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

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        <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>
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