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 |< < (21) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="34">
          <pb o="21" file="0053" n="53" rhead="DE IIS QVAE VEH. IN AQVA."/>
          <p style="it">
            <s xml:space="preserve">Producatur enim u s ad lineam qm in x: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à puncto x duca
              <lb/>
            tur ad diametrum x y ipſi bd æquidistans. </s>
            <s xml:space="preserve">erit gt minor quàm
              <lb/>
            gy, quoniam u s minor eſt quàm ux: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex primo lemmate yg
              <lb/>
            ad uc erit, ut h g ad n c; </s>
            <s xml:space="preserve">uidelicet ut g b ad c k, quod proxime de
              <lb/>
            monstrauimus: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando yg ad gb, ut uc ad c k. </s>
            <s xml:space="preserve">Sed t g
              <lb/>
            cum ſit ipſa y g minor, habet ad g b proportionem minorem, quàm
              <lb/>
            y g ad eandem. </s>
            <s xml:space="preserve">ergo u c ad c K maiorem proportioné habet, quàm
              <lb/>
            t g ad g b. </s>
            <s xml:space="preserve">quod demonstraſſe oportuit. </s>
            <s xml:space="preserve">Itaque poſitione data g K
              <lb/>
            unum duntaxat erit in ſectione punctum, uidelicet m, à quo ductis
              <lb/>
            duabus lineis m e h, mno, habeat n c ad c K proportionem ean-
              <lb/>
            dem, quam h g ad g b. </s>
            <s xml:space="preserve">nam ſi ab alijs omnibus ducantur, ſemper
              <lb/>
            ea, quæ inter a c, & </s>
            <s xml:space="preserve">lineam ipſi æquidistantem interijcitur, ad c K
              <lb/>
            proportionem maiorem habebit, quàm quæ inter g K atque ei æqui
              <lb/>
            diſtantem, ad ipſam g b. </s>
            <s xml:space="preserve">Conſtat igitur id, quod ab Archimede di-
              <lb/>
            ctum est; </s>
            <s xml:space="preserve">nempe lineam pi ad p h uel eandem, quam n ω ad ω o,
              <lb/>
            uel maiorem habere proportionem.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Quare p h ipſius h i aut dupla eſt, aut minor quàm du
              <lb/>
              <anchor type="note" xlink:label="note-0053-01a" xlink:href="note-0053-01"/>
            pla.</s>
            <s xml:space="preserve">] _Si quidé_
              <lb/>
              <anchor type="figure" xlink:label="fig-0053-01a" xlink:href="fig-0053-01"/>
            _minor, quàm du-_
              <lb/>
            _pla, ſit pt dupl. </s>
            <s xml:space="preserve">2_
              <lb/>
            _ti. </s>
            <s xml:space="preserve">erit centrum_
              <lb/>
            _grauitatis eius,_
              <lb/>
            _quod in humido_
              <lb/>
            _est, punctumt. </s>
            <s xml:space="preserve">ſi_
              <lb/>
            _uero p h ſit ip-_
              <lb/>
            _ſius h i dupla,_
              <lb/>
            _erit h grauitatis_
              <lb/>
            _centrum: </s>
            <s xml:space="preserve">ductâq;_
              <lb/>
            </s>
            <s xml:space="preserve">_h f, & </s>
            <s xml:space="preserve">producta_
              <lb/>
            _ad centrum eius,_
              <lb/>
            _quod est extra humidum, uidelicct ad g, alia ſimiliter demonstra-_
              <lb/>
            _buntur. </s>
            <s xml:space="preserve">atque idem intelligendum est in propoſitione, quæ ſe_-
              <lb/>
            _quitur._</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <note position="right" xlink:label="note-0053-01" xlink:href="note-0053-01a" xml:space="preserve">D</note>
            <figure xlink:label="fig-0053-01" xlink:href="fig-0053-01a">
              <image file="0053-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0053-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Reuoluetur ergo ſolidum a p o l, & </s>
            <s xml:space="preserve">baſis ipſius nullo
              <lb/>
              <anchor type="note" xlink:label="note-0053-02a" xlink:href="note-0053-02"/>
            </s>
          </p>
        </div>
      </text>
    </echo>