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
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
251 213
252 214
253 215
254 216
255 217
256 218
257 219
258 220
259 221
260 222
< >
page |< < (205) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div693" type="section" level="1" n="229">
          <pb o="205" file="0243" n="243" rhead="Conicor. Lib. VI."/>
          <p style="it">
            <s xml:id="echoid-s7697" xml:space="preserve">Sed B T ad B I erat vt X E ad E K propter ſimilitudinem duarum ſe-
              <lb/>
              <note position="left" xlink:label="note-0243-01" xlink:href="note-0243-01a" xml:space="preserve">e</note>
            ctionum, &</s>
            <s xml:id="echoid-s7698" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7699" xml:space="preserve">Quoniam ex hypotheſi abſcißa axis I B ad latus rectum B G
              <lb/>
            erat vt abſciſſa K E ad latus rectum E H; </s>
            <s xml:id="echoid-s7700" xml:space="preserve">& </s>
            <s xml:id="echoid-s7701" xml:space="preserve">propter ſimilitudinem ſectionum
              <lb/>
              <note position="right" xlink:label="note-0243-02" xlink:href="note-0243-02a" xml:space="preserve">12. huius.</note>
            latera erecta G B, & </s>
            <s xml:id="echoid-s7702" xml:space="preserve">H E ad axes tranſuerſos, & </s>
            <s xml:id="echoid-s7703" xml:space="preserve">ideo ad eorum ſemißes T B
              <lb/>
            & </s>
            <s xml:id="echoid-s7704" xml:space="preserve">E X eandem proportionem habebunt; </s>
            <s xml:id="echoid-s7705" xml:space="preserve">ergo ex æquali I B ad B T erit vt K
              <lb/>
            E ad E X, & </s>
            <s xml:id="echoid-s7706" xml:space="preserve">inuertendo T B
              <lb/>
              <figure xlink:label="fig-0243-01" xlink:href="fig-0243-01a" number="277">
                <image file="0243-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0243-01"/>
              </figure>
            ad B I erit vt X E ad E K.
              <lb/>
            </s>
            <s xml:id="echoid-s7707" xml:space="preserve">Sed libet aliam expoſitionem
              <lb/>
            afferre Apollonij principijs cõue-
              <lb/>
            nientiorẽ. </s>
            <s xml:id="echoid-s7708" xml:space="preserve">Quia ex definitione
              <lb/>
            2. </s>
            <s xml:id="echoid-s7709" xml:space="preserve">huius libri legitime inter pre-
              <lb/>
            tata, & </s>
            <s xml:id="echoid-s7710" xml:space="preserve">ſicuticõſtat ex 12. </s>
            <s xml:id="echoid-s7711" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s7712" xml:space="preserve">
              <lb/>
            huius. </s>
            <s xml:id="echoid-s7713" xml:space="preserve">In ſectionibus ſimilibus
              <lb/>
            non quælibet axium abſcißæ ad
              <lb/>
            conterminas potentiales habent
              <lb/>
            eandem rationem; </s>
            <s xml:id="echoid-s7714" xml:space="preserve">ſed illæ tan-
              <lb/>
            tummodo, quæ figuræ lateribus
              <lb/>
            proportionales ſunt: </s>
            <s xml:id="echoid-s7715" xml:space="preserve">itaq; </s>
            <s xml:id="echoid-s7716" xml:space="preserve">in ſe-
              <lb/>
            ctionibus ſimilibus A B, D E
              <lb/>
            vt quælibet axium, abſcißæ B
              <lb/>
            I, E K ad conterminas poten-
              <lb/>
            tiales I A, K D ſint proportio-
              <lb/>
            nales, neceße eſt, vt eædem I B,
              <lb/>
            & </s>
            <s xml:id="echoid-s7717" xml:space="preserve">E K lateribus figurarum B
              <lb/>
            T, E X proportionales ſint.</s>
            <s xml:id="echoid-s7718" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7719" xml:space="preserve">Et quadratum V Z ad quadratum Z e eſt, vt quadratum a Y ad qua-
              <lb/>
              <note position="left" xlink:label="note-0243-03" xlink:href="note-0243-03a" xml:space="preserve">f</note>
            dratum a f, &</s>
            <s xml:id="echoid-s7720" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7721" xml:space="preserve">oſtenſa enim fuerunt duo trìangula V Z e, & </s>
            <s xml:id="echoid-s7722" xml:space="preserve">γ a f ſimilia
              <lb/>
            inter ſe; </s>
            <s xml:id="echoid-s7723" xml:space="preserve">& </s>
            <s xml:id="echoid-s7724" xml:space="preserve">ideo latera circa angulos rectos Z, & </s>
            <s xml:id="echoid-s7725" xml:space="preserve">a proportionalia erunt; </s>
            <s xml:id="echoid-s7726" xml:space="preserve">& </s>
            <s xml:id="echoid-s7727" xml:space="preserve">
              <lb/>
            pariter eorum quadrata.</s>
            <s xml:id="echoid-s7728" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7729" xml:space="preserve">Inſuper dico non eſſe ſimilia alicui alteri ſegmento, &</s>
            <s xml:id="echoid-s7730" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7731" xml:space="preserve">Sicutì in præ-
              <lb/>
              <note position="left" xlink:label="note-0243-04" xlink:href="note-0243-04a" xml:space="preserve">g</note>
            cedenti propoſitione factum eſt oſtendetur, quod ſegmentum N C non eſt ſimile
              <lb/>
            alicui alio ſegmento in altera ſectione P E, quando non compræhenduntur ab
              <lb/>
            ordinatim ad axes applicatis, & </s>
            <s xml:id="echoid-s7732" xml:space="preserve">in ellipſibus æqualiter à centris diſtant.</s>
            <s xml:id="echoid-s7733" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div701" type="section" level="1" n="230">
          <head xml:id="echoid-head290" xml:space="preserve">Notæ in Propoſit. XXII.</head>
          <p style="it">
            <s xml:id="echoid-s7734" xml:space="preserve">ET propterea duo ſectiones A B C, D E F ſimiles erunt, &</s>
            <s xml:id="echoid-s7735" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7736" xml:space="preserve">Quo-
              <lb/>
              <note position="right" xlink:label="note-0243-05" xlink:href="note-0243-05a" xml:space="preserve">Lem. 8.
                <lb/>
              huius.</note>
            niam ſegmenta G B C, & </s>
            <s xml:id="echoid-s7737" xml:space="preserve">H E F poſita ſunt ſimilia, erunt diamctrorum
              <lb/>
              <figure xlink:label="fig-0243-02" xlink:href="fig-0243-02a" number="278">
                <image file="0243-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0243-02"/>
              </figure>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum