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 |< < (217) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div539" type="section" level="1" n="323">
          <pb o="217" file="0237" n="237" rhead="LIBER III."/>
        </div>
        <div xml:id="echoid-div541" type="section" level="1" n="324">
          <head xml:id="echoid-head341" xml:space="preserve">THEOREMA XII. PROPOS. XIII.</head>
          <p>
            <s xml:id="echoid-s5276" xml:space="preserve">SI circulum, vel ellipſim duæ rectæ lineæ in terminis
              <lb/>
            coniugatarum diametrorum tetigetint inter ſe conue-
              <lb/>
            nientes, eiſdem diametris ductis. </s>
            <s xml:id="echoid-s5277" xml:space="preserve">Omnia quadrata conſti-
              <lb/>
            tuti parallelogrammiad omnia quadrata trilinei à dictis tan-
              <lb/>
            gentibus, & </s>
            <s xml:id="echoid-s5278" xml:space="preserve">ab incluſa curua comprehenſi, regula altera
              <lb/>
            diametrorum, erunt vt dictum parallelogrammum ad ſui
              <lb/>
            reliquum, dempto quadrante circuli, vel ellipſis iam dictæ,
              <lb/>
            quod inſcribitur prædicto parallelogrammo, ſimul cum ex-
              <lb/>
            ceſſu dicti quadrantis ſuper duas tertias iam dicti parallelo-
              <lb/>
            grammi, quæ ratio erit proximè, vt 21. </s>
            <s xml:id="echoid-s5279" xml:space="preserve">ad 2.</s>
            <s xml:id="echoid-s5280" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5281" xml:space="preserve">Sit circulus, vel ellipſis, ABCD, cuius diametri coniugatæ, A
              <lb/>
            C, BD, in quorum terminis, C, D, duæ rectæ lineę ipſum tangen-
              <lb/>
            tesinter ſe conueniant in, V. </s>
            <s xml:id="echoid-s5282" xml:space="preserve">Dico ergo (ſumpta regula qualibet
              <lb/>
            diametrorum, vt, BD,) quod omnia quadrata parallelogrammi, O
              <lb/>
            V, ad omnia quadrata trilinei, DCV, duabus tangentibus, DV,
              <lb/>
            VC, & </s>
            <s xml:id="echoid-s5283" xml:space="preserve">ab ijs incluſa curua, DC, comprehenſi ſunt, vt idem paral-
              <lb/>
              <figure xlink:label="fig-0237-01" xlink:href="fig-0237-01a" number="148">
                <image file="0237-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0237-01"/>
              </figure>
            lelogrammum, OV, ad ſui reliquum
              <lb/>
            dempto quadrante, OCD, circuli,
              <lb/>
            vel ellipſis, ABCD, ſimul cum eo
              <lb/>
            ſpatio, quo idem quadrans excedit
              <lb/>
            duas tertias parallelogrammi, OV.
              <lb/>
            </s>
            <s xml:id="echoid-s5284" xml:space="preserve">Sumatur intra, OC, vtcunque pun
              <lb/>
            ctum, E, & </s>
            <s xml:id="echoid-s5285" xml:space="preserve">per, E, ducatur ipſi, B
              <lb/>
            D, parallela, EF, ſecans curuam, D
              <lb/>
            C, in, I. </s>
            <s xml:id="echoid-s5286" xml:space="preserve">Omnia ergo quadrata pa-
              <lb/>
            rallelogrammi, OV, ad rectangula
              <lb/>
            ſub parallelogrammo, OV, & </s>
            <s xml:id="echoid-s5287" xml:space="preserve">ſemi-
              <lb/>
            portione, OCD, ſunt vt parallelo
              <lb/>
              <note position="right" xlink:label="note-0237-01" xlink:href="note-0237-01a" xml:space="preserve">Coroll.1.
                <lb/>
              26.lib.2.</note>
            grammum, OV, ad eandem ſemiportionem, OCD; </s>
            <s xml:id="echoid-s5288" xml:space="preserve">ſed eadem ad
              <lb/>
              <note position="right" xlink:label="note-0237-02" xlink:href="note-0237-02a" xml:space="preserve">Coroll.1.
                <lb/>
              huius.</note>
            omnia quadrata ſemiportionis, OCD, ſunt ſexquialtera, ergo ad
              <lb/>
            reſiduum erunt vt parallelogrammum, OV, ad reſiduum ſemipor-
              <lb/>
            tionis, OCD, demptis ab ea, {2/3}, parallelogrammi, OV, quarum
              <lb/>
            idem parallelogrammum, OV, eſt ſexquialterum; </s>
            <s xml:id="echoid-s5289" xml:space="preserve">reſiduum autem
              <lb/>
            rectangulorum ſub parallelogrammo, OV, & </s>
            <s xml:id="echoid-s5290" xml:space="preserve">ſemiportione, OC
              <lb/>
            D, demptis omnibus quadratis ſemiportionis, OCD, ſunt rectan-
              <lb/>
              <note position="right" xlink:label="note-0237-03" xlink:href="note-0237-03a" xml:space="preserve">Vide ibid.
                <lb/>
              dicta.</note>
            gula ſub ſemiportione, OCD, & </s>
            <s xml:id="echoid-s5291" xml:space="preserve">trilineo, CDV, nam veluti </s>
          </p>
        </div>
      </text>
    </echo>
Impressum