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="id004161">
                <pb pagenum="244" xlink:href="015/01/263.jpg"/>
              uidat in h, igitur h e & h f cùm angulum conſtituant, quanto magis
                <lb/>
              protrahentur eo magis diſtabunt, nec unquam concurrent.</s>
            </p>
            <p type="margin">
              <s id="id004162">
                <margin.target id="marg824"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id004163">
                <margin.target id="marg825"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              29.
                <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="id004164">
                <margin.target id="marg826"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              13.
                <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="id004165">
                <margin.target id="marg827"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              6. & 4.
                <lb/>
                <emph type="italics"/>
              ſexti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004166">
                <margin.target id="marg828"/>
              P
                <emph type="italics"/>
              er
                <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="margin">
              <s id="id004167">
                <margin.target id="marg829"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              6.
                <emph type="italics"/>
              ter­
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004168">Propoſitio ducenteſima duodecima.</s>
            </p>
            <p type="main">
              <s id="id004169">Si ab eodem puncto ad circuli peripheriam, lineæ quotuis du­
                <lb/>
              cantur, tres inuenire lineas, quæ
                <expan abbr="nõ">non</expan>
              in alium punctum reflectentur.
                <lb/>
                <arrow.to.target n="marg830"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004170">
                <margin.target id="marg830"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004171">Quouis conſtituto puncto ueluti a extra circu
                <lb/>
              lum b c d, dico poſſe trahi tres lineas ad ipſam cir­
                <lb/>
              culi peripheriam, uelut a b, a c, a d, quæ ad alium
                <lb/>
              punctum non reflectentur. </s>
              <s id="id004172">Ducantur ergo a e ad </s>
            </p>
            <p type="main">
              <s id="id004173">
                <arrow.to.target n="marg831"/>
                <lb/>
              centrum, & a b & a d ad contingentes illius peri­
                <lb/>
              pheriam, quas conſtat non reflecti ſed progredi,
                <lb/>
                <arrow.to.target n="marg832"/>
                <lb/>
              a c autem reflectitur in ſe ipſam per demonſtrata
                <lb/>
                <arrow.to.target n="marg833"/>
                <lb/>
              ſuperius, igitur conſtat propoſitum.
                <lb/>
                <figure id="id.015.01.263.1.jpg" xlink:href="015/01/263/1.jpg" number="266"/>
                <lb/>
                <arrow.to.target n="marg834"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004174">
                <margin.target id="marg831"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              17.
                <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="id004175">
                <margin.target id="marg832"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              61.
                <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="id004176">
                <margin.target id="marg833"/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              210.</s>
            </p>
            <p type="margin">
              <s id="id004177">
                <margin.target id="marg834"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              m. </s>
              <s id="id004178">1.</s>
            </p>
            <p type="main">
              <s id="id004179">Ex hoc patet, quod omnia puncta ſub linea
                <lb/>
              contingente poſſunt reflecti ad ipſum per arcum
                <lb/>
              interceptum à contingente, & ea quæ ad centrum.</s>
            </p>
            <p type="main">
              <s id="id004180">
                <arrow.to.target n="marg835"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004181">
                <margin.target id="marg835"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004182">Id eſt, quod omnia puncta infra lineam a b f ductam quantum­
                <lb/>
              libet poſſunt reflecti per arcum b c ad punctum a æqualibus an­
                <lb/>
              gulis. </s>
              <s id="id004183">Quoniam ex a per c b reflectuntur ad quælibet puncta infra
                <lb/>
              a b f, eo quòd termini ſunt punctum a, per ea quæ ſunt hic demon­
                <lb/>
              ſtrata, & a b f, ipſa ergo ſi extrema in extremis, media in medijs con­
                <lb/>
              tinentur per regulam illam Dialecticam: igitur omnia puncta ſub
                <lb/>
              a b f etiam in infinitum producta continentur in reflexione à pun­
                <lb/>
              cto a per arcum b c.</s>
            </p>
            <p type="main">
              <s id="id004184">
                <arrow.to.target n="marg836"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004185">
                <margin.target id="marg836"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id004186">Et rurſus, ſi à circulo ad circulum extremæ ducantur, nec illæ re­
                <lb/>
              flectentur, ſed tranſibunt: mediæ autem omnes reflecti poterunt à
                <lb/>
              quouis puncto.</s>
            </p>
            <figure id="id.015.01.263.2.jpg" xlink:href="015/01/263/2.jpg" number="267"/>
            <p type="main">
              <s id="id004187">Quia ſi a b ſit Sol, c d Luna, Sole
                <lb/>
              minor extremum in utroque lumina­
                <lb/>
              ri a c, b d quæ contingant utrunque
                <lb/>
              circulum, quod facile fiat, ductis a c
                <lb/>
              & b d ex punctis non oppoſitis, æ­
                <lb/>
              quidiſtarent enim, ſed iuxta quan­
                <lb/>
              titatem dimetientis minoris. </s>
              <s id="id004188">Erit er­
                <lb/>
              go ut h e non reflectantur, aliæ o­
                <lb/>
              mnes mediæ reflectentur per demonſtrata à quolibet puncto, ergo
                <lb/>
              idem de totis circulis & punctis.</s>
            </p>
            <p type="head">
              <s id="id004189">SCHOLIVM.</s>
            </p>
            <p type="main">
              <s id="id004190">Propoſitis duobus circulis lineam ambos
                <expan abbr="cõtingentem">contingentem</expan>
              ducere.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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