Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
171 30
172
173 31
174
175 32
176
177 33
178
179 34
180
181 35
182
183 36
184
185 37
186
187 38
188
189 39
190
191 40
192
193 41
194
195 42
196
197 43
198
199 44
200
< >
page |< < of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div263" type="section" level="1" n="90">
          <p>
            <s xml:id="echoid-s4485" xml:space="preserve">
              <pb file="0180" n="180" rhead="FED. COMMANDINI"/>
            fruſtum a d. </s>
            <s xml:id="echoid-s4486" xml:space="preserve">Sed pyramis q æqualis eſt fruſto à pyramide
              <lb/>
            abſciſſo, ut dem onſtrauimus. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s4488" xml:space="preserve">conus, uel coni por-
              <lb/>
            tio q, cuius baſis ex tribus circulis, uel ellipſibus a b, e f, c d
              <lb/>
            conſtat, & </s>
            <s xml:id="echoid-s4489" xml:space="preserve">altitudo eadem, quæ fruſti: </s>
            <s xml:id="echoid-s4490" xml:space="preserve">ipſi fruſto a d eſt æ-
              <lb/>
            qualis. </s>
            <s xml:id="echoid-s4491" xml:space="preserve">atque illud eſt, quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s4492" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div268" type="section" level="1" n="91">
          <head xml:id="echoid-head98" xml:space="preserve">THEOREMA XXI. PROPOSITIO XXVI.</head>
          <p>
            <s xml:id="echoid-s4493" xml:space="preserve">
              <emph style="sc">Cvivslibet</emph>
            fruſti à pyramide, uel cono,
              <lb/>
            uel coni portione abſcisſi, centrum grauitatis eſt
              <lb/>
            in axe, ita ut eo primum in duas portiones diui-
              <lb/>
            ſo, portio ſuperior, quæ minorem baſim attingit
              <lb/>
            ad portionem reliquam eam habeat proportio-
              <lb/>
            nem, quam duplum lateris, uel diametri maioris
              <lb/>
            baſis, vnà cum latere, uel diametro minoris, ipſi
              <lb/>
            reſpondente, habet ad duplum lateris, uel diame-
              <lb/>
            tri minoris baſis vnà cũ latere, uel diametro ma-
              <lb/>
            ioris: </s>
            <s xml:id="echoid-s4494" xml:space="preserve">deinde à puncto diuiſionis quarta parte ſu
              <lb/>
            perioris portionis in ipſa ſumpta: </s>
            <s xml:id="echoid-s4495" xml:space="preserve">& </s>
            <s xml:id="echoid-s4496" xml:space="preserve">rurſus ab in-
              <lb/>
            ferioris portionis termino, qui eſt ad baſim maio
              <lb/>
            rem, ſumpta quarta parte totius axis: </s>
            <s xml:id="echoid-s4497" xml:space="preserve">centrum ſit
              <lb/>
            in linea, quæ his finibus continetur, atque in eo li
              <lb/>
            neæ puncto, quo ſic diuiditur, ut tota linea ad par
              <lb/>
            tem propinquiorem minori baſi, eãdem propor-
              <lb/>
            tionem habeat, quam fruſtum ad pyramidẽ, uel
              <lb/>
            conum, uel coni portionem, cuius baſis ſit ea-
              <lb/>
            dem, quæ baſis maior, & </s>
            <s xml:id="echoid-s4498" xml:space="preserve">altitudo fruſti altitudini
              <lb/>
            æqualis.</s>
            <s xml:id="echoid-s4499" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>