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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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id001844">
                <pb pagenum="101" xlink:href="015/01/120.jpg"/>
                <figure id="id.015.01.120.1.jpg" xlink:href="015/01/120/1.jpg" number="115"/>
                <lb/>
              tes a b, & c d: erunt que anguli q & n recti
                <lb/>
                <arrow.to.target n="marg381"/>
                <lb/>
              & anguli f e a, & f e c ęquales, igitur uter
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                <arrow.to.target n="marg382"/>
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              que dimidium recti: igitur per dicta in
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              primo Elementorum Euclidis e n ęqua
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                <arrow.to.target n="marg383"/>
                <lb/>
              lis n k, igitur c q æqualis e n, quare h p
                <lb/>
              æqualis g o, ſed quod fit ex o k in k g eſt
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                <arrow.to.target n="marg384"/>
                <lb/>
              æquale ei, quod fit ex p k in k h, igitur
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                <arrow.to.target n="marg385"/>
                <lb/>
              k h eſt æqualis k g ex eisdem oſtendi­
                <lb/>
              tur f l m k quadratum eſſe. </s>
              <s id="id001845">Quia ergo
                <lb/>
              k h eſt æqualis k g, & k l æqualis k m, erit l g æqualis m h. </s>
              <s id="id001846">Er­
                <lb/>
              go deſcendendo ex g in f, quantum f l ſuperat l g, tantum deſcen­
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              dendo ex f in h, f m ſuperat m h per communem animi ſententi­
                <lb/>
              am. </s>
              <s id="id001847">At f m eſt deſcenſus f in linea a e, & m h diſtantia, quæ acqui­
                <lb/>
              ritur in linea f r, n m enim eſt æqualis f r, igitur n h excedit f r in
                <lb/>
              h m, & ita a n excedit a r in n r ęquali f m. </s>
              <s id="id001848">Quantum ergo in g f,
                <lb/>
              l f excedit l g, tantum in deſcenſu ex f in h, f m, quæ refert g l, ex­
                <lb/>
              cedit h m, quæ refert f l. </s>
              <s id="id001849">Arcus autem f g eſt æqualis arcui f h,
                <lb/>
              quod
                <expan abbr="cũ">cum</expan>
              poſſem oſtendere pluribus modis ſatis conſtat, quia chor
                <lb/>
                <arrow.to.target n="marg386"/>
                <lb/>
              darum illorum quadrata ſunt inuicem æqualia, quia lineæ f m, &
                <lb/>
                <arrow.to.target n="marg387"/>
                <lb/>
              f l item que m h & l g ſunt æquales, & anguli m, & l recti. </s>
              <s id="id001850">Igitur cum
                <lb/>
              ad quod uis punctum in linea e f ſemper linea deſcenſus in parte
                <lb/>
              inferiore eſt maior linea diſtantiæ tanto, quanto per æqualem ar­
                <lb/>
              cum in ſuperiore linea diſtantiæ eſt maior linea, deſcenſus ſequitur
                <lb/>
              per regulam Dialecticam quod punctus f, eſt punctus ęqualitatis.
                <lb/>
              </s>
              <s id="id001851">Per idem diceremus in quarta parte inferiore.</s>
            </p>
            <p type="margin">
              <s id="id001852">
                <margin.target id="marg380"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id001853">
                <margin.target id="marg381"/>
              P
                <emph type="italics"/>
              er
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              29.
                <emph type="italics"/>
              pri
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              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001854">
                <margin.target id="marg382"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              23.
                <emph type="italics"/>
              ter
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001855">
                <margin.target id="marg383"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              32.
                <lb/>
              & 6.</s>
            </p>
            <p type="margin">
              <s id="id001856">
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              P
                <emph type="italics"/>
              er
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              34.
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              pri
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              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001857">
                <margin.target id="marg385"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              7.
                <emph type="italics"/>
              tertij
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001858">
                <margin.target id="marg386"/>
              P
                <emph type="italics"/>
              er
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              47.
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              pri
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              mi
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              E
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              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001859">
                <margin.target id="marg387"/>
              P
                <emph type="italics"/>
              er
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              47.
                <emph type="italics"/>
              ter­
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001860">Propoſitio centeſima nona.</s>
            </p>
            <p type="main">
              <s id="id001861">Rationem libræ expendere.</s>
            </p>
            <p type="main">
              <s id="id001862">Cum libra moueatur, uelut rota circa axem, quia trutina manet,
                <lb/>
              ideò ſi pondus ponatur, dum iugum fuerit in linea a b nihil mo­
                <lb/>
              uebitur, quia appetitus deſcenſus ex puncto a maximus eſt, & ni­
                <lb/>
              hil iuuat motum extra naturam, idem dico de graui poſito in uerti­
                <lb/>
              ce b a. </s>
              <s id="id001863">Nam duo ſunt motus in rota, & in libra unus, per quem
                <lb/>
              dum fertur per arcum a f, gratia exempli deſcendit, quantum eſt
                <lb/>
                <arrow.to.target n="marg388"/>
                <lb/>
              a r, quæ eſt minor dimidio e r, & ideò minor e r, quæ eſt maior di­
                <lb/>
              midio, ut demonſtratum eſt, & etiam minor r f, quæ æqualis eſt r e
                <lb/>
                <arrow.to.target n="marg389"/>
                <lb/>
              per demonſtrata rurſus: & hic eſt naturalis ut palam eſt: alter præ­
                <lb/>
              ter
                <expan abbr="naturã">naturam</expan>
              , & eſt ferri ad latus, quoniam hoc eſt
                <expan abbr="propriũ">proprium</expan>
              immortali­
                <lb/>
              bus: cun que hic ſit ad latus eſt etiam
                <expan abbr="cõtra">contra</expan>
              naturam, quia magis diſtat
                <lb/>
              a centro, nam e f eſt longior c r, ſi ergo r ferretur in f, moueretur à
                <lb/>
              centro, & contra naturam. </s>
              <s id="id001864">Dum ergo fertur ex a in f, multo lentius </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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