8.
                <emph type="italics"/>
              de
                <emph.end type="italics"/>
              R
                <emph type="italics"/>
              epub.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004002">Propoſitio ducenteſima quinta, ſuper uerbis Platonis,
                <lb/>
              de fine Reipub.</s>
            </p>
            <p type="main">
              <s id="id004003">“Eſt autem ei quod diuinitus generandum eſt circuitus, quem nu
                <lb/>
              merus
                <expan abbr="cõtinet">continet</expan>
              perfectus. </s>
              <s id="id004004">Humanæ uerò, in quo primum argumen
                <lb/>
              tationes ſuperantes, ut ſuperatæ tres diſtantiæ: quatuor autem ter­
                <lb/>
              minos accipientes, ſimilium & diſsimilium, ab
                <expan abbr="undantiũ">undantium</expan>
              & deficien
                <lb/>
              tium cuncta correſpondentia, & rationem habentia inuicem effece
                <lb/>
              runt. </s>
              <s id="id004005">Quorum ſexquitertium fundamentum quinario
                <expan abbr="iunctũ">iunctum</expan>
              duas
                <lb/>
              efficit harmonias ter aucta quidem: æqualem æqualiter centum to
                <lb/>
              ties, quandam autem æqualem quidem, longitudine
                <expan abbr="aũt">aunt</expan>
              ſingulum
                <lb/>
              quidem numerorum à diametris
                <expan abbr="rationẽ">rationem</expan>
              habentibus quinarij indi
                <lb/>
              gentibus uno ſingulis: non habentibus rationem
                <expan abbr="aũt">aunt</expan>
              duobus, cen­
                <lb/>
              tum autem cuborum ternarij. </s>
              <s id="id004006">Totus autem hic numerus geometri
                <lb/>
              cus talem authoritatem habet ad potiorem deterioremque
                <expan abbr="genera­tionẽ">genera­
                  <lb/>
                tionem</expan>
              . </s>
              <s id="id004007">Quem locum Ariſtoteles ita declarat. </s>
              <s id="id004008">Quorum ſexquiter­
                <lb/>
              tium fundamentum quinario coniunctum duas exhibet harmo­
                <lb/>
              nias,
                <expan abbr="inquiẽs">inquiens</expan>
              ,
                <expan abbr="quãdo">quando</expan>
              numerus diagrammatis huius
                <expan abbr="efficiat̃">efficiatur</expan>
              ſolidus.”</s>
            </p>
            <p type="main">
              <s id="id004009">
                <arrow.to.target n="marg784"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004010">
                <margin.target id="marg784"/>
              Q
                <emph type="italics"/>
              uin
                <emph.end type="italics"/>
              P
                <emph type="italics"/>
              olyt.
                <emph.end type="italics"/>
                <lb/>
              C
                <emph type="italics"/>
              ap.
                <emph.end type="italics"/>
              12.</s>
            </p>
            <p type="main">
              <s id="id004011">
                <foreign lang="grc">Γυσθμὴν</foreign>
                <expan abbr="fundamẽtum">fundamentum</expan>
              interpretatus ſum, quod radix pro latere in
                <lb/>
              hac materia accipi poſſet. </s>
              <s id="id004012">Par eſt ut in diuina generatione numerus </s>
            </p>
            <p type="main">
              <s id="id004013">
                <arrow.to.target n="marg785"/>
                <lb/>
                <expan abbr="acciperet̃">acciperetur</expan>
              perfectus: ut intelligat generationem confeſtim ſequi cor
                <lb/>
              ruptionem: nam ſermo eſt de corruptione, corrumpitur
                <expan abbr="aũt">aunt</expan>
              unum­
                <lb/>
              quodque ut aliud generetur, malum enim eſt ob bonum, non contrà.
                <lb/>
              </s>
              <s id="id004014">Liquet autem ex Euclide talem numerum eſſe octies mille
                <expan abbr="centũ">centum</expan>
              ui­
                <lb/>
              ginti octo. </s>
              <s id="id004015">Et hic eſt finis
                <expan abbr="omniũ">omnium</expan>
              urbium diuinus, cuius
                <expan abbr="quadruplũ">quadruplum</expan>
                <lb/>
              uelut in cœli reſtitutionibus, ac continuato ordine ſolet obſeruari,
                <lb/>
              eſt propè annus magnus: ueriſimile eſt enim
                <expan abbr="tãto">tanto</expan>
              tempore
                <expan abbr="cõfundi">confundi</expan>
                <lb/>
              decima, ſcilicet totius circuitus parte. </s>
              <s id="id004016">Humanæ uerò intelligit qua­
                <lb/>
                <figure id="id.015.01.253.2.jpg" xlink:href="015/01/253/2.jpg" number="252"/>
                <arrow.to.target n="table29"/>
                <lb/>
              tuor à monade numeros, aut in quauis ratione principium li­
                <lb/>
              neam ſuperficiem corpus, ut
                <expan abbr="unũ">unum</expan>
              , duo, quatuor, octo pariter
                <lb/>
              octo: duodecim decem octo uiginti
                <expan abbr="ſeptẽ">ſeptem</expan>
              : inter hæc ſunt tria
                <lb/>
              ſpatia, & octo cum uiginti ſeptem ſunt diſsimilia & deficien­
                <lb/>
              tia: maiora
                <expan abbr="em̃">emm</expan>
              ſunt ſuis partibus à quibus numerantur. </s>
              <s id="id004017">Contrà de­
                <lb/>
              cem octo & duodecim ſunt ſimilia atque ab
                <expan abbr="undãtia">undantia</expan>
              , & correſponden </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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