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="id002398">
                <pb pagenum="134" xlink:href="015/01/153.jpg"/>
              quadrati 2 quod eſt 12 exit 1/4 detrahe ex 2 fit 1 3/4 cuius cubus eſt 5 23/64
                <lb/>
              differentia eſt 23/64 diuide per triplum quadrati 1 3/4 quòd eſt 9 3/16 exit
                <lb/>
              23/588 detrahe ex 1 3/4
                <expan abbr="relinquũtur">relinquuntur</expan>
              1 107/147 cuius cubus eſt 5 504449/3176523 Ita diuides
                <lb/>
              hunc exceſſum ſi placet per triplum quadrati 1 107/147 & eſt fermè 9 exit
                <lb/>
              56050/3176523 quaſi detrahe ex 1 107/147 relinquuntur 323159/453789.</s>
            </p>
            <p type="main">
              <s id="id002399">Tertius modus eſt ſubtilior, tu ſcis, q̊d duo decima denominatio
                <lb/>
              eſt quadrata ſextę, & quadrata quad, tertiæ, & cuba quarti, quarta
                <lb/>
              autem eſt inter
                <expan abbr="tertiã">tertiam</expan>
              & ſextam ſecunda quantitas in continua pro­
                <lb/>
              portione: ergo inuenta <02> numeri propoſiti & <02> radicis inuentæ
                <lb/>
                <expan abbr="reducã">reducam</expan>
              ad unam denominationem, et inter numeratores collo cabo
                <lb/>
              duas quantitates, quod facile erit ſenſim procedendo, & habebo <02>
                <lb/>
              cu. </s>
              <s id="id002400">quæſitam, ſcilicet minorem ex duabus intermedijs. </s>
              <s id="id002401">Et ſimiliter
                <lb/>
              pro relata prima, capiam ſexaginta denominationes, & ſcis, quòd
                <lb/>
              quinta decima eſt <02> <02> ſexageſimę, & decima eſt <02> cu. </s>
              <s id="id002402"><02> ſexageſimę,
                <lb/>
              & duodecima <02> relata prima ſexageſimæ per eandem inuenta, er­
                <lb/>
              go <02> numeri propoſiti tanquam ille ſit ſexageſima denominatio,
                <lb/>
              inueniam illius radicis inuentæ <02> quadratam, & cubicam, &
                <lb/>
              quia duodecima quantitas quæ eſt <02> relata prima numeri eſt
                <lb/>
              ſecunda, quatuor intermediarum inter ponam inter <02> quadra­
                <lb/>
              tum, quadratum, & cubicam quadratam quatuor numeros in
                <lb/>
              continua proportione, & ſecundus ex minoribus erit <02> relata
                <lb/>
              prima numeri propoſiti. </s>
              <s id="id002403">Exemplum cubicæ uolo <02> cu: 5 habui <02>
                <lb/>
              quadratam eius 2 5/21 ſed uolo proximiorem diuidendo 4/441 per 4,
                <lb/>
              quod eſt fermè duplum 2 5/21 exit 1/441 detraho ex 2 5/21 relinquitur ualde
                <lb/>
              proxima <02> 5. 2 104/441 huius igitur radix quadrata, primo inuenta eſt 1 1/2
                <lb/>
              ſecunda proximior eſt 1 41/84 reduco ad eandem denominationem fi­
                <lb/>
              ent 284/9261 2 416/1764 & 1 861/1764 inter 3944, & 2625, inueniemus duos nume­
                <lb/>
              ros in continua proportione, ut uides, & erit ſecunda quantitas
                <lb/>
                <figure id="id.015.01.153.1.jpg" xlink:href="015/01/153/1.jpg" number="148"/>
                <lb/>
              3006/7641, quod eſt 167/98 proximum ad 1 5/7, <02> cubica. </s>
              <s id="id002404">5.
                <lb/>
                <expan abbr="nã">nam</expan>
              eius cubus eſt 5. 13/343 at exactiſsima eſt ergo 1 69/98.
                <lb/>
              ut liquet. </s>
              <s id="id002405">Pro relata prima ergo ponamus, ut ue­
                <lb/>
              lim <02> relatam
                <expan abbr="primã">primam</expan>
              25, accipio 5 <02> 25 cuius <02> eſt, ut uiſum eſt, 2 104/441
                <lb/>
              ſimiliter <02> cu: 5 fuit 1 69/98 igitur reducam ad unam denominationem,
                <lb/>
              & inueniam quatuor numeros in
                <expan abbr="cõtinua">continua</expan>
              proportione inter illos,
                <lb/>
              & ſecundus poſt minimum ex illis erit <02> relata prima propinquiſ­
                <lb/>
              ſima 25. Quomodo uerò inueniantur facillimè illi termini, do­
                <lb/>
              cui in ſexto libro operis perfecti.</s>
            </p>
            <p type="main">
              <s id="id002406">Quarta regula eſt utilior, licet minus uideatur nobilis, & eſt fun­
                <lb/>
              data in hoc, quod ſi a b ſit maior c & eis ad dantur b e, & d f æqua­
                <lb/>
              les dico, quod erit minor proportio a c ad c f, quam a b ad c d, & ex
                <lb/>
              conſequenti per
                <expan abbr="uiã">uiam</expan>
              fracti maior pars unius erit c f ipſius a e, quàm </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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