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-div260" type="section" level="1" n="89">
          <p>
            <s xml:id="echoid-s4353" xml:space="preserve">
              <pb file="0174" n="174" rhead="FED. COMMANDINI"/>
            per f planum baſibus æquidiſtans ducatur, ut ſit ſectio cir
              <lb/>
            culus, uel ellipſis circa diametrum f g. </s>
            <s xml:id="echoid-s4354" xml:space="preserve">Dico ſectionem a b
              <lb/>
            ad ſectionem f g eandem proportionem habere, quam f g
              <lb/>
            ad ipſam c d. </s>
            <s xml:id="echoid-s4355" xml:space="preserve">Simili enim ratione, qua ſupra, demonſtrabi-
              <lb/>
            tur quadratum a b ad quadratum f g ita eſſe, ut quadratũ
              <lb/>
            f g ad c d quadratum. </s>
            <s xml:id="echoid-s4356" xml:space="preserve">Sed circuli inter ſe eandem propor-
              <lb/>
              <note position="left" xlink:label="note-0174-01" xlink:href="note-0174-01a" xml:space="preserve">2. duode
                <lb/>
              cimi</note>
            tionem habent, quam diametrorum quadrata. </s>
            <s xml:id="echoid-s4357" xml:space="preserve">ellipſes au-
              <lb/>
            tem circa a b, f g, c d, quæ ſimiles ſunt, ut oſten dimus in cõ-
              <lb/>
            mentariis in principium libri Archimedis de conoidibus,
              <lb/>
            & </s>
            <s xml:id="echoid-s4358" xml:space="preserve">ſphæroidibus, eam habẽt proportionem, quam quadrar
              <lb/>
            ta diametrorum, quæ eiuſdem rationis ſunt, ex corollaio-
              <lb/>
            ſeptimæ propoſitionis eiuſdem li-
              <lb/>
              <figure xlink:label="fig-0174-01" xlink:href="fig-0174-01a" number="128">
                <image file="0174-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0174-01"/>
              </figure>
            bri. </s>
            <s xml:id="echoid-s4359" xml:space="preserve">ellipſes enim nunc appello ip-
              <lb/>
            ſa ſpacia ellipſibus contenta. </s>
            <s xml:id="echoid-s4360" xml:space="preserve">ergo
              <lb/>
            circulus, uel ellipſis a b ad circulũ,
              <lb/>
            uel ellipſim f g eam proportionem
              <lb/>
            habet, quam circulus, uel ellipſis
              <lb/>
            f g ad circulum uel ellipſim c d.
              <lb/>
            </s>
            <s xml:id="echoid-s4361" xml:space="preserve">quod quidem facienduni propo-
              <lb/>
            ſuimus.</s>
            <s xml:id="echoid-s4362" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div263" type="section" level="1" n="90">
          <head xml:id="echoid-head97" xml:space="preserve">THEOREMA XX. PROPOSITIO XXV.</head>
          <p>
            <s xml:id="echoid-s4363" xml:space="preserve">
              <emph style="sc">Qvodlibet</emph>
            fruſtum pyramidis, uel coni,
              <lb/>
            uel coni portionis ad pyramidem, uel conum, uel
              <lb/>
            coni portionem, cuius baſis eadem eſt, & </s>
            <s xml:id="echoid-s4364" xml:space="preserve">æqualis
              <lb/>
            altitudo, eandem proportionẽ habet, quam utræ
              <lb/>
            que baſes, maior, & </s>
            <s xml:id="echoid-s4365" xml:space="preserve">minor ſimul ſumptæ vnà cũ
              <lb/>
            ea, quæ inter ipſas ſit proportionalis, ad baſim ma
              <lb/>
            iorem.</s>
            <s xml:id="echoid-s4366" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>