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 ...

Page concordance

< >
Scan Original
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id000261">
                <pb pagenum="12" xlink:href="015/01/031.jpg"/>
              dem tamen generis, cum illis dico quòd proportio e ad d eſt com­
                <lb/>
              poſita ex proportionibus e ad a c, & e ad b c. </s>
              <s id="id000262">Poſita ergo e tan<08> ſu­
                <lb/>
              periore numero, & a c & c b inferioribus, erit ex octaua propoſitio­
                <lb/>
              ne huius proportio productorum ex e in a c, & coniunctorum, &
                <lb/>
              ex conſequenti per primam ſecundi Elementorum producti ex e in
                <lb/>
              a b ad productum ex a c in c b compoſita ex proportionibus e ad
                <lb/>
              a c, & e ad c b: at quod fit ex a c in c b, eſt æquale ei quod fit ex a b in
                <lb/>
              d, eo quòd a b, a c, c b & d ſunt omiologæ per decimam ſextam ſexti
                <lb/>
                <expan abbr="Elemẽtorum">Elementorum</expan>
              : Proportio igitur producti ex e in a b ad productum
                <lb/>
              ex d in a b eſt compoſita ex proportionibus e ad a c, & e ad e b: At
                <lb/>
              proportio producti ex e in a b ad productum ex d in a b, eſt uelut e
                <lb/>
                <arrow.to.target n="marg32"/>
                <lb/>
              ad d. </s>
              <s id="id000263">per ſuppoſita igitur proportio e ad d eſt compoſita ex propor
                <lb/>
              tionibus e ad a c, & e ad b c, quod fuit demonſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id000264">
                <margin.target id="marg32"/>
              13. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000265">Propoſitio undecima.</s>
            </p>
            <p type="main">
              <s id="id000266">Proportio aggregati quarumlibet duarum quantitatum ad ag­
                <lb/>
              gregatum duarum æqualium quantitatum eſt compoſita ex pro­
                <lb/>
              portionibus primis, & diuiſa per duplam.
                <lb/>
                <arrow.to.target n="marg33"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000267">
                <margin.target id="marg33"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000268">Sit proportio a ad c, & b ad d, & ſint c & d
                <lb/>
                <figure id="id.015.01.031.1.jpg" xlink:href="015/01/031/1.jpg" number="19"/>
                <lb/>
              æquales, dico quòd proportio a b ad c d eſt
                <lb/>
              compoſita ex proportionibus a ad c, & b ad
                <lb/>
              d diuiſo compoſito per duplam. </s>
              <s id="id000269">Quia enim </s>
            </p>
            <p type="main">
              <s id="id000270">
                <arrow.to.target n="marg34"/>
                <lb/>
              c & d ſunt æquales, erit b ad c, ut b ad d, qua­
                <lb/>
              re ex diffinitione cùm proportio a b ad c d
                <lb/>
                <arrow.to.target n="marg35"/>
                <lb/>
              ſit compoſita ex proportionibus a ad c, & b
                <lb/>
              ad c, erit etiam compoſita ex dictis ex propoſitione a ad c, & b ad d,
                <lb/>
                <arrow.to.target n="marg36"/>
                <lb/>
              ſtatuatur ergo e æqualis c d media inter a b & c. </s>
              <s id="id000271">Et erit per ſecun­
                <lb/>
              dam propoſitionem proportio aggregati a b ad c producta ex
                <lb/>
                <arrow.to.target n="marg37"/>
                <lb/>
              proportione aggregati a b ad c, & e ad c, igitur proportio a b ad e
                <lb/>
              erit proportio a b ad c, diuiſa per proportionem e ad c, ſed e ad c eſt
                <lb/>
                <arrow.to.target n="marg38"/>
                <lb/>
              dupla: igitur proportio a b ad c d eſt proportio a b ad c diuiſa per
                <lb/>
              duplam.</s>
            </p>
            <p type="margin">
              <s id="id000272">
                <margin.target id="marg34"/>
              E
                <emph type="italics"/>
              x ſexta
                <emph.end type="italics"/>
              A
                <emph type="italics"/>
              nim.
                <lb/>
              com. </s>
              <s id="id000273">ſententia.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000274">
                <margin.target id="marg35"/>
              D
                <emph type="italics"/>
              ecimaquarta
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000275">
                <margin.target id="marg36"/>
              13. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000276">
                <margin.target id="marg37"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              2. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000277">
                <margin.target id="marg38"/>
              P
                <emph type="italics"/>
              er quintam
                <emph.end type="italics"/>
                <lb/>
              A
                <emph type="italics"/>
              nim. </s>
              <s id="id000278">com. </s>
              <s id="id000279">ſen
                <lb/>
              tentiam.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000280">Propoſitio duodecima.</s>
            </p>
            <p type="main">
              <s id="id000281">Propoſitis duabus proportionibus unam alteri iungere abſque
                <lb/>
              multiplicatione.
                <lb/>
                <arrow.to.target n="marg39"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000282">
                <margin.target id="marg39"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.
                <lb/>
              10. P
                <emph type="italics"/>
              etit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000283">Sint propoſitæ proportiones a ad c &
                <lb/>
                <figure id="id.015.01.031.2.jpg" xlink:href="015/01/031/2.jpg" number="20"/>
                <lb/>
              b ad d, & aſſumo e ad c, iuxta ea quæ Eu­
                <lb/>
              clides demonſtrauit, ut b ad d, erit igitur </s>
            </p>
            <p type="main">
              <s id="id000284">
                <arrow.to.target n="marg40"/>
                <lb/>
              proportio a e ad c, compoſita ex proportionibus a ad c, & e ad c,
                <lb/>
              ſed proportio e ad c eſt, ut b ad d, igitur proportio a e ad c compo­
                <lb/>
              ſita eſt ex proportionibus a ad c, & b ad d.</s>
            </p>
            <p type="margin">
              <s id="id000285">
                <margin.target id="marg40"/>
              E
                <emph type="italics"/>
              x generali
                <lb/>
              com.
                <emph.end type="italics"/>
              A
                <emph type="italics"/>
              nim. ſen
                <lb/>
              tentia.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000286">Aliter ex b in c fiat f ex a in d, g ex c in d h coniunctum ex f g, k.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum