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
221 183
222 184
223 185
224 186
225 187
226 188
227 189
228 190
229 191
230 192
231 193
232 194
233 195
234 196
235 197
236 198
237 199
238 200
239 201
240 202
241 203
242 204
243 205
244 206
245 207
246 208
247 209
248 210
249 211
250 212
< >
page |< < (184) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div650" type="section" level="1" n="216">
          <pb o="184" file="0222" n="222" rhead="Apollonij Pergæi"/>
          <figure number="248">
            <image file="0222-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0222-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s6987" xml:space="preserve">Secentur diametrorum abſciſſæ G B, & </s>
            <s xml:id="echoid-s6988" xml:space="preserve">H E in ijſdem rationibus in L, M,
              <lb/>
            N, O, & </s>
            <s xml:id="echoid-s6989" xml:space="preserve">ab ijſdem punctis educantur baſibus æquiſtantes, ſeu ad diametros or-
              <lb/>
            dinatim applicatæ P Q, R S, T V, X Y
              <unsure/>
            . </s>
            <s xml:id="echoid-s6990" xml:space="preserve">Quoniam ex hypotheſi G B ad B I
              <lb/>
            eſt, vt H E ad E K; </s>
            <s xml:id="echoid-s6991" xml:space="preserve">eſtque A G media proportionalis inter G B, & </s>
            <s xml:id="echoid-s6992" xml:space="preserve">B I; </s>
            <s xml:id="echoid-s6993" xml:space="preserve">pari-
              <lb/>
              <note position="left" xlink:label="note-0222-01" xlink:href="note-0222-01a" xml:space="preserve">II. lib. I.</note>
            terque D H media proportionalis eſt inter H E, & </s>
            <s xml:id="echoid-s6994" xml:space="preserve">E K; </s>
            <s xml:id="echoid-s6995" xml:space="preserve">igitur A G ad G B
              <lb/>
            eſt, vt D H ad H E; </s>
            <s xml:id="echoid-s6996" xml:space="preserve">Et quoniam inuertendo L B ad B G eſt, vt N E ad E H,
              <lb/>
            atque B G ad B I poſita fuit, vt H E ad E K; </s>
            <s xml:id="echoid-s6997" xml:space="preserve">ergo ex æquali ordinata L B ad
              <lb/>
            B I erit, vt N E ad E K, quare vt L B ad P L, mediã proportionalẽ inter L B,
              <lb/>
            & </s>
            <s xml:id="echoid-s6998" xml:space="preserve">I B, ita erit N E ad N T mediam proportionalem inter N E, & </s>
            <s xml:id="echoid-s6999" xml:space="preserve">E K. </s>
            <s xml:id="echoid-s7000" xml:space="preserve">Eo-
              <lb/>
            dem modo oſtendetur, quod R M ad M B eandem proportionem habet, quàm X
              <lb/>
            O ad O E: </s>
            <s xml:id="echoid-s7001" xml:space="preserve">& </s>
            <s xml:id="echoid-s7002" xml:space="preserve">hoc ſemper continget in quibuslibet alijs diuiſionibus proportiona-
              <lb/>
            libus abſciſſarum, ſuntque anguli G, & </s>
            <s xml:id="echoid-s7003" xml:space="preserve">H æquales; </s>
            <s xml:id="echoid-s7004" xml:space="preserve">igitur ſegmenta A B C, & </s>
            <s xml:id="echoid-s7005" xml:space="preserve">
              <lb/>
            D E F ſimilia ſunt inter ſe. </s>
            <s xml:id="echoid-s7006" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s7007" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Defin. 7.
            <lb/>
          huius.</note>
        </div>
        <div xml:id="echoid-div652" type="section" level="1" n="217">
          <head xml:id="echoid-head274" xml:space="preserve">LEMMA VII.</head>
          <p style="it">
            <s xml:id="echoid-s7008" xml:space="preserve">S I in duobus ſegmentis A B C, & </s>
            <s xml:id="echoid-s7009" xml:space="preserve">D E F hyperbolicis, aut ellipti-
              <lb/>
            cis, baſes A C, & </s>
            <s xml:id="echoid-s7010" xml:space="preserve">D F cum diametris G B, & </s>
            <s xml:id="echoid-s7011" xml:space="preserve">H E, æquales
              <lb/>
            angulos G, & </s>
            <s xml:id="echoid-s7012" xml:space="preserve">H obliquos continentes, efficiant abſciſſas G B, & </s>
            <s xml:id="echoid-s7013" xml:space="preserve">H E
              <lb/>
            proportionales lateribus rectis B I, & </s>
            <s xml:id="echoid-s7014" xml:space="preserve">E K, atque tranſuerſis B Z, & </s>
            <s xml:id="echoid-s7015" xml:space="preserve">
              <lb/>
            E a, erunt ſegmenta ſimilia inter ſe.</s>
            <s xml:id="echoid-s7016" xml:space="preserve"/>
          </p>
          <figure number="249">
            <image file="0222-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0222-02"/>
          </figure>
        </div>
      </text>
    </echo>
Impressum