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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              <s id="id002406">
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              c d ipſius a f ex Euclide. </s>
              <s id="id002407">Dico ergo quod maior eſt proportio a b
                <lb/>
                <figure id="id.015.01.154.1.jpg" xlink:href="015/01/154/1.jpg" number="149"/>
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              ad c d, quàm a e ad e f, fiat d g ad quam ſit b c ut
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                <arrow.to.target n="marg467"/>
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              a b ad c d, eritque a e ad c g ut a b ad c d, minor au­
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              tem eſt a e ad c f, quam ad c g, igitur minor a e ad
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              c f quàm a b ad c d quod fuit propoſitum. </s>
              <s id="id002408">Simili
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              ter ſi fuerint duæ quantitates, a b & c d, quarum a b ſit maiore, c d
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              autem eadem e minor, dico, quòd dimidium aggregati a b & c d
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              maiorem habebit proportionem ad e, quàm c d & minor, nam iun­
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              cta b f æquali d e ad a b, ita ut f g ſit dimidium totius a f, qùia ergo
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                <figure id="id.015.01.154.2.jpg" xlink:href="015/01/154/2.jpg" number="150"/>
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              f g eſt dimidium f a & fb eſt minor dimidio
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                <arrow.to.target n="marg468"/>
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              f a cum ſit minor b a, & ſimiliter f g eſt mi­
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              nor a b, quia a b eſt maior dimidio a f, quia
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              eſt maior b f, ergo proportio g f ad c eſt ma
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              ior quam b f ad e, ita quam c d ad e, & mi­
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                <arrow.to.target n="marg469"/>
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              nor quàm a b ad e, quod fuit propoſitum. </s>
              <s id="id002409">Quo uiſo uolo <02> 1000
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              quadratam, & quòd de quadrata dico, dico etiam de alijs radici­
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              bus & erit ex ſecunda regula harum 31 39/62 & quadratum erit 1000
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              1521/3844. Iuxta ergo primam partem regulæ 31 38/61 erit minus, & in ueritate
                <lb/>
              in eo, quod fit ducendo, ut uides, & hoc eſt pro­
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                <figure id="id.015.01.154.3.jpg" xlink:href="015/01/154/3.jpg" number="151"/>
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              ximum ad 11/160, multiplico igitur duplum 31 39/62,
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              quod eſt fermè 63 1/4 in 1/160 fient 63/160 detrahe ex
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              1521/3844 hoc modo, diuide 3844 per 160 exit 24 /40
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              diuide 1521 per 24, exit 63 3/8, habes igitur quod
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              1521/3844 ſunt 63/160, igitur detracto 63/160 ex 63/160 nihil relinquitur, & erit <02> exa­
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              cta ualde 1000 hoc 31 38/61 cuius quadratum 1000 41/3421 uides breuita
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              tem, & propinquitatem in producto differentia eſt 1/100 aut parum
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              maius quod ad radicem comparatum cum debeat diuidi per du­
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              plum eius erit paulo maius 1/6300. Vnde facilior eſt, & breuior hæc
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              uia quàm per 00 additus. </s>
              <s id="id002410">Rurſus uolo aliquid
                <expan abbr="adim̃ere">adimere</expan>
              & cum pro
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              pinquitate ita facio. </s>
              <s id="id002411">Conſidero quòd 31 38/61 eſt maius 1/6300 radice, di­
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              uido 6300 per 62 exit 103 fermè, neque enim curo in hoc fractiones,
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              multiplico ergo 103 in 38/61 & habeo 3914/6283 hic denominator eſt proxi­
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              mus 6300, aufero ergo 1 ex 3914, habebo ualde proximam <02> 1000,
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              31 3913/6283 cuius quadratum eſt 1000 minus 1/1048 hoc ut dixi diuiſum
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              per duplum <02> quod eſt 63 eſt omnino inſenſile in radice.</s>
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            <p type="margin">
              <s id="id002412">
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              8. P
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              ropoſ.
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              quinti
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              E
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              lem.
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              P
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              er
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              18.
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                <emph type="italics"/>
              quinti
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              E
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              lem.
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              </s>
            </p>
            <p type="margin">
              <s id="id002413">
                <margin.target id="marg468"/>
              P
                <emph type="italics"/>
              er
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              11.
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                <emph type="italics"/>
              quinti
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              E
                <emph type="italics"/>
              lem.
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                <expan abbr="amplificatã">amplificatam</expan>
              .
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              </s>
            </p>
            <p type="margin">
              <s id="id002414">
                <margin.target id="marg469"/>
              P
                <emph type="italics"/>
              er
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              8.
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              quin­
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              ti
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              E
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              lem.
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              </s>
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              <s id="id002415">Quinta regula eſt omnium pulcherrima, & eſt communis omni
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              bus & fractis & integris & omnibus generibus radicum, & ſit ex­
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              emplum, uolo <02> radicis ſupraſcriptæ ſcilicet 31 3913/6283 multiplico 31
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              in 6283, & fit 194793, cui addo 3913, fit 198686 manifeſtum eſt igi­
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              tur, quod 198686/6283 æquiualet 31 3913/6283 hoc facto, quod eſt commune </s>
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          </chap>
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      </text>
    </archimedes>