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

Page concordance

< >
Scan Original
161 141
162 142
163 143
164 144
165 145
166 146
167 147
168 148
169 149
170 150
171 151
172 152
173 153
174 154
175 155
176 156
177 157
178 158
179 159
180 160
181 161
182 162
183 163
184 164
185 165
186 166
187 167
188 168
189 169
190 170
< >
page |< < (201) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div501" type="section" level="1" n="302">
          <p>
            <s xml:id="echoid-s4941" xml:space="preserve">
              <pb o="201" file="0221" n="221" rhead="LIBER III."/>
            ad rectangulum ſub, BM, &</s>
            <s xml:id="echoid-s4942" xml:space="preserve">, MOA, quod verum eſſe oſtendetur,
              <lb/>
            vt in antecedente, etiam ſi parallelogrammum, DN, non ſit circa
              <lb/>
            axim, vel diametrum, BM, vnde patet, &</s>
            <s xml:id="echoid-s4943" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4944" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div503" type="section" level="1" n="303">
          <head xml:id="echoid-head320" xml:space="preserve">THEOREMA III. PROPOS. III.</head>
          <p>
            <s xml:id="echoid-s4945" xml:space="preserve">SI intra circulum, velellipſim, duæ ad axim, vel diame-
              <lb/>
            trum ordinatim applicentur rectæ lineę, ſit autem paral-
              <lb/>
            lelogrammum, & </s>
            <s xml:id="echoid-s4946" xml:space="preserve">triangulum in eadem altitudine cum por-
              <lb/>
            tione inter applicatas concluſa, ſed in baſi altera applicata-
              <lb/>
            rum: </s>
            <s xml:id="echoid-s4947" xml:space="preserve">Omnia quadrata dicti parallelogrammia ad omnia qua-
              <lb/>
            drata concluſę portionis (regula baſi) erunt, vt rectangulum
              <lb/>
            ſub partibus axis, vel diametri per baſim conſtitutis ad re-
              <lb/>
            ctangulum ſub abſciſſa per baſim ab extremitate axis, vel
              <lb/>
            diametri, & </s>
            <s xml:id="echoid-s4948" xml:space="preserve">ſub compoſita ex medietate portionis axis, vel
              <lb/>
            diametri eiſdem applicatis intermedię, & </s>
            <s xml:id="echoid-s4949" xml:space="preserve">abſciſſa per aliam
              <lb/>
            applicatam ab eiuſdem extremitate, vna cum rectangulo ſub
              <lb/>
            eadem intermedia, & </s>
            <s xml:id="echoid-s4950" xml:space="preserve">ſub compoſita ex, @, eiuſdem, &</s>
            <s xml:id="echoid-s4951" xml:space="preserve">, {1/2}, ab-
              <lb/>
            ſciſſæ per eandem applicatam ab eiuſdem extremitate: </s>
            <s xml:id="echoid-s4952" xml:space="preserve">Om-
              <lb/>
            nia verò quadrata incluſę portionis ad omnia quadrata dicti
              <lb/>
            trianguli erunt, vt rectangulum ſub compoſita ex abſciſſis ab
              <lb/>
            axi, vel diametro per ordinatim applicatas verſus terminum,
              <lb/>
            cui baſis propinquior eſt, & </s>
            <s xml:id="echoid-s4953" xml:space="preserve">ſub ſexquialtera abſciſſæ ab alio
              <lb/>
            extremo per applicatam, quę non eſt baſis, vna cum rectan-
              <lb/>
            gulo ſub huius reliqua, & </s>
            <s xml:id="echoid-s4954" xml:space="preserve">ſub dupla abſciſſę per baſim ab ex-
              <lb/>
            tremo, cui ipſa baſis propinquior eſt, ad rectangulum ſub
              <lb/>
            partibus axis, vel diametri per baſim conſtitutis.</s>
            <s xml:id="echoid-s4955" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4956" xml:space="preserve">Sit ergo circulus, velellipſis, ACDF,
              <lb/>
              <figure xlink:label="fig-0221-01" xlink:href="fig-0221-01a" number="134">
                <image file="0221-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0221-01"/>
              </figure>
            centrum, O, axis, vel diameter, AD, duæ
              <lb/>
            ad ipſam ordinatim applicatæ ſint, IS, C
              <lb/>
            F, intercipientes portionem, ICFS, ſit
              <lb/>
            autem parallelogrammum, BF, in baſi
              <lb/>
            vtrauis applicatarum, vt in, CF, & </s>
            <s xml:id="echoid-s4957" xml:space="preserve">eadem
              <lb/>
            altitudine cum fruſto, CISF, ſit etiam
              <lb/>
            nunc circa axim, vel diametrum, MR, re-
              <lb/>
            gula verò, CF; </s>
            <s xml:id="echoid-s4958" xml:space="preserve">Dico ergo omnia quadra-
              <lb/>
            ta parallelogrammi, BF, ad omnia qua-
              <lb/>
            drata portionis, ICFS, eſſe vt rectangulum, DRA, ad </s>
          </p>
        </div>
      </text>
    </echo>
Impressum