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-div258" type="section" level="1" n="88">
          <p>
            <s xml:id="echoid-s4303" xml:space="preserve">
              <pb file="0172" n="172" rhead="FED. COMMANDINI"/>
            Dico eas proportion ales eſſe in proportione, quæ eſt la-
              <lb/>
            teris a b adlatus d e, itaut earum maior ſit a b c e, me-
              <lb/>
            dia a d c e, & </s>
            <s xml:id="echoid-s4304" xml:space="preserve">minor d e f c. </s>
            <s xml:id="echoid-s4305" xml:space="preserve">Quoniam enim lineæ d e,
              <lb/>
            a b æquidiſtant; </s>
            <s xml:id="echoid-s4306" xml:space="preserve">& </s>
            <s xml:id="echoid-s4307" xml:space="preserve">interipſas ſunt triangula a b e, a d e;
              <lb/>
            </s>
            <s xml:id="echoid-s4308" xml:space="preserve">erit triangulum a b e
              <lb/>
              <figure xlink:label="fig-0172-01" xlink:href="fig-0172-01a" number="126">
                <image file="0172-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0172-01"/>
              </figure>
              <note position="left" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">1. ſextí.</note>
            ad triangulum a d e,
              <lb/>
            ut linea a b ad lineam
              <lb/>
            d e. </s>
            <s xml:id="echoid-s4309" xml:space="preserve">ut autem triangu
              <lb/>
            lum a b e ad triangu-
              <lb/>
            lum a d e, ita pyramis
              <lb/>
              <note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">5. duodeci
                <lb/>
              mi.</note>
            a b e c ad pyramidem
              <lb/>
            a d e c: </s>
            <s xml:id="echoid-s4310" xml:space="preserve">habent enim
              <lb/>
            altitudinem eandem,
              <lb/>
            quæ eſt à puncto c ad
              <lb/>
            planum, in quo qua-
              <lb/>
            drilaterum a b e d. </s>
            <s xml:id="echoid-s4311" xml:space="preserve">er-
              <lb/>
              <note position="left" xlink:label="note-0172-03" xlink:href="note-0172-03a" xml:space="preserve">11. quinti.</note>
            go ut a b ad d e, ita pyramis a b e c ad pyramidem a d e c.
              <lb/>
            </s>
            <s xml:id="echoid-s4312" xml:space="preserve">Rurſus quoniam æquidiſtantes ſunt a c, d f; </s>
            <s xml:id="echoid-s4313" xml:space="preserve">erit eadem
              <lb/>
            ratione pyramis a d c e ad pyramidem c d f e, ut a c ad
              <lb/>
              <note position="left" xlink:label="note-0172-04" xlink:href="note-0172-04a" xml:space="preserve">4 ſexti.</note>
            d f. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">Sed ut a c a l d f, ita a b ad d e, quoniam triangula
              <lb/>
            a b c, d e f ſimilia ſunt, ex nona huius. </s>
            <s xml:id="echoid-s4315" xml:space="preserve">quare ut pyramis
              <lb/>
            a b c e ad pyramidem a d c e, ita pyramis a d c e ad ipſam
              <lb/>
            d e f c. </s>
            <s xml:id="echoid-s4316" xml:space="preserve">fruſtum igitur a b c d e f diuiditur in tres pyramides
              <lb/>
            proportionales in ea proportione, quæ eſt lateris a b ad d e
              <lb/>
            latus, & </s>
            <s xml:id="echoid-s4317" xml:space="preserve">earum maior eſt c a b e, media a d c e, & </s>
            <s xml:id="echoid-s4318" xml:space="preserve">minor
              <lb/>
            d e f c. </s>
            <s xml:id="echoid-s4319" xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s4320" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div260" type="section" level="1" n="89">
          <head xml:id="echoid-head96" xml:space="preserve">PROBLEMA V. PROPOSITIO XXIIII.</head>
          <p>
            <s xml:id="echoid-s4321" xml:space="preserve">
              <emph style="sc">Qvodlibet</emph>
            fruſtum pyramidis, uel coni,
              <lb/>
            uel coni portionis, plano baſi æquidiſtanti ita ſe-
              <lb/>
            care, ut ſectio ſit proportionalis inter maiorem,
              <lb/>
            & </s>
            <s xml:id="echoid-s4322" xml:space="preserve">minorem baſim.</s>
            <s xml:id="echoid-s4323" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>