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>
            <pb pagenum="77" xlink:href="015/01/096.jpg"/>
            <p type="margin">
              <s id="id001431">
                <margin.target id="marg298"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              178.</s>
            </p>
            <p type="main">
              <s id="id001432">Ex hoc etiam patet modus
                <expan abbr="cognoſcẽdi">cognoſcendi</expan>
              proportionem grauium
                <lb/>
                <arrow.to.target n="marg299"/>
                <lb/>
              inuicem per ſolam aquam, uelut auri ad plumbum, ad lapides uel
                <lb/>
              æs, aut æris ad lapidem & ſimilia, ut in præcedenti operatione de­
                <lb/>
              prehendiſti: nam cum ſit nota proportio auri ad aquam & æris uel
                <lb/>
              lapidis ad eandem, erit auri ad æs uel lapidem nota.</s>
            </p>
            <p type="margin">
              <s id="id001433">
                <margin.target id="marg299"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 4.</s>
            </p>
            <p type="main">
              <s id="id001434">Et ſimiliter ſciemus per hoc accipere partes diuerſorum, quę iun
                <lb/>
                <arrow.to.target n="marg300"/>
                <lb/>
              ctæ faciant conſtitutum pondus. </s>
              <s id="id001435">Velut uolo facere maſſam ex mel­
                <lb/>
                <figure id="id.015.01.096.1.jpg" xlink:href="015/01/096/1.jpg" number="90"/>
                <lb/>
              le & aqua, quæ impleat uas, quod mellis contineat
                <lb/>
              quindecim, aquæ duodecim, uolo ut contentum ſit
                <lb/>
              ponderis quatuordecim, operabor, ut in
                <expan abbr="cõſolatio­nibus">conſolatio­
                  <lb/>
                nibus</expan>
              , ponam duas partes mellis & unam aquæ, ut
                <lb/>
              uides in operatione à latere.</s>
            </p>
            <p type="margin">
              <s id="id001436">
                <margin.target id="marg300"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 5.</s>
            </p>
            <p type="main">
              <s id="id001437">Propoſitio octuageſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id001438">Si circuli in æquales, ſeu in ſphæra, ſeu in plano ſe ſecuerint nun­
                <lb/>
              quam oppoſitos angulos æquales habent.</s>
            </p>
            <p type="main">
              <s id="id001439">Capiantur tres quartæ circulorum magnorum a b, a c, b c, & alia
                <lb/>
                <arrow.to.target n="marg301"/>
                <lb/>
              b d ad rectos angulos
                <expan abbr="erũtque">eruntque</expan>
              uiciſsim poli, & ducatur per medium
                <lb/>
              parallelus, erit ergo e f æqualis e g, & f e æqualis f g, ſed baſis c g eſt
                <lb/>
                <figure id="id.015.01.096.2.jpg" xlink:href="015/01/096/2.jpg" number="91"/>
                <lb/>
              quarta circuli, & baſis c b dimidium quartæ
                <lb/>
              circuli eo quod tota b a eſt quarta circuli, igi­
                <lb/>
              tur per modum 25 primi Elementorum quæ
                <lb/>
              tenet, erit angulus c f g maior oppoſito c f b.
                <lb/>
              </s>
              <s id="id001440">Hoc autem tenet in eiuſdem rationis ſuperfi­
                <lb/>
              ciebus, quales ſunt hæ, quæ ſunt ſuperficies eiuſdem ſphęræ. </s>
              <s id="id001441">poſſet
                <lb/>
              etiam demonſtrari per modum quartæ primi Elementorum. </s>
              <s id="id001442">Et eti­
                <lb/>
              am conſtituta ſphæra e f g, cuius hic circulus eſſet maior circulus, &
                <lb/>
              non tangeret niſi in illa linea ſphæra maiorem, & utrin que ſecaret eo­
                <lb/>
              dem circulo. </s>
              <s id="id001443">Et etiam per cordas & trigonos rectilineos, auxilio
                <lb/>
                <expan abbr="tamẽ">tamen</expan>
              regulæ dialecticæ. </s>
              <s id="id001444">Ex hoc ſequitur auxilio regulæ dialecticæ,
                <lb/>
                <figure id="id.015.01.096.3.jpg" xlink:href="015/01/096/3.jpg" number="92"/>
                <lb/>
              quod in omnibus parallelis a c d & e f g cum b c circulo
                <lb/>
              maiore, & per aliam regulam dialecticam in omnibus cira
                <lb/>
              culis inæqualibus inter ſe ad æquales angulos ſecanti­
                <lb/>
              bus & ex tertia demum regula dialectica, ſequitur in o­
                <lb/>
              mnibus circulis in æqualibus ſe ſecantibus ad quemuis
                <lb/>
              angulum in ſphæræ ſuperficie. </s>
              <s id="id001445">Sunt autem hæ regulæ mediæ inter
                <lb/>
              axiomata & demonſtrata. </s>
              <s id="id001446">Et ex logica propria illi arti. </s>
              <s id="id001447">In plano au­
                <lb/>
                <arrow.to.target n="marg302"/>
                <lb/>
              tem ſpatium d b c minus eſt a b c, ſed ſpatium c b d eſt unum, ergo
                <lb/>
              per communem animi ſententiam ſpatium a b d, maius eſt ſpatio
                <lb/>
              c b c, quod fuit probandum.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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