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="id001145">
                <pb pagenum="60" xlink:href="015/01/079.jpg"/>
              ipſam uelut dimidiæ ad differentiam eius, & detractæ. </s>
              <s id="id001146">Rurſusque li­
                <lb/>
              neæ compoſitæ ex dimidio & reſiduo dimidiæ ac detractæ ad li­
                <lb/>
              neam compoſitam ex addita & detracta ut reſidui dimidiæ, & de­
                <lb/>
              tractæ ad partem detractam. </s>
              <s id="id001147">Et rurſus totius compoſitæ ad com­
                <lb/>
              poſitam ex dimidia & addita, uelut compoſitæ ex addita, & diffe­
                <lb/>
              rentia ad ipſam additam. </s>
              <s id="id001148">Velut ſit propoſita a b per æqualia diuiſa
                <lb/>
              in c, addita b d, & detracta b e, ſit proportio a d ad d b, ut a e ad e b,
                <lb/>
              dico eſſe, ut c d ad cb, ita ab ad c e. </s>
              <s id="id001149">Et ut a e ad e d ut c e ad e b. </s>
              <s id="id001150">Et ite­
                <lb/>
                <arrow.to.target n="marg232"/>
                <lb/>
              rum ut a d ad c d uelut e d ad d b. </s>
              <s id="id001151">In parabole proportio partium
                <lb/>
              diametri ad uerticem terminantium duplicata eſt proportioni li­
                <lb/>
              nearum ab eiſdem punctis ordinatim ductarum ad ipſam ſectio­
                <lb/>
                <arrow.to.target n="marg233"/>
                <lb/>
              nem. </s>
              <s id="id001152">In hyperbole autem & ellipſi & circuli circumferentia erit
                <lb/>
              quadratorum linearum ordinatim ductarum inter ſe uelut rectan­
                <lb/>
                <arrow.to.target n="marg234"/>
                <lb/>
              gulorum partium diametri ad eadem puncta terminantium. </s>
              <s id="id001153">Et in
                <lb/>
              eiſdem ſi à puncto peripheriæ contingens ad diametrum ducatur,
                <lb/>
              & ab eodem ordinata, erit ut partis diametri interceptę inter extre­
                <lb/>
              mum, & ordinatam ad partem inter ordinatam & peripheriam, ue­
                <lb/>
              lut interceptæ inter extremum & contingentem ad interceptam
                <lb/>
                <arrow.to.target n="marg235"/>
                <lb/>
              exterius inter finem contingentis & peripheriam. </s>
              <s id="id001154">Et in eiſdem
                <lb/>
              quadratum ſemidiametri æquale eſſe rectangulo ex intercepta in­
                <lb/>
              ter centrum & caſum contingentis in interceptam inter centrum &
                <lb/>
                <arrow.to.target n="marg236"/>
                <lb/>
              caſum ordinatæ à loco contactus productæ. </s>
              <s id="id001155">Si parabolen recta
                <lb/>
              linea contingens ad diametrum perueniat, ſumptoque puncto alio
                <lb/>
              in ſectione æquidiſtans ab eo ducatur contingenti: & ab utroque
                <lb/>
              etiam ad diametrum ordinatæ, demum à uertice æquidiſtans illis,
                <lb/>
              & à priore puncto diametro æquidiſtans donec concurrant, erit
                <lb/>
              triangulus ex ordinata, & æquidiſtante à ſecundo puncto, & dia­
                <lb/>
              metri parte contentus rectangulo ex prima ordinata & parte dia­
                <lb/>
              metri inter uerticem & ſecundam ordinatam contento æqualis.
                <lb/>
                <arrow.to.target n="marg237"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001156">
                <margin.target id="marg231"/>
              1</s>
            </p>
            <p type="margin">
              <s id="id001157">
                <margin.target id="marg232"/>
              2</s>
            </p>
            <p type="margin">
              <s id="id001158">
                <margin.target id="marg233"/>
              3</s>
            </p>
            <p type="margin">
              <s id="id001159">
                <margin.target id="marg234"/>
              4</s>
            </p>
            <p type="margin">
              <s id="id001160">
                <margin.target id="marg235"/>
              5</s>
            </p>
            <p type="margin">
              <s id="id001161">
                <margin.target id="marg236"/>
              6</s>
            </p>
            <p type="margin">
              <s id="id001162">
                <margin.target id="marg237"/>
              7</s>
            </p>
            <p type="main">
              <s id="id001163">Si in parabole contingente ad diametrum ducta ex alio puncto
                <lb/>
              ei æquidiſtans ducatur ex ipſa ſectione, ubi iterum ſecat ſectionem
                <lb/>
              intercepta per æqualia diuidetur linea à puncto contingentis dia­</s>
            </p>
            <p type="main">
              <s id="id001164">
                <arrow.to.target n="marg238"/>
                <lb/>
              metro æquidiſtanti ducta. </s>
              <s id="id001165">Idem uerò fermè continget ducta li­
                <lb/>
              nea à centro in locum contactus, ſecabit enim omnes contingenti
                <lb/>
                <arrow.to.target n="marg239"/>
                <lb/>
              æquidiſtantes in hyperbole, ellipſi at que circulo. </s>
              <s id="id001166">Eſt autem omne
                <lb/>
              centrum in medio diametri: diameter autem in circulo & ellipſi il­
                <lb/>
              las per æqualia diuidit intus enim eſt: in contrapoſitis inter uerti­
                <lb/>
              cem, & uerticem poſita eſt exterius utriuſque contingenti ad per­
                <lb/>
              pendiculum inſiſtens. </s>
              <s id="id001167">In hyperbole autem exterius etiam adiacet,
                <lb/>
              ut in contrapoſitis eadem & tranſuerſa uocatur: cuius terminus eſt
                <lb/>
              punctus concurſus cum latere trianguli, qui conum per axem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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