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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            <s xml:id="echoid-s9785" xml:space="preserve">
              <pb o="260" file="0298" n="298" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0298-01" xlink:href="fig-0298-01a" number="345">
                <image file="0298-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0298-01"/>
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            las A O, K H ſunt anguli alterni A O K, & </s>
            <s xml:id="echoid-s9786" xml:space="preserve">H K O æquales inter ſe; </s>
            <s xml:id="echoid-s9787" xml:space="preserve">igitur
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            angulus A O K æqualis erit angulo C A H; </s>
            <s xml:id="echoid-s9788" xml:space="preserve">& </s>
            <s xml:id="echoid-s9789" xml:space="preserve">propterea in duobus triangulis
              <lb/>
            K A O, & </s>
            <s xml:id="echoid-s9790" xml:space="preserve">H C A tertius angulus A C H æqualis erit tertio angulo K A O,
              <lb/>
            & </s>
            <s xml:id="echoid-s9791" xml:space="preserve">propterea triangulum K A O iſoſcelium, & </s>
            <s xml:id="echoid-s9792" xml:space="preserve">ſimile erit triangulo H A C,
              <lb/>
            ſiuè F G E; </s>
            <s xml:id="echoid-s9793" xml:space="preserve">igitur conus, cuius vertex K baſis circulus A O perpendicularis
              <lb/>
            ad planum trianguli A K O erit conus rectus, & </s>
            <s xml:id="echoid-s9794" xml:space="preserve">ſimilis cono E F G dato.</s>
            <s xml:id="echoid-s9795" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9796" xml:space="preserve">Alioquin contineat illum conus alius, cuius vertex ſit Q, & </s>
            <s xml:id="echoid-s9797" xml:space="preserve">triangu-
              <lb/>
              <note position="right" xlink:label="note-0298-01" xlink:href="note-0298-01a" xml:space="preserve">d</note>
            lum Q A P, & </s>
            <s xml:id="echoid-s9798" xml:space="preserve">oſtendetur quemadmodum dictum eſt, quod planum
              <lb/>
            tranſiens per axim illius coni erectum ad planum ſectionis A B C ſectio
              <lb/>
            communis cum plano ſectionis eſt A C, & </s>
            <s xml:id="echoid-s9799" xml:space="preserve">quod punctum verticis illius
              <lb/>
            coni ſit in circumferentia ſegmenti A H C, &</s>
            <s xml:id="echoid-s9800" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9801" xml:space="preserve">Quia ſupponitur, quod
              <lb/>
            conus Q A P ſimilis cono E F G contineat ellipſim A B C, cuius axis tranſuer-
              <lb/>
            ſus C A, & </s>
            <s xml:id="echoid-s9802" xml:space="preserve">latus rectum A D; </s>
            <s xml:id="echoid-s9803" xml:space="preserve">igitur triangulum per axim coni ductum Q
              <lb/>
            A P, nedum ſimile erit triangulo E F G, ſed etiam perpendiculare erit ad pla-
              <lb/>
            num ellipſis A B C, & </s>
            <s xml:id="echoid-s9804" xml:space="preserve">propterea conſiſtet in plano circularis ſegmenti A H C
              <lb/>
            pariter erecti ad planum A B C, per idem axim A C extenſum, & </s>
            <s xml:id="echoid-s9805" xml:space="preserve">eſt angu-
              <lb/>
            lus A Q C æqualis angulo verticali F propter ſimilitudinem duorum triangu-
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            lorum, & </s>
            <s xml:id="echoid-s9806" xml:space="preserve">ex conſtructione primæ partis huius propoſitionis, eſt ſegmentum A
              <lb/>
            H C capax anguli æqualis angulo F; </s>
            <s xml:id="echoid-s9807" xml:space="preserve">ſecaturque bifariam in H; </s>
            <s xml:id="echoid-s9808" xml:space="preserve">igitur angulus
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            A Q C æqualis ipſi F in peripheria ſegmenti A H C exiſtit. </s>
            <s xml:id="echoid-s9809" xml:space="preserve">Ducatur poſtea
              <lb/>
            Q S parallela lateri tranſuer ſo ellipſis A C, quæ ſecet baſim trianguli per axim
              <lb/>
            Q A P productam in S, & </s>
            <s xml:id="echoid-s9810" xml:space="preserve">à puncto H bipartitæ diuiſionis ſegmenti A H C
              <lb/>
            coniungatur recta linea H Q producaturq; </s>
            <s xml:id="echoid-s9811" xml:space="preserve">quouſq; </s>
            <s xml:id="echoid-s9812" xml:space="preserve">occurratrectæ lineæ C A in R.
              <lb/>
            </s>
            <s xml:id="echoid-s9813" xml:space="preserve">Quoniã duo anguli A H C, & </s>
            <s xml:id="echoid-s9814" xml:space="preserve">A Q C in eodẽ circuli ſegmento conſtituti æqua-
              <lb/>
            les ſunt inter ſe; </s>
            <s xml:id="echoid-s9815" xml:space="preserve">pariterq; </s>
            <s xml:id="echoid-s9816" xml:space="preserve">duo anguli C A H, & </s>
            <s xml:id="echoid-s9817" xml:space="preserve">C Q H in eodẽ circuli ſegmento
              <lb/>
            exiſtentes ſunt æquales, & </s>
            <s xml:id="echoid-s9818" xml:space="preserve">eſt angulus A P Q æqualis angulo P A Q in triangu-
              <lb/>
            lo iſoſcelio Q A P; </s>
            <s xml:id="echoid-s9819" xml:space="preserve">& </s>
            <s xml:id="echoid-s9820" xml:space="preserve">angulus P A Q æqualis angulo C A H in triangulis ſimi-
              <lb/>
            libus; </s>
            <s xml:id="echoid-s9821" xml:space="preserve">igitur angulus A P Q æqualis eſt alterno angulo P Q H; </s>
            <s xml:id="echoid-s9822" xml:space="preserve">& </s>
            <s xml:id="echoid-s9823" xml:space="preserve"/>
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