Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
31 10
32
33 11
34
35 12
36
37 13
38
39 14
40
41 15
42
43 16
44
45 17
46
47 18
48
49 19
50
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
< >
page |< < (35) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="46">
          <p style="it">
            <s xml:space="preserve">
              <pb o="35" file="0081" n="81" rhead="DE IIS QVAE VEH. IN AQVA."/>
            proportionem, quam c e ad e a. </s>
            <s xml:space="preserve">ſimiliter demonſtrabitur eandem
              <lb/>
            babere n o ad o f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">reliquas eiuſmodi, at uero b K ad K e eam
              <lb/>
            habere proportionem, quam habet c e ad e a, ex eadem quinta. </s>
            <s xml:space="preserve">Ar-
              <lb/>
            chimedis perſpicue apparet. </s>
            <s xml:space="preserve">at que illud eſt, quod demonſtr andum
              <lb/>
            propoſuimus.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0079-01" xlink:href="fig-0079-01a">
              <image file="0079-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0079-01"/>
            </figure>
            <note position="right" xlink:label="note-0079-01" xlink:href="note-0079-01a" xml:space="preserve">4. ſexti:</note>
            <note position="right" xlink:label="note-0079-02" xlink:href="note-0079-02a" xml:space="preserve">11. quinti</note>
            <note position="right" xlink:label="note-0079-03" xlink:href="note-0079-03a" xml:space="preserve">14. quinti</note>
            <figure xlink:label="fig-0080-01" xlink:href="fig-0080-01a">
              <image file="0080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0080-01"/>
            </figure>
            <note position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve">2. ſexti.</note>
          </div>
        </div>
        <div type="section" level="1" n="47">
          <head xml:space="preserve">LEMMA VI.</head>
          <p style="it">
            <s xml:space="preserve">Itaque maneant eadem, quæ ſupra: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">itidem deſcri-
              <lb/>
            batur alia portio ſimilis contenta recta linea & </s>
            <s xml:space="preserve">rectan-
              <lb/>
            guli coni ſectione d r c; </s>
            <s xml:space="preserve">cuius diameter r s, ut ſecet li-
              <lb/>
            neam f g in t: </s>
            <s xml:space="preserve">producaturque s r ad lineam c h in u;
              <lb/>
            </s>
            <s xml:space="preserve">cuiſectio a b c occurrat in x, & </s>
            <s xml:space="preserve">e f c in y. </s>
            <s xml:space="preserve">Dico b m
              <lb/>
            ad m d proportionem habere compoſitam ex propor-
              <lb/>
            tione, quam babet e a ad a c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex ea, quam c d ba-
              <lb/>
            bet ad de.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">
              <emph style="sc">S_imiliter_</emph>
            enim ut ſupra, demonſtrabimus lineam c h con-
              <lb/>
            tingere ſectioné d r c in c puncto: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">l m ad m d, itêmq; </s>
            <s xml:space="preserve">n f ad f t;
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">u y ad y r ita eſſe, ut c d ad d e. </s>
            <s xml:space="preserve">Quoniam igitur lb ad b m eſt,
              <lb/>
            ut c e ad e a; </s>
            <s xml:space="preserve">erit componendo, conuertendôq; </s>
            <s xml:space="preserve">bm ad lm, ut e a ad
              <lb/>
            a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut lm ad m d, ita c d ad d e. </s>
            <s xml:space="preserve">proportio autem b m ad m d
              <lb/>
            compoſita eſt ex proportione, quam habet b m ad l m, & </s>
            <s xml:space="preserve">ex propor
              <lb/>
            tione, quam l m habet ad m d. </s>
            <s xml:space="preserve">ergo proportio b m ad m d etiam com
              <lb/>
            poſita erit ex proportione, quam habet e a, ad a c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex ea, quam
              <lb/>
            c d habet ad d e. </s>
            <s xml:space="preserve">Eadem ratione demonſtrabitur o f ad f t; </s>
            <s xml:space="preserve">itêmq; </s>
            <s xml:space="preserve">
              <lb/>
            x y ad y r proportionem habere ex eiſdem proportionibus compo-
              <lb/>
            ſitam: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita in aijs. </s>
            <s xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">Ex quibus apparet lineas ſic ductas, quæ inter ſectio
              <lb/>
            nes a b c, d r c interiiciuntur à ſectione e f c in eandem
              <lb/>
            proportionem diuidi.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>