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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            <p type="main">
              <s id="id000430">
                <pb pagenum="23" xlink:href="015/01/042.jpg"/>
              c, ergo k producetur ex c d in b, ergo ex c d in a fit h, ex c d in b fit k.
                <lb/>
              </s>
              <s id="id000431">erit a ad b ut h ad k, igitur ex prima harum cum ex c in f producatur
                <lb/>
              h, & ex d in g k, & dicatur produci proportio h ad k ex proportio­
                <lb/>
              ne c ad d, & f ad g, & proportio h ad k ſit eadem, quæ a ad b, ergo
                <lb/>
              proportio a ad b producitur ex c ad d, & f ad g, ergo diuiſa propor­
                <lb/>
              tione a ad b prodibit proportio f ad g, quod fuit propoſitum.</s>
            </p>
            <p type="margin">
              <s id="id000432">
                <margin.target id="marg72"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10. P
                <emph type="italics"/>
              et.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000433">Propoſitio uigeſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id000434">Cùm fuerit proportio primæ ad ſecundam maior, quàm tertiæ
                <lb/>
              ad quartam, erit confuſa ex his maior quàm tertiæ ad quartam, mi­
                <lb/>
              nor autem quàm primæ ad ſecundam.</s>
            </p>
            <figure id="id.015.01.042.1.jpg" xlink:href="015/01/042/1.jpg" number="34"/>
            <p type="main">
              <s id="id000435">Sit proportio a ad b maior quàm c
                <lb/>
                <arrow.to.target n="marg73"/>
                <lb/>
              ad d, dico, quod confuſa ex a c ad b d
                <lb/>
              eſt maior, quàm c ad d, et minor quàm
                <lb/>
              a ad b, ut enim c ad d ita fiat e ad b, erit que per tertiam decimam ha­
                <lb/>
                <arrow.to.target n="marg74"/>
                <lb/>
              rum e c ad b d confuſa minor quàm a c ad b d, nam e eſt minor a,
                <lb/>
              quia proportionem habent minorem ad b quam a eo quòd e ha­
                <lb/>
              bet proportionem ad b, quam c ad d, quæ
                <expan abbr="autẽ">autem</expan>
              c ad d minor, quám
                <lb/>
              a ad b, ut ſuppoſitum eſt, igitur e c ad b d minor, quàm a b ad c d, e b
                <lb/>
              autem ad c d eſt, ut demonſtratum eſt qualis c ad d, ergo c ad d mi­
                <lb/>
              nor, quàm confuſa a b ad c d, quod eſt ſecundum per idem proba­
                <lb/>
              bitur, & primum poſita f ad d, ut a ad b, eritque a maior c, igitur ma­
                <lb/>
              ior proportio a f ad b d, quàm a c ad b d, ſed a f ad b d, ut a ad b per
                <lb/>
              eandem tertiam decimam huius ergo proportio confuſa a b ad c d
                <lb/>
              eſt minor, quàm a ad b.</s>
            </p>
            <p type="margin">
              <s id="id000436">
                <margin.target id="marg73"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id000437">
                <margin.target id="marg74"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10. P
                <emph type="italics"/>
              et.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000438">Propoſitio uigeſima tertia.</s>
            </p>
            <p type="main">
              <s id="id000439">Omnis motus naturalis ad locum ſuum eſt: ideo per rectam li­
                <lb/>
              neam fit.
                <lb/>
                <arrow.to.target n="marg75"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000440">
                <margin.target id="marg75"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000441">Motus naturalis eſt, ut conſeruetur corpus, & conueniat locus
                <lb/>
              corpori, igitur fit ad ſuum locum. </s>
              <s id="id000442">Locus autem dicitur in compara
                <lb/>
              tione ad uniuerſum. </s>
              <s id="id000443">ideo omnis motus naturalis eſt à centro mun­
                <lb/>
              di ſurſum, uel ad centrum deorſum. </s>
              <s id="id000444">Et quia quanto natura celerius
                <lb/>
              ſuum finem poteſt aſſequi (quia finis bonus eſt aliter non illum ap­
                <lb/>
              peteret) eum quærit, cùm ſit ſapientiſsimæ uitæ miniſtra: at linea re­</s>
            </p>
            <p type="main">
              <s id="id000445">
                <arrow.to.target n="marg76"/>
                <lb/>
              cta breuiſsima eſt Euclide teſte à puncto ad punctum, igitur omnis
                <lb/>
              motus naturalis eſt ſurſum aut deorſum per rectam lineam.</s>
            </p>
            <p type="margin">
              <s id="id000446">
                <margin.target id="marg76"/>
              D
                <emph type="italics"/>
              iſt. tertia
                <lb/>
              primi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000447">Propoſitio uigeſima quarta.</s>
            </p>
            <p type="main">
              <s id="id000448">Omnis motus circularis uoluntarius eſt.</s>
            </p>
            <p type="main">
              <s id="id000449">Sit motus in circulo ſeu per circulum in orbe cuius ſit centrum,
                <lb/>
              ſit c mundi centrum: igitur ex diffinitione circuli tantum diſtabit a,
                <lb/>
              quantum b ab ipſo c: ſed in motu naturali per pręcedentem neceſſe
                <lb/>
              eſt, ut recta feratur ad c, uel recedat, igitur motus a eſt uoluntarius, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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