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="id001600">
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              & d cognitæ ſunt erit & b c, quod eſt primum. </s>
              <s id="id001601">Per hæc eadem pro­
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              bantur quatuor ſequentes partes eodem modo. </s>
              <s id="id001602">Sexta ſic: ſit pro­
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              portio a c ad c b, nota igitur in comparatione ad monadem, ſed pro
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              portio a c ad c b b a eſt monas, igitur proportio a c ad a b nota eſt,
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              quoniam aliter non poſſet dici proportio a c ad b c nota. </s>
              <s id="id001603">Aliter, ſit
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              proportio a c ad c b e nota, ex ſuppoſito igitur conuerſa nota quæ
                <lb/>
              ſit f ex f, igitur in a c fit b c ex g in a c, fiat a b ergo ex a c in f g fit a, c igi
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              tur f g eſt monas, f autem nota eſt, igitur in comparatione ad mona­
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                <arrow.to.target n="marg321"/>
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              dem, ergo reſiduum g notum. </s>
              <s id="id001604">Cum uerò proportio a c ad c b com­
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              ponatur ex proportione a b b c ad b c, & proportio b c ad b c ſit
                <lb/>
              monas, & proportio a c ad b c nota, erit proportio a b ad b c cogni
                <lb/>
                <arrow.to.target n="marg322"/>
                <lb/>
              ta, & monade minor proportione a c ad b c. </s>
              <s id="id001605">Per idem octaua pars
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                <figure id="id.015.01.107.1.jpg" xlink:href="015/01/107/1.jpg" number="102"/>
                <lb/>
              demonſtrabitur. </s>
              <s id="id001606">Inde ſit proportio a ad b, & ad c no­
                <lb/>
              ta, erit ergo b, & c ad a nota, quare b c ad a nota, ſed
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                <arrow.to.target n="marg323"/>
                <lb/>
              hæc eſt conuerſa ad b c confuſa, igitur proportio a
                <lb/>
              ad b confuſa nota eſt. </s>
              <s id="id001607">Vltimum ſit, ſint a b c omiologæ, & ſint a & b
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                <arrow.to.target n="marg324"/>
                <lb/>
              notæ duo, quod c nota eſt, nam a b, ſi notæ ſunt, nota eſt proportio
                <lb/>
              earum. </s>
              <s id="id001608">Ergo & proportio b ad c ergo per primam partem huius
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                <arrow.to.target n="marg325"/>
                <lb/>
              cum ſit b nota, exit & c. </s>
              <s id="id001609">Et ſi ponantur a c notæ, dico, quòd b nota
                <lb/>
              erit: nam proportio a c ad c nota eſt, quæ ſit d, igitur d ad monadem
                <lb/>
              ut a ad c, ergo latus notum erit, quod ductum in c producit b, b igi­
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                <arrow.to.target n="marg326"/>
                <lb/>
              tur nota. </s>
              <s id="id001610">Et ſimiliter in analogis ſint a b c notæ: & ideò erit propor­
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              tio a ad b nota ergo c ad d. </s>
              <s id="id001611">cumque c nota ſit, ergo per primam par­
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              tem huius erit d nota, quod fuit demonſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id001612">
                <margin.target id="marg321"/>
              P
                <emph type="italics"/>
              er demon­
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              ſtrat.
                <emph.end type="italics"/>
              12.
                <lb/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001613">
                <margin.target id="marg322"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11. P
                <emph type="italics"/>
              et.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001614">
                <margin.target id="marg323"/>
              E
                <emph type="italics"/>
              x demonſt.
                <emph.end type="italics"/>
                <lb/>
              12. P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001615">
                <margin.target id="marg324"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              14.
                <lb/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001616">
                <margin.target id="marg325"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              3. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001617">
                <margin.target id="marg326"/>
              E
                <emph type="italics"/>
              x
                <emph.end type="italics"/>
              2. A
                <emph type="italics"/>
              nimi
                <lb/>
              ſententia.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001618">Propoſitio nonageſima quinta.</s>
            </p>
            <p type="main">
              <s id="id001619">Cuiuſuis trigoni rectanguli, aut cuius duo anguli ſint in dupla
                <lb/>
              proportione, aut qui circulo inſcriptus ſit cognita quantitate uni­
                <lb/>
              us lateris in comparatione ad dimetientem ſi proportio
                <expan abbr="duorũ">duorum</expan>
              la­
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              terum cognita fuerit, erunt omnia eius latera cognita.
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                <arrow.to.target n="marg327"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001620">
                <margin.target id="marg327"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001621">Non de cognitione propinqua
                <expan abbr="aſtronomorũ">aſtronomorum</expan>
              , de qua abundè ab
                <lb/>
              Heber tractatum eſt, ſed de exacta, de qua ſuperius egi nunc ſermo </s>
            </p>
            <p type="main">
              <s id="id001622">
                <arrow.to.target n="marg328"/>
                <lb/>
              eſt: ſit igitur primum a b c trigonus orthogonius: & ſit a rectus, &
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              proportio
                <expan abbr="duorũ">duorum</expan>
              laterum cognita, dico, quod omnia latera cognita
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                <arrow.to.target n="marg329"/>
                <lb/>
                <figure id="id.015.01.107.2.jpg" xlink:href="015/01/107/2.jpg" number="103"/>
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              erunt: nam ſit proportio, gratia exempli,
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              a b ad b c, erit ergo quadrati a b ad qua­
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              dratum b c cognita, quia duplicata: at
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              quadrata a b, & a c perficiunt quadratum
                <lb/>
              b c, igitur proportio quadrati a b ad a c et
                <lb/>
              eſt 1 p: cognita erit, quare & a b ad a c, &
                <expan abbr="eodẽ">eodem</expan>
              modo a c ad b c: quod
                <lb/>
              eſt primum. </s>
              <s id="id001623">Exemplum, ponatur b c dupla a b, erit a b quadratum
                <lb/>
              ſub quadruplum quadrato a b quare ſubtriplum quadrato a c igi­</s>
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