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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            <p type="main">
              <s id="id001757">
                <pb pagenum="97" xlink:href="015/01/116.jpg"/>
              incumbat, nec impellat, ſed tantum ſuſtineat nihilo ſecius res uera
                <lb/>
              eſt. </s>
              <s id="id001758">Et etiam quia non eſt uerum, quòd qui longius incumbit, ma­
                <lb/>
              iorem uim inferat. </s>
              <s id="id001759">Propterea dicendum eſt, quòd qui ex commu­
                <lb/>
              nibus propria nituntur demonſtrare, omnes corrumpunt diſcipli­
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              nas. </s>
              <s id="id001760">Nihil deterius eſt his monſtris. </s>
              <s id="id001761">Nam etſi hæc ratio uera eſſet:
                <lb/>
              non tamen reddit cauſam, quia non eſt ex proprijs principijs. </s>
              <s id="id001762">Dico
                <lb/>
              ergo, quod ſi c deſcendat in e, per perpendiculum deſcendet, igitur
                <lb/>
              d b eſt longior d a, quare angulus e a b maior e b a: igitur pondus c
                <lb/>
              plus deſcendit comparatione a, quàm b, ergo plus grauat c ipſum a
                <lb/>
              quàm b, ſeu ex cauſa, quod magis premat, ſeu ex effectu, quòd ma­
                <lb/>
              gis deceſſerit. </s>
              <s id="id001763">Cauſa ergo erroris eſt, quod ſi ponatur angulus f b a
                <lb/>
              æqualis angulo f a b, & ponatur b f ęqualis b c, tun c in eodem tem­
                <lb/>
              pore, in quo tranſit dimidium c in e, tranſibit aliud dimidium c in f.
                <lb/>
              </s>
              <s id="id001764">quia ſeparatę partes grauiores ſunt in c b, quàm c a, propter diſtan­
                <lb/>
              tiam ab hypomochlio, ſed tunc uelocius mouentur, & angulus fit
                <lb/>
              ęqualis. </s>
              <s id="id001765">Sed quando pondus eſt unum, & c deſcendit ad e, cum de­
                <lb/>
              ſcendat inæquali tempore, & peragat maiorem angulum compa­
                <lb/>
              ratione a, quam b, ſequitur, ut uelocius moueatur comparatione a
                <lb/>
              quàm b. </s>
              <s id="id001766">Ergo ſi non mouetur, cum omnis potentia ſit ſimilis actui,
                <lb/>
              tum quia ab eo producitur, & effectus eſt ſimilis cauſæ: tum quia
                <lb/>
              eſt initium actus, igitur etiam quod a b non inclinetur, nec deſcen­
                <lb/>
              dat, grauius erit pondus, comparatione a quàm b, quod erat de­
                <lb/>
              monſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id001767">
                <margin.target id="marg360"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id001768">
                <margin.target id="marg361"/>
              Q
                <emph type="italics"/>
              usſt.
                <emph.end type="italics"/>
              59.
                <lb/>
              M
                <emph type="italics"/>
              echanic.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001769">
                <margin.target id="marg362"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              45.</s>
            </p>
            <p type="margin">
              <s id="id001770">
                <margin.target id="marg363"/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              103.</s>
            </p>
            <p type="main">
              <s id="id001771">Ex hoc ſequitur, quòd aliqua iuncta erunt grauiora reſpectu u­
                <lb/>
              nius, quæ erunt mutato ordine diuiſa leuiora. </s>
              <s id="id001772">Quoniam diuiſa,
                <lb/>
              quæ longius diſtant æqualem, aut maiorem angulum faciunt, iun­
                <lb/>
              cta minorem.</s>
            </p>
            <p type="main">
              <s id="id001773">Propoſitio centeſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id001774">Quales proportiones angulorum doceant laterum proportio­
                <lb/>
              nes. </s>
              <s id="id001775">At que uiciſsim determinare.</s>
            </p>
            <p type="main">
              <s id="id001776">Sit circulus a b c, cuius dimetiens, nota b d ſit b, erit ergo latus
                <lb/>
                <arrow.to.target n="marg364"/>
                <lb/>
                <figure id="id.015.01.116.1.jpg" xlink:href="015/01/116/1.jpg" number="110"/>
                <lb/>
              exagoni a b dimidium b d, id eſt 3. igitur
                <lb/>
              cum angulus a ſit rectus, erit a d <02> 27 latus
                <lb/>
              trianguli. </s>
              <s id="id001777">Et latus quadrati per eandem <02>
                <lb/>
              18. Vt latus exagoni ſit <02> 9. Quadrati <02> 18
                <lb/>
              Trianguli <02> 27, & ita poteſtate ſe habent
                <lb/>
              hæc ut 1. 2. 3. Et ſunt nota. </s>
              <s id="id001778">Et quia latus d e c
                <lb/>
              agoni eſt <02> 11 1/4 m, 1 1/2. & ipſum erit notum.
                <lb/>
              </s>
              <s id="id001779">Quare latus pentagoni eſt <02> v 22 1/2 m: <02>
                <lb/>
              101 1/4 notum. </s>
              <s id="id001780">Et iam notum fuit latus epta­
                <lb/>
              goni. </s>
              <s id="id001781">Habebimus igitur latera Trianguli </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>