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="259" file="0297" n="297" rhead="Conicor. Lib. VI."/>
              <figure xlink:label="fig-0297-01" xlink:href="fig-0297-01a" number="344">
                <image file="0297-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0297-01"/>
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            lum H I K ad quadratum I K, vt H I ad I K ſeu vt C A ad A D; </s>
            <s xml:id="echoid-s9746" xml:space="preserve">eſtque
              <lb/>
            rectangulum C I A æquale rectangulo H I K; </s>
            <s xml:id="echoid-s9747" xml:space="preserve">igitur rectangulum C I A ad qua-
              <lb/>
            dratum I K eandem proportionem habet, quàm C A ad A D; </s>
            <s xml:id="echoid-s9748" xml:space="preserve">componitur verò
              <lb/>
            proportio rectanguli C I A ad quadratum I K ex duabus proportionibus laterum
              <lb/>
            C I ad I K, & </s>
            <s xml:id="echoid-s9749" xml:space="preserve">A I ad I K: </s>
            <s xml:id="echoid-s9750" xml:space="preserve">& </s>
            <s xml:id="echoid-s9751" xml:space="preserve">propter parallelas N O, I K, atque K N, & </s>
            <s xml:id="echoid-s9752" xml:space="preserve">
              <lb/>
            C I, & </s>
            <s xml:id="echoid-s9753" xml:space="preserve">latus commune C O K duo triangula C I K, & </s>
            <s xml:id="echoid-s9754" xml:space="preserve">K O N ſimilia ſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s9755" xml:space="preserve">igitur K N ad N O eſt, vt C I ad I K; </s>
            <s xml:id="echoid-s9756" xml:space="preserve">& </s>
            <s xml:id="echoid-s9757" xml:space="preserve">quia in parallelogrammo I N la-
              <lb/>
            tera oppoſita ſunt æqualia K N ad N A eandem proportionem habebit quàm A I
              <lb/>
            ad I K; </s>
            <s xml:id="echoid-s9758" xml:space="preserve">quapropter duæ rationes K N ad N O, & </s>
            <s xml:id="echoid-s9759" xml:space="preserve">K N ad N A componunt
              <lb/>
            proportionem quadrati K N ad rectangulum A N O, quæ eadem eſt proportioni
              <lb/>
            rectanguli C I A ad quadratum I K; </s>
            <s xml:id="echoid-s9760" xml:space="preserve">& </s>
            <s xml:id="echoid-s9761" xml:space="preserve">propterea quadratum K N ad rectan-
              <lb/>
            gulum A N O eandem proportionem habebit, quàm A G ad A D. </s>
            <s xml:id="echoid-s9762" xml:space="preserve">Si igitur
              <lb/>
            fiat conus, cuius vertex K baſis circulus diametro A O deſcriptus, cuius pla-
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            num perpendiculare ſit ad planum A K C; </s>
            <s xml:id="echoid-s9763" xml:space="preserve">atque per rectam A C æquidiſtan-
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            tem ipſi K N planum ducatur perpendiculare ad idem planum A K C genera-
              <lb/>
            bitur ellipſis, cuius axis tranſuerſus erit A C, & </s>
            <s xml:id="echoid-s9764" xml:space="preserve">latus rectum A D. </s>
            <s xml:id="echoid-s9765" xml:space="preserve">Textus
              <lb/>
            igitur corrigi debere ex dictis manifeſtum eſt.</s>
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            <s xml:id="echoid-s9767" xml:space="preserve">Et quia angulus H K C nempe A O K æqualis eſt H A C, & </s>
            <s xml:id="echoid-s9768" xml:space="preserve">angulus
              <lb/>
              <note position="left" xlink:label="note-0297-01" xlink:href="note-0297-01a" xml:space="preserve">C</note>
            C H A æqualis eſt C K A remanet angulus H C A æqualis O A K erit
              <lb/>
            H C A ſimile F E G ſimile quoque O K A; </s>
            <s xml:id="echoid-s9769" xml:space="preserve">ergo, &</s>
            <s xml:id="echoid-s9770" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9771" xml:space="preserve">Quoniam ex con-
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            ſtructione ſegmentum A H C capax eſt anguli æqualis angulo F erit angulus A
              <lb/>
            H C æqualis angulo F; </s>
            <s xml:id="echoid-s9772" xml:space="preserve">& </s>
            <s xml:id="echoid-s9773" xml:space="preserve">quia peripheria A H C ſecta eſt bifariam in H; </s>
            <s xml:id="echoid-s9774" xml:space="preserve">ergo
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            ſubtenſa latera A H, & </s>
            <s xml:id="echoid-s9775" xml:space="preserve">H C æqualia ſunt: </s>
            <s xml:id="echoid-s9776" xml:space="preserve">& </s>
            <s xml:id="echoid-s9777" xml:space="preserve">propterea triangulum A H C
              <lb/>
            iſoſcelium, & </s>
            <s xml:id="echoid-s9778" xml:space="preserve">ſimile erit triangulo E F G; </s>
            <s xml:id="echoid-s9779" xml:space="preserve">propterea quod anguli verticales æ-
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            quales ſunt inter ſe; </s>
            <s xml:id="echoid-s9780" xml:space="preserve">ſunt verò duo anguli A H C, & </s>
            <s xml:id="echoid-s9781" xml:space="preserve">A K C in eodem circuli
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            ſegmento; </s>
            <s xml:id="echoid-s9782" xml:space="preserve">ergo æquales ſunt inter ſe; </s>
            <s xml:id="echoid-s9783" xml:space="preserve">pariterque duo anguli C A H, & </s>
            <s xml:id="echoid-s9784" xml:space="preserve">C K H
              <lb/>
            in eodem circuli ſegmento conſtituti, æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s9785" xml:space="preserve">propter </s>
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