Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
161 25
162
163 26
164
165 27
166
167 28
168
169 29
170
171 30
172
173 31
174
175 32
176
177 33
178
179 34
180
< >
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>