Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Page concordance

< >
Scan Original
201 163
202 164
203 165
204 166
205 167
206 168
207 169
208 170
209 171
210 172
211 173
212 174
213 175
214 176
215 177
216 178
217 179
218 180
219 181
220 182
221 183
222 184
223 185
224 186
225 187
226 188
227 189
228 190
229 191
230 192
< >
page |< < (186) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div652" type="section" level="1" n="217">
          <pb o="186" file="0224" n="224" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div654" type="section" level="1" n="218">
          <head xml:id="echoid-head275" xml:space="preserve">LEMMA VIII.</head>
          <p style="it">
            <s xml:id="echoid-s7044" xml:space="preserve">SI duo hyperbolica, aut elliptica ſegmenta A B C, D E F fuerint
              <lb/>
            ſimilia, quorum baſes A C, D F efficiant cum diametrorum ab-
              <lb/>
            ſciſsis B M, E O angulos æquales M, & </s>
            <s xml:id="echoid-s7045" xml:space="preserve">O; </s>
            <s xml:id="echoid-s7046" xml:space="preserve">ſintque eorum tranſ-
              <lb/>
            uerſa latera T B, Z E, recta vero B L, E Q. </s>
            <s xml:id="echoid-s7047" xml:space="preserve">Dico figuras eorum;
              <lb/>
            </s>
            <s xml:id="echoid-s7048" xml:space="preserve">ſiue rectangula T B L, & </s>
            <s xml:id="echoid-s7049" xml:space="preserve">Z E Q ſimilia eße.</s>
            <s xml:id="echoid-s7050" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7051" xml:space="preserve">Secentur ſegmentorum abſciſſæ M B, O E proportionaliter in N, P, & </s>
            <s xml:id="echoid-s7052" xml:space="preserve">per
              <lb/>
            ea puncta ducantur ordinatim ad diametros applicatæ G N, I P æquidiſtantes
              <lb/>
            baſibus, efficientes abſciſſas B N, E P, coniunganturq; </s>
            <s xml:id="echoid-s7053" xml:space="preserve">duæ rectæ lineæ T L, Z
              <lb/>
            Q ſecantes rectas lineas N H, M V, P K, O S æquidiſtantes lateribus rectis B
              <lb/>
            L, E Q in punctis H, V,
              <lb/>
              <figure xlink:label="fig-0224-01" xlink:href="fig-0224-01a" number="251">
                <image file="0224-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0224-01"/>
              </figure>
            K, S, atque à punctis H, & </s>
            <s xml:id="echoid-s7054" xml:space="preserve">
              <lb/>
            K ducantur rectæ lineæ H X,
              <lb/>
            K R parallelæ diametris occur-
              <lb/>
            rentes ipſis M V, O S in X,
              <lb/>
              <note position="left" xlink:label="note-0224-01" xlink:href="note-0224-01a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            & </s>
            <s xml:id="echoid-s7055" xml:space="preserve">R. </s>
            <s xml:id="echoid-s7056" xml:space="preserve">Quoniam ſegmenta ſup-
              <lb/>
            ponuntur ſimilia erit A M ad
              <lb/>
            M B, vt D O ad O E, & </s>
            <s xml:id="echoid-s7057" xml:space="preserve">G
              <lb/>
            N ad N B erit vt I P ad P
              <lb/>
            E, atque quadratum A M, ſeu
              <lb/>
            ei æquale rectangulum B M V,
              <lb/>
              <note position="left" xlink:label="note-0224-02" xlink:href="note-0224-02a" xml:space="preserve">12. 13.
                <lb/>
              lib. 1.</note>
            ad quadratum M B eandem
              <lb/>
            proportionem habebit, quàm,
              <lb/>
              <note position="left" xlink:label="note-0224-03" xlink:href="note-0224-03a" xml:space="preserve">Ibidem.</note>
            quadratum D O, ſeu ei æquale
              <lb/>
            rectangulum E O S ad quadratum O E; </s>
            <s xml:id="echoid-s7058" xml:space="preserve">ſed vt rectangulum B M V ad quadra-
              <lb/>
            tum M B ita eſt M V ad M B (cum M B ſit eorum altitudo communis) pari-
              <lb/>
            terque vt rectangulum E O S ad quadratum O E, ita eſt O S ad O E; </s>
            <s xml:id="echoid-s7059" xml:space="preserve">quare
              <lb/>
            M V ad M B eandem proportionem habebit, quàm O S ad O E; </s>
            <s xml:id="echoid-s7060" xml:space="preserve">non aliter oſten-
              <lb/>
            detur N H ad N B eandem proportionem
              <lb/>
              <figure xlink:label="fig-0224-02" xlink:href="fig-0224-02a" number="252">
                <image file="0224-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0224-02"/>
              </figure>
            habere, quàm P K ad P E: </s>
            <s xml:id="echoid-s7061" xml:space="preserve">erat autem
              <lb/>
              <note position="left" xlink:label="note-0224-04" xlink:href="note-0224-04a" xml:space="preserve">Lem. 1.
                <lb/>
              lib. 5.</note>
            M B ad B N vt O E ad E P; </s>
            <s xml:id="echoid-s7062" xml:space="preserve">ergo compa-
              <lb/>
            rando antecedentes, & </s>
            <s xml:id="echoid-s7063" xml:space="preserve">poſtea conſequentes
              <lb/>
            ad differentias terminorum erit B M ad M
              <lb/>
            N vt E O ad O P; </s>
            <s xml:id="echoid-s7064" xml:space="preserve">atque B N ad N M eã-
              <lb/>
            dem proportionem habebit, quàm E P ad P
              <lb/>
            O. </s>
            <s xml:id="echoid-s7065" xml:space="preserve">Quare ex æquali V M ad M N erit vt
              <lb/>
            S O ad O P, atque H N ad N M erit vt K
              <lb/>
            P ad P O; </s>
            <s xml:id="echoid-s7066" xml:space="preserve">& </s>
            <s xml:id="echoid-s7067" xml:space="preserve">differentia ipſarum V M & </s>
            <s xml:id="echoid-s7068" xml:space="preserve">
              <lb/>
            H N ideſt X V ad M N, ſeu ad X H ean-
              <lb/>
            dem proportionem habebit, quàm differentia ipſarum S O, & </s>
            <s xml:id="echoid-s7069" xml:space="preserve">K P, ideſt S R
              <lb/>
            ad O P, ſeu ad R K; </s>
            <s xml:id="echoid-s7070" xml:space="preserve">quapropter V X ad X H erit vt S R ad R K; </s>
            <s xml:id="echoid-s7071" xml:space="preserve">ſed quia
              <lb/>
            X V, L B inter ſe, nec non X H, & </s>
            <s xml:id="echoid-s7072" xml:space="preserve">B T ſunt parallelæ, atq; </s>
            <s xml:id="echoid-s7073" xml:space="preserve">etiam S R, Q E
              <lb/>
            inter ſe, nec nõ R K, & </s>
            <s xml:id="echoid-s7074" xml:space="preserve">E Z ſunt æquidiſtantes; </s>
            <s xml:id="echoid-s7075" xml:space="preserve">erunt triangula V X H, & </s>
            <s xml:id="echoid-s7076" xml:space="preserve">L </s>
          </p>
        </div>
      </text>
    </echo>
Impressum