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

Page concordance

< >
Scan Original
221 201
222 202
223 203
224 204
225 205
226 206
227 207
228 208
229 209
230 210
231 211
232 212
233 213
234 214
235 215
236 216
237 217
238 218
239 219
240 220
241 221
242 222
243 223
244 224
245 225
246 226
247 227
248 228
249 229
250 230
< >
page |< < (237) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div577" type="section" level="1" n="341">
          <pb o="237" file="0257" n="257" rhead="LIBER III."/>
        </div>
        <div xml:id="echoid-div579" type="section" level="1" n="342">
          <head xml:id="echoid-head359" xml:space="preserve">THEOREMA XXI. PROPOS. XXII.</head>
          <p>
            <s xml:id="echoid-s5840" xml:space="preserve">SI intra parallelogrammum, quod circulo, vel ellipſi ſit
              <lb/>
            circumſcriptum, ducatur lateribus eiuſdem parallela
              <lb/>
            quædam rectalinea, per circuli, vel ellipſis centrum non
              <lb/>
            tranſiens, altero reliquorum laterum regula exiſtente. </s>
            <s xml:id="echoid-s5841" xml:space="preserve">Om-
              <lb/>
            nia quadrata parallelogrammi, quod maiori portioni circu-
              <lb/>
            li, vel ellipſis iam dicti, remanent circumſcriptum, ad om-
              <lb/>
            nia quadrata figuræ compoſitæ ex maiori portione, & </s>
            <s xml:id="echoid-s5842" xml:space="preserve">duo-
              <lb/>
            bus trilineis, quiad baſim eiuſdem hinc inde extra conſtitu-
              <lb/>
            untur, demptis eorundem trilineorum omnibus quadratis,
              <lb/>
            erunt in circulo, vt parallelepipedum ſub baſi parallelo-
              <lb/>
            grammo dictæ portioni maiori circumſcripto, altitudine
              <lb/>
            eiuſdem portionis diametro ad cylindricum ſub baſi eadem
              <lb/>
            maiori portione, altitudine differentia diametrorum maio-
              <lb/>
            ris, acminoris factarum portionum, vna cum ſexta parte cu-
              <lb/>
            bi baſis eiuſdem portionis In ellipſi verò erunt, vt paralle-
              <lb/>
            lepipedum ſub baſi parallelogrammo maiori portioni ſimili-
              <lb/>
            ter circumſcripto, altitudine eiuſdem portionis diametro,
              <lb/>
            ad cylindricum ſub baſi eadem maiori portione, altitudine
              <lb/>
            differentia diametrorum maioris, ac minoris factarum por-
              <lb/>
            tionum, vna cum ea porte cubi baſis eiuſdem portionis, ad
              <lb/>
            quam ſexta pars eiuſdem cubi ſit, vt quadratum primæ dia-
              <lb/>
            metriad quadratum ſecundæ, vel, ſi diametrinon ſint axes,
              <lb/>
            vna cum ea parte parallelepipedi ſub altitudine baſi eiu-
              <lb/>
            ſdem portionis, ac ſub baſi rhombo ab eadem deſcripto, ad
              <lb/>
            quam eiuſdem parallelepipedi pars ſexta ſit, vt quadratum
              <lb/>
            primę diametri ad quadratum ſecundæ.</s>
            <s xml:id="echoid-s5843" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5844" xml:space="preserve">Sit ergo circulus, vel ellipſis, CFEH, cui ſit circumſcriptum pa-
              <lb/>
            rallelogrammum, AQ, & </s>
            <s xml:id="echoid-s5845" xml:space="preserve">centrum ſit, N, diametriautem tranſeun-
              <lb/>
            tesper puncta contactuum laterum circumſcripti parallelogrammi,
              <lb/>
            & </s>
            <s xml:id="echoid-s5846" xml:space="preserve">per centrum, N. </s>
            <s xml:id="echoid-s5847" xml:space="preserve">ſint, CE, FH; </s>
            <s xml:id="echoid-s5848" xml:space="preserve">ſit autem, FH, regula, cui in-
              <lb/>
            ſiſtens, & </s>
            <s xml:id="echoid-s5849" xml:space="preserve">lateribus, AP, DQ, parallela intra ipſum ducta ſit, LG.
              <lb/>
            </s>
            <s xml:id="echoid-s5850" xml:space="preserve">Dico ergo omnia quadrata parallelogrammi, AG, ad omnia qua-
              <lb/>
            drata figuræ, LCFEG, demptis omnibus quadratis trilineorum,
              <lb/>
            CLI, YGE, eſſe, in circulo, vt parallelepipedum ſub </s>
          </p>
        </div>
      </text>
    </echo>
Impressum