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 ...

Table of figures

< >
[Figure 141]
Page: 147
[Figure 142]
Page: 147
[Figure 143]
Page: 150
[Figure 144]
Page: 151
[Figure 145]
Page: 151
[Figure 146]
Page: 151
[Figure 147]
Page: 151
[Figure 148]
Page: 153
[Figure 149]
Page: 154
[Figure 150]
Page: 154
[Figure 151]
Page: 154
[Figure 152]
Page: 156
[Figure 153]
Page: 157
[Figure 154]
Page: 157
[Figure 155]
Page: 158
[Figure 156]
Page: 158
[Figure 157]
Page: 158
[Figure 158]
Page: 159
[Figure 159]
Page: 159
[Figure 160]
Page: 160
[Figure 161]
Page: 160
[Figure 162]
Page: 160
[Figure 163]
Page: 161
[Figure 164]
Page: 161
[Figure 165]
Page: 162
[Figure 166]
Page: 162
[Figure 167]
Page: 162
[Figure 168]
Page: 163
[Figure 169]
Page: 163
[Figure 170]
Page: 164
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="230" xlink:href="015/01/249.jpg"/>
            <p type="margin">
              <s id="id003906">
                <margin.target id="marg751"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10.
                <emph type="italics"/>
              quin
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003907">
                <margin.target id="marg752"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              16.
                <emph type="italics"/>
              eiuſ
                <lb/>
              dem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003908">
                <margin.target id="marg753"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              eiuſ­
                <lb/>
              dem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003909">
                <margin.target id="marg754"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <emph type="italics"/>
              eiuſ
                <lb/>
              dem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s id="id003910">LEMMA SECVNDVM.</s>
            </p>
            <p type="main">
              <s id="id003911">Si fuerint quatuor quanti­
                <lb/>
                <arrow.to.target n="marg755"/>
                <lb/>
              tates, quarum exceſſus primæ
                <lb/>
              ſupra ſecundam, fit minor ex­
                <lb/>
                <figure id="id.015.01.249.1.jpg" xlink:href="015/01/249/1.jpg" number="244"/>
                <lb/>
              ceſſu tertię ſupra quartam, ſitque prima non minor tertia, erit propor
                <lb/>
                <arrow.to.target n="marg756"/>
                <lb/>
              tio primæ ad ſecundam minor quàm tertiæ ad quartam.
                <lb/>
                <arrow.to.target n="marg757"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003912">
                <margin.target id="marg755"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              quin­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem. par
                <lb/>
              tes ambas.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003913">
                <margin.target id="marg756"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10.
                <emph type="italics"/>
              quin
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003914">
                <margin.target id="marg757"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003915">Sit exceſſus a ſupra b c, g b minor exceſſu d ſupra e f qui ſit h e, di­</s>
            </p>
            <p type="main">
              <s id="id003916">
                <arrow.to.target n="marg758"/>
                <lb/>
              co quod proportio a ad b c eſt minor proportione d ad e f. </s>
              <s id="id003917">Quia
                <lb/>
              enim a eſt maior d, & b g minor h e, erit maior proportio a ad b g
                <lb/>
                <arrow.to.target n="marg759"/>
                <lb/>
              quàm d ad h e, igitur fiat a ad g k ut d ad h e, erit ergo g k maior g b
                <lb/>
                <arrow.to.target n="marg760"/>
                <lb/>
              quare k e minor b c ex communi animi ſententia, eſt autem a ad k c
                <lb/>
              ut d ad e f, minor autem a ad c b quàm ad k c, igitur minor a ad b c
                <lb/>
              quam d ad e f.</s>
            </p>
            <p type="margin">
              <s id="id003918">
                <margin.target id="marg758"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              19.
                <emph type="italics"/>
              eiuſ
                <lb/>
              dem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003919">
                <margin.target id="marg759"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              eiuſ­
                <lb/>
              dem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003920">
                <margin.target id="marg760"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <emph type="italics"/>
              quin
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003921">Si intra circulum æquicurium, & ſuper eandem baſim figura æ­
                <lb/>
              quilatera & æquiangula
                <expan abbr="cõſtituatur">conſtituatur</expan>
              ,
                <expan abbr="erũt">erunt</expan>
              omnia illius latera pariter
                <lb/>
              accepta minora duobus trianguli lateribus.
                <lb/>
                <arrow.to.target n="marg761"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003922">
                <margin.target id="marg761"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003923">Sit ut proponitur, & producantur b d &
                <lb/>
              c e quæ concurrent intra triangulum, quia
                <lb/>
              anguli d b c & e c b ſupponuntur ęquales, &
                <lb/>
              ducta d e producantur d fl, & e g l quæ
                <expan abbr="con­currẽt">con­
                  <lb/>
                current</expan>
              intra triangulum k d e ut propter ean­
                <lb/>
              dem cauſam, igitur a b & a c ſunt maiores k b
                <lb/>
              & k c, ergo maiores k d, d b, & k e, e c quia
                <lb/>
              ſunt eædem. </s>
              <s id="id003924">Ductę quo que de ſimili modo
                <lb/>
                <figure id="id.015.01.249.2.jpg" xlink:href="015/01/249/2.jpg" number="245"/>
                <lb/>
              k d & d e, ſunt maiores l d & l e, igitur l f, f d & l g, g e, igitur a b & a c
                <lb/>
              maiores ſunt b d, d f, f l c e e g g l pariter acceptis. </s>
              <s id="id003925">Rurſus ducta f g:
                <lb/>
              f l & l g maiores ſunt m f & m g, igitur a b & a c ſunt maiores omni­
                <lb/>
              bus lateribus figuræ inſcriptæ.</s>
            </p>
            <p type="main">
              <s id="id003926">
                <arrow.to.target n="marg762"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003927">
                <margin.target id="marg762"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id003928">Ex hoc patet quod latera polygoniæ fi­
                <lb/>
              guræ ęquilateræ & æquiangulæ inſcriptę
                <lb/>
              portioni circuli ſunt minora lateribus tra­
                <lb/>
              pezij circunſcripti eidem peripheriæ.</s>
            </p>
            <figure id="id.015.01.249.3.jpg" xlink:href="015/01/249/3.jpg" number="246"/>
            <p type="main">
              <s id="id003929">Sit ergo trapezium a g h b circa periphe</s>
            </p>
            <p type="main">
              <s id="id003930">
                <arrow.to.target n="marg763"/>
                <lb/>
                <expan abbr="riã">riam</expan>
              a b, & in ea inſcripta figura polygonia
                <lb/>
              æquilatera & æquiangula a c, d f b. </s>
              <s id="id003931">Et quia
                <lb/>
              trapezium eſt figura cuius oppoſita duo
                <lb/>
              latera ſunt ęqualia, & duo anguli ſupra ba
                <lb/>
              ſim æquales: itemque duo in ſummitate inui
                <lb/>
              cem ęquales,
                <expan abbr="tãget">tanget</expan>
              in medio peripheriam
                <lb/>
                <arrow.to.target n="marg764"/>
                <lb/>
              quod patet ductis lineis ex centro ad ex­
                <lb/>
                <figure id="id.015.01.249.4.jpg" xlink:href="015/01/249/4.jpg" number="247"/>
                <lb/>
              trema trapezij. </s>
              <s id="id003932">Et ideo etiam
                <expan abbr="punctũ">punctum</expan>
              medium polygoniæ, quare ex </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum