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="id004211">
                <pb pagenum="246" xlink:href="015/01/265.jpg"/>
                <arrow.to.target n="marg850"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004212">
                <margin.target id="marg850"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="main">
              <s id="id004213">Sint puncta b c, æqualiter diſtantia à cen</s>
            </p>
            <p type="main">
              <s id="id004214">
                <arrow.to.target n="marg851"/>
                <lb/>
              tro a circuli d e, & reflectantur c f, b f, dico f
                <lb/>
                <arrow.to.target n="marg852"/>
                <lb/>
              eſſe in medio arcus d e: producta enim f a,
                <lb/>
              erunt anguli d a f & e a f æquales: ſupponi­
                <lb/>
              tur enim
                <expan abbr="primũ">primum</expan>
              f eſſe in medio: igitur cum
                <lb/>
              a b & a c ſint æquales, & a f communis, erit
                <lb/>
              a f c æqualis a f b, igitur reflectentur æqua­
                <lb/>
              liter: ergo ſi ęqualiter reflectentur, ex f re­
                <lb/>
              flectentur, ut ex ſecunda parte: quare ex
                <lb/>
              medio.
                <lb/>
                <figure id="id.015.01.265.1.jpg" xlink:href="015/01/265/1.jpg" number="270"/>
                <lb/>
                <arrow.to.target n="marg853"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004215">
                <margin.target id="marg851"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              21.
                <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="id004216">
                <margin.target id="marg852"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              4.
                <emph type="italics"/>
              primi
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004217">
                <margin.target id="marg853"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              210.
                <lb/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004218">Sumatur rurſus punctum g, remotius ab
                <lb/>
              a quam b, dico quòd reflexio erit in arcu f e.
                <lb/>
              </s>
              <s id="id004219">Nam non in e, quoniam fic g e d eſſet æqualis b e k, cui rurſus eſt æ­
                <lb/>
              qualis b e d, ergo g e d æqualis b e d, pars toti. </s>
              <s id="id004220">Sed neque ultra e, nam
                <lb/>
              multo magis pars æqualis eſſet toti aut maior etiam. </s>
              <s id="id004221">Sed neque ex f,
                <lb/>
              nam eadem ratione pars eſſet maior toto. </s>
              <s id="id004222">Neque in toto arcu f d:
                <lb/>
              nam ſit punctum l, & ducantur al, g f, igitur g l a maior g f a, g f a au
                <lb/>
              tem maior e f a, igitur g l a maior c f a, ęqualis ex ſuppoſito b f a, b f a </s>
            </p>
            <p type="main">
              <s id="id004223">
                <arrow.to.target n="marg854"/>
                <lb/>
              rurſus maior b l a: multo igitur maior g l a quam b l a, non ergo re­
                <lb/>
              flexio æqualis eſſe poteſt. </s>
              <s id="id004224">Cum ergo reflexio fiat, & non ex arcu d f,
                <lb/>
                <arrow.to.target n="marg855"/>
                <lb/>
              nec puncto f, nec e, nec ultra e, nec extra d, erit neceſſarium, ut fiat ex
                <lb/>
              puncto in arcu e f.
                <lb/>
                <arrow.to.target n="marg856"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004225">
                <margin.target id="marg854"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              21.
                <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="id004226">
                <margin.target id="marg855"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              1 C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              _{m}.
                <lb/>
                <emph type="italics"/>
              præcedentis.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004227">
                <margin.target id="marg856"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id004228">Ex hoc patet, quod linea a puncto ducta, quo
                <lb/>
              longius fertur, eo etiam longius reſilit.</s>
            </p>
            <figure id="id.015.01.265.2.jpg" xlink:href="015/01/265/2.jpg" number="271"/>
            <p type="main">
              <s id="id004229">
                <arrow.to.target n="marg857"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004230">
                <margin.target id="marg857"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004231">Cum enim a c b maior ſit a d b, & angulus e c b </s>
            </p>
            <p type="main">
              <s id="id004232">
                <arrow.to.target n="marg858"/>
                <lb/>
              æqualis a c b & f d b æqualis a d b, erunt duo an­
                <lb/>
              guli a c b & e c b, maiores a d b & f d b, quare
                <lb/>
              reliquus f d a maior a c e, igitur'd f reſilit latius
                <lb/>
              quam c e.
                <lb/>
                <arrow.to.target n="marg859"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004233">
                <margin.target id="marg858"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              21.
                <lb/>
                <emph type="italics"/>
              tertij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004234">
                <margin.target id="marg859"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id004235">Ex hoc patet, quod tales lineæ quæ reſiliunt
                <lb/>
              nunquam concurrent.</s>
            </p>
            <p type="main">
              <s id="id004236">
                <arrow.to.target n="marg860"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004237">
                <margin.target id="marg860"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004238">Scilicet c e & d f nam conſtat ducta c d, angulos e c d f & d e, ma­</s>
            </p>
            <p type="main">
              <s id="id004239">
                <arrow.to.target n="marg861"/>
                <lb/>
              iores eſſe duobus rectis, ergo non concurrentin partem e f.</s>
            </p>
            <p type="margin">
              <s id="id004240">
                <margin.target id="marg861"/>
              P
                <emph type="italics"/>
              er conuer­
                <lb/>
              ſam
                <emph.end type="italics"/>
              5.
                <emph type="italics"/>
              petit.
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              uclid.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004241">Propoſitio ducenteſima quinta decima.</s>
            </p>
            <p type="main">
              <s id="id004242">Punctum reflexionis punctorum inæqualiter diſtantium à cen­
                <lb/>
              tro, æqualiter diſtat à lineis ductis à centro ad puncta, æqualiter di
                <lb/>
              ſtantia alterutrinque.
                <lb/>
                <arrow.to.target n="marg862"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004243">
                <margin.target id="marg862"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004244">Sint g h a & b h a æquales, & abſcindatur h f æqualis h b, & pro­
                <lb/>
              ducatur h b uſque a d c, ut ſit h c æqualis h g, & producantur f a & </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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