Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
131 10
132
133 11
134
135 12
136
137 13
138
139 14
140
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
< >
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