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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          <p>
            <s xml:id="echoid-s4782" xml:space="preserve">
              <pb o="121" file="0159" n="159" rhead="Conicor. Lib. V."/>
            dratum maximi, qui eſt I B, ſuperat quadratum cuiuslibet illorum exem-
              <lb/>
            plari applicato abſciſſionibus eorum potentialium, &</s>
            <s xml:id="echoid-s4783" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4784" xml:space="preserve">Senſus buius tex-
              <lb/>
            tus penè vix diuinari poteſt inter tot menda, & </s>
            <s xml:id="echoid-s4785" xml:space="preserve">phraſis Arabicæ obſcuritatem;
              <lb/>
            </s>
            <s xml:id="echoid-s4786" xml:space="preserve">puto tamen, eum eſſe, quem in textu appoſui, vbi paucula verba immutaui,
              <lb/>
            quæ deſiderari videbantur, aliqua verò tranſpoſui, vt ſenſus continuari poſſet.</s>
            <s xml:id="echoid-s4787" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4788" xml:space="preserve">Cæterum animaduertendum eſt in biſce propoſitionibus, ſicuti in 8. </s>
            <s xml:id="echoid-s4789" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4790" xml:space="preserve">& </s>
            <s xml:id="echoid-s4791" xml:space="preserve">10.
              <lb/>
            </s>
            <s xml:id="echoid-s4792" xml:space="preserve">buius libri ſupponi vt res manifeſta intra ſectionem duci poſſe à puncto originis
              <lb/>
            ramum maximum, vel breuiſsimum, ideſt neceſſario reperiri debere ramum,
              <lb/>
            cuius potentialis abſcindit à menſura verſus originem rectam lineam, ad quàm
              <lb/>
            inuerſa eandem proportionem babeant quàm axis tranſuerſus ad ſuum erectum: </s>
            <s xml:id="echoid-s4793" xml:space="preserve">
              <lb/>
            boc autem ſine demonſtratione admittere nefas eſt. </s>
            <s xml:id="echoid-s4794" xml:space="preserve">Ergo quod in textu deſidera-
              <lb/>
            tur ſuppleri poteſt bac ratione. </s>
            <s xml:id="echoid-s4795" xml:space="preserve">Quia C I maior eſt, quàm C E, ſed minor,
              <lb/>
            quàm C F; </s>
            <s xml:id="echoid-s4796" xml:space="preserve">ergo eadem E C ad minorem C I maiorem proportionẽ babet, quàm
              <lb/>
            ad C F; </s>
            <s xml:id="echoid-s4797" xml:space="preserve">& </s>
            <s xml:id="echoid-s4798" xml:space="preserve">comparando antecedentes ad differentias terminorum C E ad E I
              <lb/>
            maiorem proportionem babebit, quàm E C ad differentiam ipſius C F à C E; </s>
            <s xml:id="echoid-s4799" xml:space="preserve">
              <lb/>
            quare aliqua magnitudo minor quàm prima ſcilicet G E ad E I eandem propor-
              <lb/>
            tionem habebit, quàm C E ad differentiam ipſarum C F, & </s>
            <s xml:id="echoid-s4800" xml:space="preserve">C E: </s>
            <s xml:id="echoid-s4801" xml:space="preserve">& </s>
            <s xml:id="echoid-s4802" xml:space="preserve">iterum
              <lb/>
            comparando antecedentes ad ſummas terminorum E G ad G I eandem proportio-
              <lb/>
            nem babebit, quàm E C ad C F; </s>
            <s xml:id="echoid-s4803" xml:space="preserve">quare punctum G cadet intra ſectionem, pa-
              <lb/>
            riterq; </s>
            <s xml:id="echoid-s4804" xml:space="preserve">G B ad axim perpendicularis occurrens ſectioni in B cadet intra eandem
              <lb/>
            ſectionem: </s>
            <s xml:id="echoid-s4805" xml:space="preserve">& </s>
            <s xml:id="echoid-s4806" xml:space="preserve">ideo duci poterit ramus I B, qui oſtendetur maximus reliquorum
              <lb/>
            omnium.</s>
            <s xml:id="echoid-s4807" xml:space="preserve"/>
          </p>
          <figure number="152">
            <image file="0159-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0159-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s4808" xml:space="preserve">Quoniam proportio G E ad E I facta eſt, vt E C ad C F, &</s>
            <s xml:id="echoid-s4809" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4810" xml:space="preserve">Nam
              <lb/>
              <note position="left" xlink:label="note-0159-01" xlink:href="note-0159-01a" xml:space="preserve">b</note>
            vt axis D C ad eius erectum, ſeu vt ſemiaxis E C ad ſemierectum C F, ita
              <lb/>
            facta eſt E G ad G I: </s>
            <s xml:id="echoid-s4811" xml:space="preserve">ſed propter parallelas G V, & </s>
            <s xml:id="echoid-s4812" xml:space="preserve">F C: </s>
            <s xml:id="echoid-s4813" xml:space="preserve">& </s>
            <s xml:id="echoid-s4814" xml:space="preserve">ſimilitudinem
              <lb/>
            triangulorum E G V, E C F eſt E G ad G V, vt E C ad C F; </s>
            <s xml:id="echoid-s4815" xml:space="preserve">& </s>
            <s xml:id="echoid-s4816" xml:space="preserve">propterea
              <lb/>
            eadem E G ad duas G V, & </s>
            <s xml:id="echoid-s4817" xml:space="preserve">G I babebit eandem proportionem, & </s>
            <s xml:id="echoid-s4818" xml:space="preserve">ideo I G æ-
              <lb/>
            qualis erit G V, & </s>
            <s xml:id="echoid-s4819" xml:space="preserve">triangulum I G V iſoſceleum, & </s>
            <s xml:id="echoid-s4820" xml:space="preserve">rectangulum erit in G;
              <lb/>
            </s>
            <s xml:id="echoid-s4821" xml:space="preserve">quare quadratum I G duplum erit trianguli I G V: </s>
            <s xml:id="echoid-s4822" xml:space="preserve">eſt verò quadratum B G
              <lb/>
            æquale duplo trapezij G C F V; </s>
            <s xml:id="echoid-s4823" xml:space="preserve">ideſt duplo trapezij G C S V, cum duplo trian-
              <lb/>
              <note position="right" xlink:label="note-0159-02" xlink:href="note-0159-02a" xml:space="preserve">1. huius.</note>
            guli F S V; </s>
            <s xml:id="echoid-s4824" xml:space="preserve">igitur quadratum I B (quod eſt æquale duobus quadratis I G, G
              <lb/>
            B circa angulum rectum G) æquale eſt duplo trianguli I G V duplo trapezij </s>
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