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="id001623">
                <pb pagenum="89" xlink:href="015/01/108.jpg"/>
              tur ſi a b ponatur 1 b c erit 2, & a c <02> 3. Rurſus ponatur angulus b
                <lb/>
              duplus angulo c qualiſcunque ſit, erit per demonſtrata ſuperius pro­
                <lb/>
              portio a b b c ad a c, ut a c ad a b, ſi igitur nota ſit proportio a c ad
                <lb/>
              a b, erit nota proportio a b b c ad a b per præcedentem. </s>
              <s id="id001624">Ergo per
                <lb/>
              eandem omnia nota ſcilicet b c ad b a, & b c ad c a. </s>
              <s id="id001625">Et ſi eſſet nota
                <lb/>
              proportio a b ad b c, dico, quod eſſent nota omnia, nam nota eſſet
                <lb/>
              a b, & b c, & quod fit ex a b in ipſum aggregatum. </s>
              <s id="id001626">Sed hoc eſt æ­
                <lb/>
                <arrow.to.target n="marg330"/>
                <lb/>
              quale quadrato a c, igitur notum eſt quadratum a c ergo a c: igitur
                <lb/>
              proportio a b b c ad a c, & a c ad a b. </s>
              <s id="id001627">Vt ſi a b eſſet 4 b c 5, eſſet a b b c
                <lb/>
              9 ducta in a b, quæ eſt, fit 36, cuius latus eſt b a c ſcilicet. </s>
              <s id="id001628">Et ſi eſſet
                <lb/>
              trigonus aliquis in circulo, cuius proportio duorum laterum ſit co
                <lb/>
              gnita ad dimetientem relata, ſequitur per demonſtrata ſupe­
                <lb/>
              rius, quod etiam tertium latus erit cognitum in comparatione ad
                <lb/>
              eadem, & ideo etiam proportio illorum laterum ad unguem co­
                <lb/>
              gnita erit.</s>
            </p>
            <p type="margin">
              <s id="id001629">
                <margin.target id="marg328"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              97.</s>
            </p>
            <p type="margin">
              <s id="id001630">
                <margin.target id="marg329"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              47.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001631">
                <margin.target id="marg330"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              17.
                <emph type="italics"/>
              ſex
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
                <lb/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              17.</s>
            </p>
            <p type="main">
              <s id="id001632">Multa præterea cognita eſſent in hoc genere, quæ nunc præter­
                <lb/>
                <arrow.to.target n="marg331"/>
                <lb/>
              mitto, quia non ſunt ad finem neceſſaria. </s>
              <s id="id001633">Alia præterea per diligen­
                <lb/>
              tem inquiſitionem maioris artis quàm alias edidimus. </s>
              <s id="id001634">tum uerò
                <lb/>
              etiam per nouas demonſtrationes.</s>
            </p>
            <p type="margin">
              <s id="id001635">
                <margin.target id="marg331"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001636">Propoſitio nonageſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id001637">Cum in perſpicuum denſum radij luminoſi inciderint, quatuor
                <lb/>
              fiunt luminis genera.
                <lb/>
                <arrow.to.target n="marg332"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001638">
                <margin.target id="marg332"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001639">Sit ſol a, & perſpicuum denſum, exempli gratia, ut ampula
                <lb/>
              magna aqua plena b c d, & ſi ſit rotunda accendit ignem ex ad­
                <lb/>
              uerſo ut in e. </s>
              <s id="id001640">Dico ergo in b c d eſſe quatuor genera luminis. </s>
              <s id="id001641">Pri­
                <lb/>
              mum quod eſt ualidius, & rectà tranſit, ualidius enim eſt, quod
                <lb/>
              tranſit quàm quod tranſire non poteſt, & etiam quia, ut dixi,
                <lb/>
              ignem accendit. </s>
              <s id="id001642">Secundum eſt quod colligitur in ampula, & dein­
                <lb/>
              de ſpargitur
                <expan abbr="circũcircà">circuncircà</expan>
              , nam id ualidius eſt, quia penetrat, & reſilit
                <lb/>
              quàm quod non penetrat, aut ſi penetrat, non ſpargitur, & hoc dif­
                <lb/>
              funditur circa uas, nec reflectitur rectè, ſed quaſi intro colligitur, &
                <lb/>
              diuerſa ratione diffunditur, eſt tamen imbecillius primo, ut dictum
                <lb/>
              eſt. </s>
              <s id="id001643">Tertium genus eſt, quod illuminat intus ingrediendo, ſed non
                <lb/>
              ſpargitur, & hoc eſt debilius ſecundo, quia
                <expan abbr="nõ">non</expan>
              poteſt ſpargi. </s>
              <s id="id001644">Quar­
                <lb/>
                <figure id="id.015.01.108.1.jpg" xlink:href="015/01/108/1.jpg" number="104"/>
                <lb/>
              tum eſt, quod non ingreditur omnino, ſed refle­
                <lb/>
              ctitur, iſtud eſt abſque dubio imbecillimum, quo­
                <lb/>
              niam penetrare non poteſt. </s>
              <s id="id001645">Et licet in ſpeculis
                <lb/>
              concauis radius reflexus uideatur eſſe ualidior,
                <lb/>
              ſtatim enim accendit ignem, hoc non contin­
                <lb/>
              git, niſi quia in ſpeculo cauo radij omnes </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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