Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of handwritten notes

< >
< >
page |< < (34) 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-s4455" xml:space="preserve">
              <pb o="34" file="0179" n="179" rhead="DE CENTRO GRAVIT. SOLID."/>
            culi, uel ellipſes c d, e ſ a b ad circulum, uel ellipſim a b. </s>
            <s xml:id="echoid-s4456" xml:space="preserve">In-
              <lb/>
            telligatur pyramis q baſim habens æqualem tribus rectan
              <lb/>
            gulis a b, e f, c d; </s>
            <s xml:id="echoid-s4457" xml:space="preserve">& </s>
            <s xml:id="echoid-s4458" xml:space="preserve">altitudinem eãdem, quam fruſtum a d.
              <lb/>
            </s>
            <s xml:id="echoid-s4459" xml:space="preserve">intelligatur etiam conus, uel coni portio q, eadem altitudi
              <lb/>
            ne, cuius baſis ſit tribus circulis, uel tribus ellipſibus a b,
              <lb/>
            e f, c d æqualis. </s>
            <s xml:id="echoid-s4460" xml:space="preserve">poſtremo intelligatur pyramis a l b, cuius
              <lb/>
            baſis ſit rectangulum m n o p, & </s>
            <s xml:id="echoid-s4461" xml:space="preserve">altitudo eadem, quæ fru-
              <lb/>
            ſti: </s>
            <s xml:id="echoid-s4462" xml:space="preserve">itemq, intelligatur conus, uel coni portio a l b, cuius
              <lb/>
            baſis circulus, uel ellipſis circa diametrum a b, & </s>
            <s xml:id="echoid-s4463" xml:space="preserve">eadem al
              <lb/>
            titudo. </s>
            <s xml:id="echoid-s4464" xml:space="preserve">ut igitur rectangula a b, e f, c d ad rectangulum a b,
              <lb/>
              <note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">6. 11. duo
                <lb/>
              decimi</note>
            ita pyramis q ad pyramidem a l b; </s>
            <s xml:id="echoid-s4465" xml:space="preserve">& </s>
            <s xml:id="echoid-s4466" xml:space="preserve">ut circuli, uel ellip-
              <lb/>
            ſes a b, e f, c d ad a b circulum, uel ellipſim, ita conus, uel co
              <lb/>
            ni portio q ad conum, uel coni portionem a l b. </s>
            <s xml:id="echoid-s4467" xml:space="preserve">conus
              <lb/>
            igitur, uel coni portio q ad conum, uel coni portionem
              <lb/>
            a l b eſt, ut pyramis q ad pyramidem a l b. </s>
            <s xml:id="echoid-s4468" xml:space="preserve">ſed pyramis
              <lb/>
            a l b ad pyramidem a g b eſt, ut altitudo ad altitudinem, ex
              <lb/>
            20. </s>
            <s xml:id="echoid-s4469" xml:space="preserve">huius: </s>
            <s xml:id="echoid-s4470" xml:space="preserve">& </s>
            <s xml:id="echoid-s4471" xml:space="preserve">ita eſt conus, uel coni portio al b ad conum,
              <lb/>
            uel coni portionem a g b ex 14. </s>
            <s xml:id="echoid-s4472" xml:space="preserve">duodecimi elementorum,
              <lb/>
            & </s>
            <s xml:id="echoid-s4473" xml:space="preserve">ex iis, quæ nos demonſtrauimus in commentariis in un-
              <lb/>
            decimam de conoidibus, & </s>
            <s xml:id="echoid-s4474" xml:space="preserve">ſphæroidibus, propoſitione
              <lb/>
            quarta. </s>
            <s xml:id="echoid-s4475" xml:space="preserve">pyramis autem a g b ad pyramidem c g d propor-
              <lb/>
            tionem habet compoſitam ex proportione baſium & </s>
            <s xml:id="echoid-s4476" xml:space="preserve">pro
              <lb/>
            portione altitudinum, ex uigeſima prima huius: </s>
            <s xml:id="echoid-s4477" xml:space="preserve">& </s>
            <s xml:id="echoid-s4478" xml:space="preserve">ſimili-
              <lb/>
            ter conus, uel coni portio a g b a d conum, uel coni portio-
              <lb/>
            nem c g d proportionem habet compoſitã ex eiſdem pro-
              <lb/>
            portionibus, per ea, quæ in dictis commentariis demon-
              <lb/>
            ſtrauimus, propoſitione quinta, & </s>
            <s xml:id="echoid-s4479" xml:space="preserve">ſexta: </s>
            <s xml:id="echoid-s4480" xml:space="preserve">altitudo enim in
              <lb/>
            utriſque eadem eſt, & </s>
            <s xml:id="echoid-s4481" xml:space="preserve">baſes inter ſe ſe eandem habent pro-
              <lb/>
            portionem. </s>
            <s xml:id="echoid-s4482" xml:space="preserve">ergo ut pyramis a g b ad pyramidem c g d, ita
              <lb/>
            eſt conus, uel coni portio a g b ad a g d conum, uel coni
              <lb/>
            portionem: </s>
            <s xml:id="echoid-s4483" xml:space="preserve">& </s>
            <s xml:id="echoid-s4484" xml:space="preserve">per conuerſionẽ rationis, ut pyramis a g b
              <lb/>
            ad fruſtū à pyramide abſciſſum, ita conus uel coni portio
              <lb/>
            a g b ad fruſtum a d. </s>
            <s xml:id="echoid-s4485" xml:space="preserve">ex æquali igitur, ut pyramis q ad fru-
              <lb/>
            ſtum à pyramide abſciſſum, ita conus uel coni portio q </s>
          </p>
        </div>
      </text>
    </echo>
Impressum