Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

Page concordance

< >
Scan Original
201 181
202 182
203 183
204 184
205 185
206 186
207 187
208 188
209 189
210 190
211 191
212 192
213 193
214 194
215 195
216
217 197
218 198
219 199
220 200
221 201
222 202
223 203
224 204
225 205
226 206
227 207
228 208
229 209
230 210
< >
page |< < (277) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div668" type="section" level="1" n="391">
          <p>
            <s xml:id="echoid-s6826" xml:space="preserve">
              <pb o="277" file="0297" n="297" rhead="LIBER III."/>
            ponatur hic vtraq; </s>
            <s xml:id="echoid-s6827" xml:space="preserve">portio, quæ reuoluantur ſemel circa, FM, & </s>
            <s xml:id="echoid-s6828" xml:space="preserve">ſe-
              <lb/>
            mel circa, RV, pateb tergo, quam rationem habeat, Malum citrium
              <lb/>
            ad ſegmentum ſphæræ genitum ab eadem portione circuli, & </s>
            <s xml:id="echoid-s6829" xml:space="preserve">quam
              <lb/>
            habeat Oliua ad ſegmentum ſphęroidis genitum ex eadem portione.</s>
            <s xml:id="echoid-s6830" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div670" type="section" level="1" n="392">
          <head xml:id="echoid-head409" xml:space="preserve">COROLLARIVM XXIV.</head>
          <p>
            <s xml:id="echoid-s6831" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s6832" xml:space="preserve">27. </s>
            <s xml:id="echoid-s6833" xml:space="preserve">aſſumitur iterum fig. </s>
            <s xml:id="echoid-s6834" xml:space="preserve">Theor. </s>
            <s xml:id="echoid-s6835" xml:space="preserve">21. </s>
            <s xml:id="echoid-s6836" xml:space="preserve">tum circuli, tum el-
              <lb/>
            lipſis, & </s>
            <s xml:id="echoid-s6837" xml:space="preserve">nunc, jſdem figuris hicappoſitis, colligimus ſolidum ſi-
              <lb/>
            milare genitum ex portione, TCFEY, tuxta regulam, FI, ad ſolidum
              <lb/>
            fibi ſimilare genitum ex eadem portione, iuxta regulam, TY, eſſe, in
              <lb/>
            fig. </s>
            <s xml:id="echoid-s6838" xml:space="preserve">circul, vt cylindr cum ſub, IM, & </s>
            <s xml:id="echoid-s6839" xml:space="preserve">portione, TCFEY, vna cum, {1/6},
              <lb/>
            cubi, TY, ad parallelepipedum ſub altitudine, FI, baſiverò rectangulo
              <lb/>
            ſub, FI, & </s>
            <s xml:id="echoid-s6840" xml:space="preserve">ſub ſexquitertia duarum, IH, HN. </s>
            <s xml:id="echoid-s6841" xml:space="preserve">In ellipſis verò fig. </s>
            <s xml:id="echoid-s6842" xml:space="preserve">habe-
              <lb/>
            re rationem cõpoſitam ex ea, quam habet cylindricus ſub, IM, & </s>
            <s xml:id="echoid-s6843" xml:space="preserve">por-
              <lb/>
              <figure xlink:label="fig-0297-01" xlink:href="fig-0297-01a" number="192">
                <image file="0297-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0297-01"/>
              </figure>
            tione, TCFEY, vna cum ea
              <lb/>
            parte cubi, TY, vel parallelep-
              <lb/>
            pedi, ſub, RV, & </s>
            <s xml:id="echoid-s6844" xml:space="preserve">rhombo, RZ,
              <lb/>
            ad quam eiuſdem cubi, vel pa-
              <lb/>
            rallelepipedi ſexta pars ſit, vt
              <lb/>
            quadratũ, CE, ad quadratum,
              <lb/>
            FH, ad parallelepipedum ſub
              <lb/>
            altitudine, CE, baſi parallelo-
              <lb/>
            grammo, AG, in fig. </s>
            <s xml:id="echoid-s6845" xml:space="preserve">Th. </s>
            <s xml:id="echoid-s6846" xml:space="preserve">6. </s>
            <s xml:id="echoid-s6847" xml:space="preserve">& </s>
            <s xml:id="echoid-s6848" xml:space="preserve">
              <lb/>
            ex ea, quã habet quadratum, F
              <lb/>
            H, ad rectangulum ſub, FI, & </s>
            <s xml:id="echoid-s6849" xml:space="preserve">
              <lb/>
            ſub ſexquitertia duarum, IH,
              <lb/>
            HN. </s>
            <s xml:id="echoid-s6850" xml:space="preserve">Pro noſtro igitur exem-
              <lb/>
            plo reuoluantur portiones, T
              <lb/>
            CFEY, ſemel circa axes ma-
              <lb/>
            nentes, TY, & </s>
            <s xml:id="echoid-s6851" xml:space="preserve">ſemel circa axes
              <lb/>
            manentes, FI; </s>
            <s xml:id="echoid-s6852" xml:space="preserve">ex reuolutione
              <lb/>
            igitur facta à portione circuli
              <lb/>
            circa, TY, fit, Malum Roſeum,
              <lb/>
            ex reuolutione verò eiuſdẽ cir-
              <lb/>
            ca, FI, fit maius ſegmentum
              <lb/>
            ſphæræ: </s>
            <s xml:id="echoid-s6853" xml:space="preserve">Item ex reuolutione
              <lb/>
            facta à portione ellipſi, TCFE
              <lb/>
            Y, fit, malum cotoneum, circa
              <lb/>
            axim, TY, ex reuolutione verò eiuſdem circa, FI, fit maius ſegmentum
              <lb/>
            ſphæroidis: </s>
            <s xml:id="echoid-s6854" xml:space="preserve">Igicur malum roſeum ad ſegmentum maius ſphæræ, & </s>
            <s xml:id="echoid-s6855" xml:space="preserve">
              <lb/>
            malum cotoneum ad ſegmentum maius ſphæroidis iam dictum, ha-
              <lb/>
            bent ſupradictam rationem, vt & </s>
            <s xml:id="echoid-s6856" xml:space="preserve">ſolida ſimilaria, &</s>
            <s xml:id="echoid-s6857" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6858" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum