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

Table of figures

< >
[Figure 151]
Page: 243
[Figure 152]
Page: 245
[Figure 153]
Page: 246
[Figure 154]
Page: 247
[Figure 155]
Page: 250
[Figure 156]
Page: 250
[Figure 157]
Page: 252
[Figure 158]
Page: 253
[Figure 159]
Page: 255
[Figure 160]
Page: 258
[Figure 161]
Page: 260
[Figure 162]
Page: 262
[Figure 163]
Page: 264
[Figure 164]
Page: 266
[Figure 165]
Page: 268
[Figure 166]
Page: 270
[Figure 167]
Page: 271
[Figure 168]
Page: 271
[Figure 169]
Page: 272
[Figure 170]
Page: 274
[Figure 171]
Page: 275
[Figure 172]
Page: 280
[Figure 173]
Page: 281
[Figure 174]
Page: 282
[Figure 175]
Page: 283
[Figure 176]
Page: 283
[Figure 177]
Page: 284
[Figure 178]
Page: 284
[Figure 179]
Page: 285
[Figure 180]
Page: 288
< >
page |< < (238) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div579" type="section" level="1" n="342">
          <p>
            <s xml:id="echoid-s5850" xml:space="preserve">
              <pb o="238" file="0258" n="258" rhead="GEOMETRIÆ"/>
            parallelogrammo, AG, altitudine, FI, ad cylindricum ſub baſi por-
              <lb/>
            tione, TCFEY, altitudine, IM, vna cum, {1/6}, cubi, TY. </s>
            <s xml:id="echoid-s5851" xml:space="preserve">In elli-
              <lb/>
            pſi verò, vt parallelepipedum ſub baſi parallelogrammo, AG, alti-
              <lb/>
            tudine, FI, ad cylindricum ſub baſi portione, TCFEY, altitudi-
              <lb/>
            ne, MI, vna cum ea parte cubi, TY, ad quam eiuſdem cubi ſexta
              <lb/>
            pars ſit, vt quadratum, CE, primę diametri, ad quadratum ſecun-
              <lb/>
            dæ .</s>
            <s xml:id="echoid-s5852" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5853" xml:space="preserve">ad quadratum, FH, vel, ſi diametri non ſint axes, vna cum
              <lb/>
            ea parte parallelepipedi ſub, TY, & </s>
            <s xml:id="echoid-s5854" xml:space="preserve">rhombo, RZ, ad quam illius
              <lb/>
            pars ſexta ſit, vt quadratum, CE, primæ diametri ad quadratum
              <lb/>
            ſecundæ. </s>
            <s xml:id="echoid-s5855" xml:space="preserve">Ducantur per, T, Y, ipſi, PQ, parallelæ, Τ Δ, Υ Φ, ſe-
              <lb/>
            cantes curuam, CFE, in punctis, R, V, quæ iungantur recta, R
              <lb/>
            V, producta in, B, K, quoniam ergo, EC, eſt diameter, ad quam
              <lb/>
              <figure xlink:label="fig-0258-01" xlink:href="fig-0258-01a" number="160">
                <image file="0258-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0258-01"/>
              </figure>
            ordinatim applicantur, RT, VY, eas
              <lb/>
            quoq; </s>
            <s xml:id="echoid-s5856" xml:space="preserve">bifariam ſecabit, eſt autem, ST,
              <lb/>
            æqualis, XY, ob parallelogrammum,
              <lb/>
            SY, ergo, VX, erit etiam æqualis ipſi,
              <lb/>
            RS, & </s>
            <s xml:id="echoid-s5857" xml:space="preserve">tota, VY, toti, RT, cui etiam
              <lb/>
            eſt parallela, ergo, RV, TY, ſunt etiam
              <lb/>
            æquales, & </s>
            <s xml:id="echoid-s5858" xml:space="preserve">parallelæ, eſtque, RV, in,
              <lb/>
            M, bifariam ſecta.</s>
            <s xml:id="echoid-s5859" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5860" xml:space="preserve">Diuidamus igitur omnia quadrata fi-
              <lb/>
            guræ, LCFEG, demptis omnibus
              <lb/>
            quadratis trilineorum, CLT, EGY, in
              <lb/>
            omnia quadrata figuræ, LCRT, dem-
              <lb/>
            ptis omnibus quadratis trilinei, LCT,
              <lb/>
            in omnia quadrata figuræ, GEVY,
              <lb/>
            demptis omnibus quadratis trilinei, E
              <lb/>
            GY, & </s>
            <s xml:id="echoid-s5861" xml:space="preserve">in omnia quadrata figuræ, TR
              <lb/>
            FVY. </s>
            <s xml:id="echoid-s5862" xml:space="preserve">Rurſus per rectam, RV, diui-
              <lb/>
              <note position="left" xlink:label="note-0258-01" xlink:href="note-0258-01a" xml:space="preserve">Per D. 23.
                <lb/>
              lib. 2.</note>
            duntur omnia quadrata figuræ, TRF
              <lb/>
            VY, in omnia quadrata, YR, in om-
              <lb/>
            nia quadrata portionis, RFV, & </s>
            <s xml:id="echoid-s5863" xml:space="preserve">in re-
              <lb/>
            ctangula bis ſub, YR, & </s>
            <s xml:id="echoid-s5864" xml:space="preserve">portione, R
              <lb/>
            FV, his ſeparatis, ad eorum ſingula comparemus nunc omnia qua-
              <lb/>
            drata parallelogrammi, KG.</s>
            <s xml:id="echoid-s5865" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5866" xml:space="preserve">Igitur omnia quadrata, KG, ad omnia quadrata, RY, ſunt vt,
              <lb/>
              <note position="left" xlink:label="note-0258-02" xlink:href="note-0258-02a" xml:space="preserve">@o. Lib. 2.</note>
            KB, ad, RV, vel vt parallelogrammum, KG, ad parallelogram-
              <lb/>
            mum, RY; </s>
            <s xml:id="echoid-s5867" xml:space="preserve">omnia inſuper quadrata, KG, ad omnia quadrata, K
              <lb/>
            T, ſunt vt, BK, ad, KR, .</s>
            <s xml:id="echoid-s5868" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5869" xml:space="preserve">vt, KG, ad, KT; </s>
            <s xml:id="echoid-s5870" xml:space="preserve">item omnia qua-
              <lb/>
            drata, KT, ad omnia quadrata figuræ, LCRT, demptis omnibus
              <lb/>
            quadratis trilinei, LCT, .</s>
            <s xml:id="echoid-s5871" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5872" xml:space="preserve">ad omnia quadrata portionis, RCT,
              <lb/>
            cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s5873" xml:space="preserve">ſub trilineo, CLT, ſunt vt, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum