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

Page concordance

< >
Scan Original
191 171
192 172
193 173
194 174
195 175
196 176
197 177
198 178
199 179
200 180
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
< >
page |< < (198) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div495" type="section" level="1" n="300">
          <p>
            <s xml:id="echoid-s4861" xml:space="preserve">
              <pb o="198" file="0218" n="218" rhead="GEOMETRIÆ"/>
            ergo intra, EB, vtcumque punctum, C, & </s>
            <s xml:id="echoid-s4862" xml:space="preserve">per, C, ducaturipſi, D
              <lb/>
            P, parallela, CM, ſecans curuam circuli, vel ellipſis, EDRP, in,
              <lb/>
            N; </s>
            <s xml:id="echoid-s4863" xml:space="preserve">Eſt igitur quadratum, BP, vel, MC, ad quadratum, CN, vt
              <lb/>
            rectangulum, RBE, ad rectangulum, RCE; </s>
            <s xml:id="echoid-s4864" xml:space="preserve">eſt autem, EP, pa-
              <lb/>
              <figure xlink:label="fig-0218-01" xlink:href="fig-0218-01a" number="132">
                <image file="0218-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0218-01"/>
              </figure>
            rallelogrammum in eadem baſi, & </s>
            <s xml:id="echoid-s4865" xml:space="preserve">alti-
              <lb/>
            tudine, cum ſemiportione, EBP, regu-
              <lb/>
            la eſt ipſa baſis, &</s>
            <s xml:id="echoid-s4866" xml:space="preserve">, CM, ducta vtcum-
              <lb/>
            que parallela ipſi baſi, repertumque eſt
              <lb/>
            quadratum, CM, ad quadratum, CN,
              <lb/>
            eſſe vt rectangulum, RBE, ad rectan
              <lb/>
            gulum, RCE, ergo magnitudines ho-
              <lb/>
            rum quatuor ordinum erunt proportio-
              <lb/>
            nales.</s>
            <s xml:id="echoid-s4867" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4868" xml:space="preserve">omnia quadrata parallelogram-
              <lb/>
              <note position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">Coroll.3.
                <lb/>
              26.lib. 2.</note>
            mi, EP, magnitudines primi ordinis col-
              <lb/>
            lectæ, iuxta primam, nempè iuxta qua-
              <lb/>
            dratum, CM, ad omnia quadrata ſemi-
              <lb/>
            portionis, EBP, magnitudines ſecundi
              <lb/>
            ordinis collectas, iuxta ſecundam. </s>
            <s xml:id="echoid-s4869" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4870" xml:space="preserve">iux-
              <lb/>
            ta quadratum, CN, erunt vt rectangu-
              <lb/>
            la ſub maximis abſciſſarum, EB, & </s>
            <s xml:id="echoid-s4871" xml:space="preserve">ſub
              <lb/>
            adiunctis, BR, magnitudines tertij or-
              <lb/>
            dinis collectæ, iuxta tertiam .</s>
            <s xml:id="echoid-s4872" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4873" xml:space="preserve">iuxta re-
              <lb/>
            ctangulum, RBE, ad rectangula ſub
              <lb/>
            omnibus abſciſſis, EB, & </s>
            <s xml:id="echoid-s4874" xml:space="preserve">reſiduis earun-
              <lb/>
            dem, adiuncta, BR, (recti, vel obliqui
              <lb/>
            tranſitus ſupradictis exiſtentibus) quæ
              <lb/>
            ſunt magnitudines quarti ordinis colle-
              <lb/>
            ctæ, iuxta quartam.</s>
            <s xml:id="echoid-s4875" xml:space="preserve">ſ.</s>
            <s xml:id="echoid-s4876" xml:space="preserve">iuxta rectangulum,
              <lb/>
            R CE; </s>
            <s xml:id="echoid-s4877" xml:space="preserve">quoniam verò rectangula ſub
              <lb/>
            maximis abſciſſarum, EB, & </s>
            <s xml:id="echoid-s4878" xml:space="preserve">ſub adiun-
              <lb/>
            ctis, BR, ad rectangula ſub omnibus ab-
              <lb/>
            ſciſſis, EB, adiuncta, BR, & </s>
            <s xml:id="echoid-s4879" xml:space="preserve">ſub earum
              <lb/>
            reſiduis, ſunt vt, BR, ad compoſitam ex
              <lb/>
              <note position="left" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">Cor. 30.
                <lb/>
              lib.2.</note>
            dimidia, BR, & </s>
            <s xml:id="echoid-s4880" xml:space="preserve">ſexta parte, EB, ergo conuertendo omnia quadrata
              <lb/>
            ſemiportionis, BEP, ad omnia quadrata parallelogrammi, EP, vel
              <lb/>
              <note position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">8. lib. 2.</note>
            iſtorum quadrupla .</s>
            <s xml:id="echoid-s4881" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s4882" xml:space="preserve">omnia quadrata portionis, DEP, ad omnia
              <lb/>
            quadrata parallelogrammi, FP, erunt vt compoſita ex, {1/6}, BE, &</s>
            <s xml:id="echoid-s4883" xml:space="preserve">,
              <lb/>
            {1/2}, BR, ad eandem, BR; </s>
            <s xml:id="echoid-s4884" xml:space="preserve">Iungantur nunc, DE, EP.</s>
            <s xml:id="echoid-s4885" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4886" xml:space="preserve">Dico vlterius omnia quadrata portionis, EDP, ad omnia qua-
              <lb/>
            drata trianguli, DEP, eſſe vt compoſita ex dimidia totius, ER, & </s>
            <s xml:id="echoid-s4887" xml:space="preserve">
              <lb/>
            ipſa, BR, ad eandem, BR. </s>
            <s xml:id="echoid-s4888" xml:space="preserve">Cum enim oſtenderimus omnia qua-
              <lb/>
            drata parallelogrammi, FP, ad omnia quadrata portionis, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum