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

Page concordance

< >
Scan Original
261 241
262 242
263 243
264 244
265 245
266 246
267 247
268 248
269 249
270 250
271 251
272 252
273 253
274 254
275 255
276 256
277 257
278 258
279 259
280 260
281 261
282 262
283 263
284 264
285 265
286 266
287 267
288 268
289 269
290 270
< >
page |< < (245) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div590" type="section" level="1" n="345">
          <p>
            <s xml:id="echoid-s6063" xml:space="preserve">
              <pb o="245" file="0265" n="265" rhead="LIBER III."/>
            culo, tum in ellipſi) eſt vt quadratum, CN, ad quadratum, NF, vel
              <lb/>
            vt quadratum, CE, ad quadratum, FH, ideò ſex rectangula, RMV,
              <lb/>
            ad rectangulum, FMH, erunt vt ſex quadrata, CE, ad vnum qua-
              <lb/>
            dra um, FH, .</s>
            <s xml:id="echoid-s6064" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6065" xml:space="preserve">erunt vt omnia quadrata, RZ, ad rectangula ſub
              <lb/>
            portione, RFV, & </s>
            <s xml:id="echoid-s6066" xml:space="preserve">quadrilineo, RTHY V, vt autem ſunt ſex re-
              <lb/>
            ctangula, RMV, ad rectangulum, FMH, ita quatuor rectangu-
              <lb/>
            la, RMV, ad, {2/3}, rectanguli, FMH, .</s>
            <s xml:id="echoid-s6067" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6068" xml:space="preserve">ad rectangulum ſub, FM,
              <lb/>
            &</s>
            <s xml:id="echoid-s6069" xml:space="preserve">, {2/3}, MH, ergo omnia quadrata, RZ, ad rectangula ſub portio-
              <lb/>
            ne, RFV, & </s>
            <s xml:id="echoid-s6070" xml:space="preserve">quadrilineo, RTHY V, erunt vt quatuor rectangu-
              <lb/>
            la, RMV, ad rectangulum ſub, FM, &</s>
            <s xml:id="echoid-s6071" xml:space="preserve">, {2/3}, MH, erant autem om-
              <lb/>
            nia quadrata, Δ V, ad omnia quadrata, RZ, vt quadratum, FM,
              <lb/>
            ad quatuor rectangula ſub, RMV, ergo ex æquali omnia quadra-
              <lb/>
            ta, Δ V, ad rectangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s6072" xml:space="preserve">quadrilineo, RTH
              <lb/>
            YV, erunt vt quadratum, FM, ad rectangulum ſub, FM, & </s>
            <s xml:id="echoid-s6073" xml:space="preserve">ſub, {2/3}, MH,
              <lb/>
            eadem verò omnia quadrata, Δ V, ad rectangula ſub portione, R
              <lb/>
            F V, & </s>
            <s xml:id="echoid-s6074" xml:space="preserve">ſub, VT, oſtenſa ſunt eſſe, vt quadratum, FM, ad rectan-
              <lb/>
            gulum, ΓΜΙ, (ex quibus habemus rectangulum ſub, ΓΜΙ, mi-
              <lb/>
            nus eſſe rectangulo ſub, FM, & </s>
            <s xml:id="echoid-s6075" xml:space="preserve">ſub, {2/3}, MH, nam rectangula ſub
              <lb/>
            portione, RFV, & </s>
            <s xml:id="echoid-s6076" xml:space="preserve">ſub, VT, minora ſunt rectangulis ſub eadem
              <lb/>
            portione, RFV, & </s>
            <s xml:id="echoid-s6077" xml:space="preserve">quadrilineo, RTHY V,) ergo omnia quadra-
              <lb/>
            ta, Δ V, ad reſiduum omnium rectangulorum ſub portione, RFV,
              <lb/>
            & </s>
            <s xml:id="echoid-s6078" xml:space="preserve">quadrilineo, RTHY V, demptis rectangulis ſub portione, RF
              <lb/>
            V, & </s>
            <s xml:id="echoid-s6079" xml:space="preserve">ſub, VT, .</s>
            <s xml:id="echoid-s6080" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6081" xml:space="preserve">ad rectangula ſub vtriſq; </s>
            <s xml:id="echoid-s6082" xml:space="preserve">portionibus, RFV, THY,
              <lb/>
            .</s>
            <s xml:id="echoid-s6083" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6084" xml:space="preserve">ad omnia quadrata portionis, RFV, erunt vt quadratum, FM,
              <lb/>
            ad reſiduum ſpatium, dempto rectangulo, ΓΜΙ, a rectangulo ſub,
              <lb/>
            F M, & </s>
            <s xml:id="echoid-s6085" xml:space="preserve">ſub, {2/3}, MH, (hoc autem vocetur reſiduum rectangulum
              <lb/>
            huius Theor.) </s>
            <s xml:id="echoid-s6086" xml:space="preserve">quod oſtendere opus erat.</s>
            <s xml:id="echoid-s6087" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div593" type="section" level="1" n="346">
          <head xml:id="echoid-head363" xml:space="preserve">THEOREMA XXV. PROPOS. XXVI.</head>
          <p>
            <s xml:id="echoid-s6088" xml:space="preserve">EXpoſita adhuc figura Theor. </s>
            <s xml:id="echoid-s6089" xml:space="preserve">antecedentis, oſtendemus
              <lb/>
            omnia quadrata portionis, RFV, regula, FM, ad om-
              <lb/>
            nia quadrata eiuſdem portionis, regula baſi, eſſe vt paralle-
              <lb/>
            lepipedum ſub b ſireſiduo rectangulo antecedentis Theor-
              <lb/>
            altitudine tripla, MH, ad parallelepipedum ſub baſi rectan-
              <lb/>
            gulo ipſius, FM, ductæ in, RV, altitudine linea compoſita
              <lb/>
            ex, MH, HN.</s>
            <s xml:id="echoid-s6090" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6091" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s6092" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6093" xml:space="preserve">quadrata portionis, RFV, regula, FM, ad omnia
              <lb/>
            quacrata eluidem, regula, RV, habent rationem compoſitam ex
              <lb/>
              <note position="right" xlink:label="note-0265-01" xlink:href="note-0265-01a" xml:space="preserve">Defin. 12.
                <lb/>
              lib. 1.</note>
            ea, quam habent omnia quadrata, RFV, ad omnia quadrata, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum