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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              <pb o="232" file="0270" n="270" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0270-01" xlink:href="fig-0270-01a" number="317">
                <image file="0270-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0270-01"/>
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            A B C, & </s>
            <s xml:id="echoid-s8685" xml:space="preserve">D E F ſimilia, & </s>
            <s xml:id="echoid-s8686" xml:space="preserve">ſimiliter poſita: </s>
            <s xml:id="echoid-s8687" xml:space="preserve">poſtea in plano per B C, M K
              <lb/>
            ducto, diametris B C, & </s>
            <s xml:id="echoid-s8688" xml:space="preserve">E F, fiant duo circuli B K C, E L F, qui ſint ba-
              <lb/>
            ſes duorum conorum, quorum vertices ſint A, & </s>
            <s xml:id="echoid-s8689" xml:space="preserve">D, & </s>
            <s xml:id="echoid-s8690" xml:space="preserve">in eorum ſuper ficie-
              <lb/>
            bus planum per H I, M K ductum efficiat ſectiones K H M, & </s>
            <s xml:id="echoid-s8691" xml:space="preserve">L X S: </s>
            <s xml:id="echoid-s8692" xml:space="preserve">Dico
              <lb/>
            eas eſſe quæſitas. </s>
            <s xml:id="echoid-s8693" xml:space="preserve">Quoniam duo triangula A B C, D E F ſimilia, & </s>
            <s xml:id="echoid-s8694" xml:space="preserve">ſimiliter
              <lb/>
            poſita in eodem ſunt plano, pariterque duo circuli baſium in vno plano exiſtunt;
              <lb/>
            </s>
            <s xml:id="echoid-s8695" xml:space="preserve">
              <note position="left" xlink:label="note-0270-01" xlink:href="note-0270-01a" xml:space="preserve">Lem. 9.
                <lb/>
              huius.</note>
            ergo duo coni A B C, & </s>
            <s xml:id="echoid-s8696" xml:space="preserve">D E F ſimiles erunt; </s>
            <s xml:id="echoid-s8697" xml:space="preserve">poſtea quia triangula A B C,
              <lb/>
            & </s>
            <s xml:id="echoid-s8698" xml:space="preserve">D E F ſimilia ſunt, & </s>
            <s xml:id="echoid-s8699" xml:space="preserve">communis ſectionum diameter H X I æque inclina-
              <lb/>
            tur ad coincidentes baſes M K, S L, & </s>
            <s xml:id="echoid-s8700" xml:space="preserve">axi communi A D G æquidiſtat, & </s>
            <s xml:id="echoid-s8701" xml:space="preserve">
              <lb/>
            in angulis æqualibus intercipiunt G I communem portionem baſium triangulorum
              <lb/>
              <note position="left" xlink:label="note-0270-02" xlink:href="note-0270-02a" xml:space="preserve">Prop. 10.
                <lb/>
              add.</note>
            ſimilium per axes; </s>
            <s xml:id="echoid-s8702" xml:space="preserve">igitur hyperbolæ K H M, & </s>
            <s xml:id="echoid-s8703" xml:space="preserve">L X S æquales ſunt, & </s>
            <s xml:id="echoid-s8704" xml:space="preserve">ſimi-
              <lb/>
            les inter ſe, & </s>
            <s xml:id="echoid-s8705" xml:space="preserve">earum figuris æqualia ſunt quadrata ex dupla interceptæ G I
              <lb/>
            deſcripta. </s>
            <s xml:id="echoid-s8706" xml:space="preserve">Secundò quia ( propter parallelas A O, & </s>
            <s xml:id="echoid-s8707" xml:space="preserve">B C ) triangula H O A,
              <lb/>
            & </s>
            <s xml:id="echoid-s8708" xml:space="preserve">A G C ſimilia ſunt; </s>
            <s xml:id="echoid-s8709" xml:space="preserve">igitur quadratum A G ad quadratum G C, ſeu ad re-
              <lb/>
            ctangulum B G C eandem proportionem habebit, quàm quadratum H O ad qua-
              <lb/>
            dratum O A, ſeu quàm latus tranſuerſum ad rectum figuræ Z; </s>
            <s xml:id="echoid-s8710" xml:space="preserve">ſed vt quadra-
              <lb/>
              <note position="left" xlink:label="note-0270-03" xlink:href="note-0270-03a" xml:space="preserve">12. lib. 1.</note>
            tum A G ad rectangulum B G C, ita eſt latus tranſuerſum ad rectum hyperbo-
              <lb/>
            les K H M; </s>
            <s xml:id="echoid-s8711" xml:space="preserve">igitur duæ hyperbolæ Z, & </s>
            <s xml:id="echoid-s8712" xml:space="preserve">K H M, habent figurarum latera,
              <lb/>
            porportionalia; </s>
            <s xml:id="echoid-s8713" xml:space="preserve">ſuntq; </s>
            <s xml:id="echoid-s8714" xml:space="preserve">prædictæ figuræ æquales cum ſint æquales quadratis ex du-
              <lb/>
            plis ipsarum A O, & </s>
            <s xml:id="echoid-s8715" xml:space="preserve">interceptæ G I: </s>
            <s xml:id="echoid-s8716" xml:space="preserve">quæ ſunt æquales in parallelogrammo G
              <lb/>
            O, & </s>
            <s xml:id="echoid-s8717" xml:space="preserve">habent angulos à diametris, & </s>
            <s xml:id="echoid-s8718" xml:space="preserve">baſibus contenti, æquales inter ſe: </s>
            <s xml:id="echoid-s8719" xml:space="preserve">erunt
              <lb/>
              <note position="left" xlink:label="note-0270-04" xlink:href="note-0270-04a" xml:space="preserve">10. 12.
                <lb/>
              huus.</note>
            hyperbolæ K H M, & </s>
            <s xml:id="echoid-s8720" xml:space="preserve">Z æquales, & </s>
            <s xml:id="echoid-s8721" xml:space="preserve">ſimiles inter ſe: </s>
            <s xml:id="echoid-s8722" xml:space="preserve">& </s>
            <s xml:id="echoid-s8723" xml:space="preserve">propterea ſectio L X S,
              <lb/>
            quæ ſimilis, & </s>
            <s xml:id="echoid-s8724" xml:space="preserve">æqualis oſtenſa eſt ipſi K H M, erit quoque æqualis, & </s>
            <s xml:id="echoid-s8725" xml:space="preserve">ſimilis
              <lb/>
            eidem ſectioni Z. </s>
            <s xml:id="echoid-s8726" xml:space="preserve">Tertiò, quia in duobus conis ſimilibus, & </s>
            <s xml:id="echoid-s8727" xml:space="preserve">ſimiliter poſitis
              <lb/>
            circa communem axim A D G, ſuperficies nunquàm conueniunt, propterea,
              <lb/>
            quod latera A B, & </s>
            <s xml:id="echoid-s8728" xml:space="preserve">D E, à quibus generantur in tota reuolutione inter </s>
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