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="198" xlink:href="015/01/217.jpg"/>
            <p type="head">
              <s id="id003388">SCHOLIVM.</s>
            </p>
            <p type="main">
              <s id="id003389">Partes omnes conſentiunt in grauitatem medij, quoniam una
                <lb/>
              aliam non uult centro mundi fieri propiorem.</s>
            </p>
            <p type="main">
              <s id="id003390">De ſecunda præcipua ſunt, quod ſi magnitudo aliqua humido
                <lb/>
              leuior ea in grauitate proportionem habebit ad humidum ęqualis
                <lb/>
              molis, quam pars magnitudinis demerſa ad totam magnitudinem,
                <lb/>
              & hoc intelligitur quando magnitudo illa fuerit è genere ſolido­
                <lb/>
              rum rectorum & rectangulorum. </s>
              <s id="id003391">Secunda eſt, quòd quæ ſimilia
                <lb/>
              ſunt ſuperficiebus, ita ut axem habeant in medio, ſecundum ſitum
                <lb/>
              axis merguntur & prominent, & ſi aliter mergantur, redeunt. </s>
              <s id="id003392">Ter­
                <lb/>
              tia, quod quę anguſtiora ſunt, ab oppoſita parte uerò latiora, incli­
                <lb/>
              nantur ad partem acutiorem, quia ſic facilius deſcendunt. </s>
              <s id="id003393">Quarta
                <lb/>
              eſt, de corporibus non æqualibus, ipſa enim neceſſe eſt, ut ab hac ſe
                <lb/>
              inflectant, & ratio horum diuerſa eſt iuxta rationem proportionis
                <lb/>
              partium quæ merguntur adinuicem. </s>
              <s id="id003394">Quinta eſt, quòd merſa in hu­
                <lb/>
              mido, quanto minus merſa fuerint, tanto facilius & eo frequenti­
                <lb/>
              us commutantur.</s>
            </p>
            <p type="main">
              <s id="id003395">Propoſitio centeſima ſeptuageſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id003396">Si proportio aliqua ex duabus proportionibus eiuſdem quanti
                <lb/>
              tatis ad alias duas componatur: erit proportio illarum duarum ea­
                <lb/>
              dem proportioni producti ex proportione in primam duarum
                <lb/>
              quantitatum detracta priore illa quantitate, quæ ad duas compara
                <lb/>
              tur, ad eandem priorem quantitatem.</s>
            </p>
            <p type="main">
              <s id="id003397">Sit proportio a ad compoſita ex proportionibus c
                <lb/>
                <arrow.to.target n="marg623"/>
                <lb/>
                <figure id="id.015.01.217.1.jpg" xlink:href="015/01/217/1.jpg" number="209"/>
                <lb/>
              ad d & c ad e, dico quòd proportio d ad e eſt, ut produ­
                <lb/>
              cti ex proportione in d detracto c ad ipſum c. </s>
              <s id="id003398">Et nos
                <lb/>
              ſuperius expoſuimus conuerſam huius. </s>
              <s id="id003399">Erit enim per
                <lb/>
                <expan abbr="ſecundã">ſecundam</expan>
              demonſtrationem illius proportio a ad b, uelut producti
                <lb/>
              ex c in d, & e ad productum d in e: at productum d in e & in propor
                <lb/>
              tionem, eſt idem quod productum proportionis in d in ipſum e: igi
                <lb/>
              tur cum in uno ſit productum e in c, & d in c, in alio productum a b
                <lb/>
              in d in de in e, quæ ſunt æqualia, detracto producto e in c ex produ­
                <lb/>
              cto proportionis in d & inde in e, relinquetur, productum c in d æ­
                <lb/>
              quale producto a b .i. </s>
              <s id="id003400">proportionis in productum d in e, detracto
                <lb/>
              numero c in e: igitur ducto c in d, & diuiſo per productum a b in d
                <lb/>
              numero c, exibit e, igitur cum illud productum fiat ex d, ſcilicet in c,
                <lb/>
              & ex e in productum proportionis in d dempto numero c, erit pro
                <lb/>
              portio d ad e, uelut producti ex d in proportionem, detracto e ad
                <lb/>
              ipſum c, uelut c ſit 12, d 4, e 6, a b erit 5 proportio d ad e, uelut d in a b,
                <lb/>
              id eſt 20, detracto c, & eſt 8 ad c 12.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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