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

Page concordance

< >
Scan Original
181 161
182 162
183 163
184 164
185 165
186 166
187 167
188 168
189 169
190 170
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
< >
page |< < (162) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div406" type="section" level="1" n="248">
          <p>
            <s xml:id="echoid-s3824" xml:space="preserve">
              <pb o="162" file="0182" n="182" rhead="GEOMETRIÆ"/>
            AE, ED, ſint, MO, OQ, & </s>
            <s xml:id="echoid-s3825" xml:space="preserve">interceptę figuris ſint, IO, OP, le-
              <lb/>
            periamus, MO, ad, OI, eſſe vt, QO, ad, OP. </s>
            <s xml:id="echoid-s3826" xml:space="preserve">Dico omnes li-
              <lb/>
            neas, AE, ad omnes lineas figurę, BCE, eſſe vt omnes lineę, BF,
              <lb/>
            ad omnes lineas figuræ, B E F, ſi verò vice linearum comparentur
              <lb/>
              <figure xlink:label="fig-0182-01" xlink:href="fig-0182-01a" number="105">
                <image file="0182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0182-01"/>
              </figure>
            ab eiſdem deſcriptę figurę, ſimi-
              <lb/>
            libus exiſtentibus, quę ab omni-
              <lb/>
            bus lineis vniuſcuiuſque propo-
              <lb/>
            ſitarum figurarum deſcribuntur,
              <lb/>
            cuius deſcribentes ſint earum li-
              <lb/>
            neę, vel latera homologa. </s>
            <s xml:id="echoid-s3827" xml:space="preserve">Di-
              <lb/>
            co omnes figuras ſimiles ipſius,
              <lb/>
            A E, ad omnes figuras ſimiles
              <lb/>
            ſigurę, BCE, eſſe vt omnes fi-
              <lb/>
            guras ſimiles ipſius, BF, ad omnes figuras ſimiles figuræ, BEF,
              <lb/>
            quia enim, MQ, vtcunque ducta eſt parallela ipſi, CF, & </s>
            <s xml:id="echoid-s3828" xml:space="preserve">eſt, M
              <lb/>
            O, ad, OI, vt, QO, ad, OP, permutando erit, vt, MO, ad, O
              <lb/>
            Q, ſic, IO, ad, OP, i. </s>
            <s xml:id="echoid-s3829" xml:space="preserve">vt, CE, ad, EF, ſic, IO, ad, OP, & </s>
            <s xml:id="echoid-s3830" xml:space="preserve">ſic
              <lb/>
            oſtendemus, vt, CE, ad, EF, ita eſſe quaſlibet alias duas in figu-
              <lb/>
            ris, BCE, BEF, exiſtentes ipſi, CF, parallelas, & </s>
            <s xml:id="echoid-s3831" xml:space="preserve">vt vna ad vnam
              <lb/>
            ſic omnia ad omnia .</s>
            <s xml:id="echoid-s3832" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3833" xml:space="preserve">vt, CE, ad, EF, ita omnes lineæ figurę, B
              <lb/>
              <note position="left" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">Coroll. 4.
                <lb/>
              huius.</note>
            CE, ad omnes lineas figurę, BEF, vt autem, CE, ad, EF, ita ſunt
              <lb/>
            omnes lineæ, AE, ad omnes lineas, ED, ergo omnes lineę, AE,
              <lb/>
            ad omnes lineas, ED, erunt vt omnes lineę figurę, BCE, ad om-
              <lb/>
            nes lineas figuræ, BEF.</s>
            <s xml:id="echoid-s3834" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3835" xml:space="preserve">Si verò vice linearum ſumamus deſcriptas, vt dictum eſt, ab eiſdem
              <lb/>
            figuras, ex. </s>
            <s xml:id="echoid-s3836" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3837" xml:space="preserve">ſi, vt quadratum, MO, ad triangulum &</s>
            <s xml:id="echoid-s3838" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3839" xml:space="preserve">quilaterum,
              <lb/>
            cuius latus, IO, ita reperiamus eſſe circulum, cuius diameter, OQ,
              <lb/>
            ad polygonum, cuius latus, OQ, omnium autem linearum, AE,
              <lb/>
            fingulæ deſcribant quadrata, & </s>
            <s xml:id="echoid-s3840" xml:space="preserve">omnium linearum figuræ, BCE,
              <lb/>
            ſingulę deſcribant, triangula &</s>
            <s xml:id="echoid-s3841" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3842" xml:space="preserve">quilatera, & </s>
            <s xml:id="echoid-s3843" xml:space="preserve">omnium linearum, BF,
              <lb/>
            ſingulæ deſcribant circulos, & </s>
            <s xml:id="echoid-s3844" xml:space="preserve">figuræ, B E F, ſingulę deſcribant po-
              <lb/>
            lygona prædicto ſimilia, ita vt quæ in eadem figura ſunt lineæ, vel
              <lb/>
            latera deſcribentia ſint homologa, erit vt quadratum, MO, permu-
              <lb/>
            tando, ad circulum, OQ, ita triangulum &</s>
            <s xml:id="echoid-s3845" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3846" xml:space="preserve">quilaterum, IO, ad po-
              <lb/>
            lygonum, OP, quia verò, MO, &</s>
            <s xml:id="echoid-s3847" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3848" xml:space="preserve">quaturipſi, CE, &</s>
            <s xml:id="echoid-s3849" xml:space="preserve">, OQ, ipſi,
              <lb/>
            EF, ideò quadratum, MO, &</s>
            <s xml:id="echoid-s3850" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3851" xml:space="preserve">quatur quadrato, CE, & </s>
            <s xml:id="echoid-s3852" xml:space="preserve">circulus,
              <lb/>
            OQ, circulo, EF, & </s>
            <s xml:id="echoid-s3853" xml:space="preserve">ideò, vt quadratum, CE, ad circulum, EF,
              <lb/>
              <note position="left" xlink:label="note-0182-02" xlink:href="note-0182-02a" xml:space="preserve">@5. lib. 1.</note>
            ita erit triangulum &</s>
            <s xml:id="echoid-s3854" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3855" xml:space="preserve">quilaterum, IO, ad polygonum, OP, vnde,
              <lb/>
            quia, MQ, vtcunq; </s>
            <s xml:id="echoid-s3856" xml:space="preserve">ducta eſt parallelaipſi, CF, concludemus om-
              <lb/>
            nia quadrata, AE, ad omnes circulos, BF, eſſe, vt omnia triangu-
              <lb/>
            la &</s>
            <s xml:id="echoid-s3857" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3858" xml:space="preserve">quilatera figuræ, BCE, ad omnia polygona vni ſimilia figuræ,
              <lb/>
              <note position="left" xlink:label="note-0182-03" xlink:href="note-0182-03a" xml:space="preserve">Ex 4. hu-
                <lb/>
              ius.</note>
            BEF, & </s>
            <s xml:id="echoid-s3859" xml:space="preserve">permutando omnia quadrata, AE, ad omnia triangula </s>
          </p>
        </div>
      </text>
    </echo>
Impressum