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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              C
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              o
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              ^{m}.</s>
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            <p type="main">
              <s id="id003847">Quia enim k a eſt poteſtate dupla ad b b, & ſeſquialtera poteſta
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              te ad k d, neceſſe eſt ut k d ſit ſexquitertia poteſtate ad b h.</s>
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            <p type="head">
              <s id="id003848">LEMMA QVINTVM.</s>
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            <p type="main">
              <s id="id003849">Priſma altitudinem habens pyramidis & triangulum eiuſdem
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              baſim, æquale eſt cubo eidem ſphæræ inſcripto.</s>
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              _{m}.</s>
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              <s id="id003852">Cum enim proportio quadrati b h ad triangulum a b c ſit uelut </s>
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            <p type="main">
              <s id="id003853">
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              a b ad a f, a b autem ad a f ſit ſexquitertia poteſtate ex demonſtratis,
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              erit quadratum b h ad triangulum a b c ſexquitertium poteſtate: at
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              cubi b h altitudo eſt ipſa b h, priſmatis autem a b c altitudo eſt k d,
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              k d autem potentia ſexquitertia ad b h, igitur priſma a b c eſt ęquale
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              cubo b h, quod fuit propoſitum.</s>
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              er
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              lem­
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              ma.
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              emmate
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              2.</s>
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              <s id="id003855">Ex hoc ſequitur, quod cum priſma ſit triplum ſuæ pyramidi, ut
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              ab Euclide habetur, quod cubus eſt triplus pyramidi, quam eadem
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              ſphæra circumſcribit.
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              </s>
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              <s id="id003856">
                <margin.target id="marg739"/>
              C
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              or
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              ^{m}.</s>
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              P
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              er
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              or
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              ^{m}.
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              lemmatis
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              4.</s>
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              P
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              er
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              34.
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              un­
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              decimi
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              E
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              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003859">Nunc uenio ad demonſtrationem propoſitionis, & dico quod
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              corpus difficile eſt ad motum, uel ob magnitudinem baſis, cui inſi­</s>
            </p>
            <p type="main">
              <s id="id003860">
                <arrow.to.target n="marg742"/>
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              det, uel ob pondus, uel ob formam: nam corpus quod forma eſt
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                <arrow.to.target n="marg743"/>
                <lb/>
              contracta, difficilè mouetur, ut pyramis, contrà, quod prominet à la
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              teribus, facile reuoluitur, ut corpus duodecim baſium pentagona­
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              rum, & uiginti triangularum: ergo cubi ſedes eſt maior quàm ſua
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              pyramis, & pondus triplo maius, & etiam non prominet cubus,
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              ideò pro re ſtabili poſitum eſt corpus eiuſmodi. </s>
              <s id="id003861">Eo quod ob gra­
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              uitatem etiam, ut dixi, ſit ſtabilius pyramide eiuſdem ſphęrę. </s>
              <s id="id003862">Quod
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              ſi etiam aſſumeres pyramidem, cuius baſis eſſet æqualis quadrato
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              cubi, ipſa ſe haberet ad pyramidem ſphæræ in grauitate, uelut latus
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              trianguli ad ſuum cathetum, & ideo proportio ponderis cubi ad
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              pyramidem eſſet, uelut tredecim ad quinque fermè: ergo ratione pon
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              deris eſſet longè ſtabilior cubus ipſa pyramide. </s>
              <s id="id003863">At in alijs corpori­
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              bus, quæ rationalia uocantur, non eſt tanta proportio ponderis, &
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              baſis eſt minor & forma prominet.</s>
            </p>
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              E
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              x
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              7.
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              duode
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              cimi
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              E
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              lem.
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              </s>
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              o
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              ^{m}.</s>
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            <p type="main">
              <s id="id003866">Propoſitio centeſima nonageſima nona.</s>
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            <p type="main">
              <s id="id003867">Rationem remorum nauim impellentium inuenire.
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              C
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              ^{m}.</s>
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            <p type="main">
              <s id="id003869">Sit a remi extremum, quod manu apprehenditur, b ſcalmus cui
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              remus inſidet: c extremum aliud latius remi, quod uocant pal­
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              mam, transferatur nixu manus, & motu corporis a in d, ut c per­</s>
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              <s id="id003870">
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              ueniat in e, ſunt enim æquales a b, d b, b c, b e etiam & angu­
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              li a d b contrapoſiti, quare trianguli a b d & c b e ſimiles, igitur
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              primum quanto maior propoſitio c b ad b a, tanto maior propor­
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                <arrow.to.target n="marg746"/>
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              tio c ad a d, & ita ex æquali motu longius transferetur remus, ſeu
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              palma. </s>
              <s id="id003871">Secundum, cum motus a d fiat nixu brachiorum & corpo­
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              ris, quanto magis transfertur corpus eo minus opus erit </s>
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          </chap>
        </body>
      </text>
    </archimedes>
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