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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          <chap>
            <pb pagenum="245" xlink:href="015/01/264.jpg"/>
            <p type="main">
              <s id="id004191">Propoſitorum circulorum a & b centra iungam recta a b, ſuper </s>
            </p>
            <p type="main">
              <s id="id004192">
                <arrow.to.target n="marg837"/>
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              quam ut ſemidiametrum deſcribo circulum b c, & ex puncto a ad
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                <arrow.to.target n="marg838"/>
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              perpendiculum a d, ex quo abſcindo æqualem ſemidiametro b e li­
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                <lb/>
                <figure id="id.015.01.264.1.jpg" xlink:href="015/01/264/1.jpg" number="268"/>
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              neam d f, ex f duco a d perpendi­
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              culum f g, ex g in a duco a g, & æ­
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              qualem angulo g a d, b a h abſcin
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              do h k
                <expan abbr="ęqualẽ">ęqualem</expan>
              d f ſeu b e, duco
                <expan abbr="aũt">aunt</expan>
                <lb/>
                <arrow.to.target n="marg840"/>
                <lb/>
              b e, ut ſit
                <expan abbr="æquidiſtãs">æquidiſtans</expan>
              h k, duco h e,
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                <arrow.to.target n="marg841"/>
                <lb/>
                <expan abbr="quã">quam</expan>
              dico contangere utrunque
                <expan abbr="cir­culũ">cir­
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                culum</expan>
              b k: produco b k, & quia duæ
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              lineæ b a & a k ſunt ęquales duo­
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              bus lineis a g & a f, duæ enim
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              prodeunt ab eodem centro, reli­
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              quæ ſunt reſidua æqualium d f & h k, & angulus b a k æqualis
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                <arrow.to.target n="marg842"/>
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              g a f, ex ſuppoſito erit angulus g f a æqualis angulo b k a, g f a au­
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              tem rectus fuit, quia g f ad perpendiculum erecta fuit, itaque b k a
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              rectus eſt, & ideo b k h rectus, quare
                <expan abbr="cũ">cum</expan>
              b e & k h ſint æquales, & æ­
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                <arrow.to.target n="marg843"/>
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              quidiſtantes, erit angulus e oppoſitus b h k rectus, igitur duo angu
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              li e b k & e h k duobus rectis æquales, quare cum ſint æquales inui
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                <arrow.to.target n="marg844"/>
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              cem, quia oppoſiti in parallelogrammo uterque eorum rectus erit.
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              Recti ergo ſunt anguli e & h, & lineæ b e & a h ex centris circulo­
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              rum, & angulos Illos conſtituit lineæ e h, igitur e h contangit u­
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                <arrow.to.target n="marg846"/>
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              trunque circulum.</s>
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              C
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              o
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              _{m}.</s>
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              P
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              er
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              11.
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              primi
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              E
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              lement.
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              </s>
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              3.
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              pri­
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              mi
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              E
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              lem.
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              23.
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              er
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              4.
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              primi
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              E
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              lem.
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              </s>
            </p>
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              13.
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              32.
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              P
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              er
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              16.
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              ter­
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              tij
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              E
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              lem.
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              </s>
            </p>
            <p type="main">
              <s id="id004203">Propoſitio ducenteſima tertia decima.</s>
            </p>
            <p type="main">
              <s id="id004204">Propoſito circulo atque in eius peripheria puncto ſignato lineas
                <lb/>
              contingentes ultra citraque, & etiam ab ipſomet deducere.</s>
            </p>
            <figure id="id.015.01.264.2.jpg" xlink:href="015/01/264/2.jpg" number="269"/>
            <p type="main">
              <s id="id004205">Sit circulus b c d, & in eius peripheria c
                <lb/>
                <arrow.to.target n="marg847"/>
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              punctum deſcriptum, & ſumatur b d por­
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              tio minor quadrante, in qua punctum c, &
                <lb/>
              ducantur a b, a c, & ducantur b e, c f, d g, ad
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                <arrow.to.target n="marg848"/>
                <lb/>
              perpendiculum, & conſtat propoſitum, &
                <lb/>
              quod nunquam ex eadem parte conuenient
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                <arrow.to.target n="marg849"/>
                <lb/>
              ex eadem parte ex demonſtratis ſuprà.</s>
            </p>
            <p type="margin">
              <s id="id004206">
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              C
                <emph type="italics"/>
              o
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              m.</s>
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              11.
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              </s>
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              <s id="id004208">
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              P
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              er
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              221.</s>
            </p>
            <p type="main">
              <s id="id004209">Propoſitio ducenteſima quarta decima.</s>
            </p>
            <p type="main">
              <s id="id004210">Si extra circulum duo puncta ęqualiter à centro diſtantia ſignen
                <lb/>
              tur, erit punctum reflexionis æqualis, in medio arcus intercepti in­
                <lb/>
              ter lineas, quæ à centro ducuntur ad illa puncta. </s>
              <s id="id004211">Si uerò unum cen
                <lb/>
              tro proximius fuerit altero punctum æqualitatis in peripheria, tan
                <lb/>
              to longius uerſus breuiorem lineam, quanto punctum aliud à cen­
                <lb/>
              tro magis </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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