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 |< < (24) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="84">
          <p>
            <s xml:space="preserve">
              <pb o="24" file="0159" n="159" rhead="DE CENTRO GRAVIT. SOLID."/>
            los contineant. </s>
            <s xml:space="preserve">Dico ſolidum a b ad ſolidum a c eãdem ha
              <lb/>
            bere proportionem, quam axis d e ad axem e f. </s>
            <s xml:space="preserve">Sienim
              <lb/>
            axes in eadem recta linea fuerint conſtituti, hæc duo ſoli-
              <lb/>
            da, in unum, atque i @m ſolidum conuenient. </s>
            <s xml:space="preserve">quare ex
              <lb/>
            iis, quæ proxime tradita ſunt, habebit ſolidum a b ad ſo-
              <lb/>
            lidum a c eandem proportionem, quam axis d e ad e f
              <lb/>
            axem. </s>
            <s xml:space="preserve">Siuero axes non ſint in eadem recta linea, demittan
              <lb/>
            tur a punctis d, f perpendiculares ad baſis planum, d g, fh:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur e g, e h. </s>
            <s xml:space="preserve">Quoniam igitur axes cum baſibus
              <lb/>
            æquales angulos eontinent, erit d e g angulus æqualis an-
              <lb/>
            gulo f e h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſunt
              <lb/>
              <anchor type="figure" xlink:label="fig-0159-01a" xlink:href="fig-0159-01"/>
            anguli ad g h re-
              <lb/>
            cti, quare & </s>
            <s xml:space="preserve">re-
              <lb/>
            liquus e d g æqua
              <lb/>
            lis erit reliquo
              <lb/>
            e fh: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangu-
              <lb/>
            lum d e g triãgu-
              <lb/>
            lo f e h ſimile. </s>
            <s xml:space="preserve">er-
              <lb/>
            go g d ad d e eſt,
              <lb/>
            ut h f ad f e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per
              <lb/>
            mutando g d ad
              <lb/>
            h f, ut d e ad e f.
              <lb/>
            </s>
            <s xml:space="preserve">Sed ſolidum a b
              <lb/>
            ad ſolidum a c
              <lb/>
            eandem propor-
              <lb/>
            tionem habet,
              <lb/>
            quam d g altitu-
              <lb/>
            do ad altitudinẽ
              <lb/>
            f h. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">ean-
              <lb/>
            dẽ habebit, quã
              <lb/>
            axis d e a l e f axẽ</s>
          </p>
          <div type="float" level="2" n="3">
            <figure xlink:label="fig-0159-01" xlink:href="fig-0159-01a">
              <image file="0159-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0159-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Poſtremo ſint
              <lb/>
            ſolida parallelepi
              <lb/>
            peda a b, c d in</s>
          </p>
        </div>
      </text>
    </echo>