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>
            <pb pagenum="159" xlink:href="015/01/178.jpg"/>
            <p type="main">
              <s id="id002779">Sit angulus a & circulus b c, dico non poſſe aliquem angulum
                <lb/>
                <arrow.to.target n="marg527"/>
                <lb/>
              contentum recta & circuli portione eſſe illi
                <lb/>
                <figure id="id.015.01.178.1.jpg" xlink:href="015/01/178/1.jpg" number="183"/>
                <lb/>
              æqualem. </s>
              <s id="id002780">ſi enim eſſe poſsit, ſit c b e. </s>
              <s id="id002781">duca­
                <lb/>
              tur recta b d faciens rectilineum d b c ęqua
                <lb/>
                <arrow.to.target n="marg528"/>
                <lb/>
              lem a, erit igitur d b c ęqualis e b c per com­
                <lb/>
              munem animi ſententiam, ſeu ergo b d ca­
                <lb/>
              dat intra circulum ſeu extra, erit pars ęqua­
                <lb/>
              lis toti quod eſſe non poteſt. </s>
              <s id="id002782">Sed neque po­
                <lb/>
              teſt cadere recta ſuper b e. </s>
              <s id="id002783">nam id eſt contra demonſtrata ab Eucli­
                <lb/>
                <arrow.to.target n="marg529"/>
                <lb/>
              de. </s>
              <s id="id002784">At ſi ſit angulus c b e exterior ſimiliter producta b d, ſeu intus,
                <lb/>
              ſeu extrà cadat, pars erit æqualis toti quod eſſe non poteſt.</s>
            </p>
            <p type="margin">
              <s id="id002785">
                <margin.target id="marg527"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="margin">
              <s id="id002786">
                <margin.target id="marg528"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              23.
                <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="id002787">
                <margin.target id="marg529"/>
              23. E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002788">Ex hoc patet quod nullus angulus peripheria circuli & recta
                <expan abbr="cõ­">con­
                  <lb/>
                </expan>
                <arrow.to.target n="marg530"/>
                <lb/>
              tentus poteſt eſſe æqualis recto, quia rectus etiam rectilineus eſt.</s>
            </p>
            <p type="margin">
              <s id="id002789">
                <margin.target id="marg530"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id002790">Et rurſus nullus angulus peripheria &
                <lb/>
                <arrow.to.target n="marg531"/>
                <lb/>
                <figure id="id.015.01.178.2.jpg" xlink:href="015/01/178/2.jpg" number="184"/>
                <lb/>
              recta contentus à recta linea per æqualia
                <lb/>
              diuidi poteſt, patet quia una pars eſſet an­
                <lb/>
              gulus rectilineus, alia contentus recta & pe
                <lb/>
              ripheria: iſti
                <expan abbr="autẽ">autem</expan>
              non poſſunt eſſe æquales,
                <lb/>
              quare nec prior potuit per æqualia diuidi.</s>
            </p>
            <p type="margin">
              <s id="id002791">
                <margin.target id="marg531"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id002792">Ex hoc etiam patet quod ſpatium con­
                <lb/>
                <arrow.to.target n="marg532"/>
                <lb/>
                <expan abbr="tentũ">tentum</expan>
              à peripheria circuli nulli angulo rectilineo ęquale eſſe poteſt.
                <lb/>
              </s>
              <s id="id002793">nam dimidium eſſet æquale dimidio, quod eſt contra demonſtrata.</s>
            </p>
            <p type="margin">
              <s id="id002794">
                <margin.target id="marg532"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 3.</s>
            </p>
            <p type="head">
              <s id="id002795">LEMMA PRIMVM.</s>
            </p>
            <p type="main">
              <s id="id002796">Inter duos circulos qui ſe diuidant infinitæ lineæ duci poſſunt.
                <lb/>
              </s>
              <s id="id002797">Inter circulos autem qui ſe tangant, recta linea duci non poteſt.
                <lb/>
                <arrow.to.target n="marg533"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002798">
                <margin.target id="marg533"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002799">Sint duo circuli a b & a c, qui ſe diuidant </s>
            </p>
            <p type="main">
              <s id="id002800">
                <arrow.to.target n="marg534"/>
                <lb/>
              in a, & ducatur ex centro inferioris d a &
                <lb/>
                <figure id="id.015.01.178.3.jpg" xlink:href="015/01/178/3.jpg" number="185"/>
                <lb/>
              a d, & ad d a cathetus a e, dico quòd a e di­
                <lb/>
              uidet angulum b a c ducatur ex centro ſu­
                <lb/>
                <arrow.to.target n="marg535"/>
                <lb/>
              perioris a c b quod ſit f, fa cui cathetus a g,
                <lb/>
              quia ergo e a cadit infra a g, & inter a g &
                <lb/>
                <arrow.to.target n="marg536"/>
                <lb/>
              a b non poteſt duci recta, igitur e a cadit in­
                <lb/>
                <figure id="id.015.01.178.4.jpg" xlink:href="015/01/178/4.jpg" number="186"/>
                <lb/>
              tra a c b circulum. </s>
              <s id="id002801">Rurſus tangant ſe circuli
                <lb/>
              c d & c e, & ducatur a b per centra
                <expan abbr="eorũ">eorum</expan>
              quę
                <lb/>
              applicabit ad c, ex c ducatur cathetus c f &
                <lb/>
                <expan abbr="quoniã">quoniam</expan>
              c f contangit
                <expan abbr="circulũ">circulum</expan>
              c e, l igitur, du­
                <lb/>
              cta quauis linea infra c f, cadet intra
                <expan abbr="circulũ">circulum</expan>
                <lb/>
              c e. </s>
              <s id="id002802">Non ergo poterit cadere inter c d & c e.</s>
            </p>
            <p type="margin">
              <s id="id002803">
                <margin.target id="marg534"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002804">
                <margin.target id="marg535"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              15.
                <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="id002805">
                <margin.target id="marg536"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <emph type="italics"/>
              ter­
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s id="id002806">LEMMA SECVNDVM.</s>
            </p>
            <p type="main">
              <s id="id002807">Dato angulo contento duabus peripherijs
                <expan abbr="æqualiũ">æqualium</expan>
              circulorum
                <lb/>
              ſe ſecantium æqualem rectilineum illi fabricare.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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