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-s9418" xml:space="preserve">
              <pb o="252" file="0290" n="290" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0290-01" xlink:href="fig-0290-01a" number="338">
                <image file="0290-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0290-01"/>
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            tudinem duorum triangulorum), & </s>
            <s xml:id="echoid-s9419" xml:space="preserve">ex ratione A I, nempe K N ad I K,
              <lb/>
            nempe ad A N ( propter parallelas ), & </s>
            <s xml:id="echoid-s9420" xml:space="preserve">ex his duabus proportionibus
              <lb/>
            componitur proportio quadrati K N ad A N in N O; </s>
            <s xml:id="echoid-s9421" xml:space="preserve">ergo quadratum.
              <lb/>
            </s>
            <s xml:id="echoid-s9422" xml:space="preserve">K N ad A N in N O eandem proportionem habet, quàm A C tranſuer-
              <lb/>
            ſus ad A D erectum; </s>
            <s xml:id="echoid-s9423" xml:space="preserve">igitur planum, in quo eſt ſectio A B C, in cono
              <lb/>
            cuius vertex eſt K, & </s>
            <s xml:id="echoid-s9424" xml:space="preserve">baſis circulus, cuius diameter A O producit ſe-
              <lb/>
              <note position="left" xlink:label="note-0290-01" xlink:href="note-0290-01a" xml:space="preserve">13. & 54.
                <lb/>
              lib. 1.
                <lb/>
              Defin. 9.
                <lb/>
              huius.</note>
            ctionem ellipticam, cuius tranſuerſus eſt A C, & </s>
            <s xml:id="echoid-s9425" xml:space="preserve">erectus A D: </s>
            <s xml:id="echoid-s9426" xml:space="preserve">quare
              <lb/>
            ſectionem B A C continet; </s>
            <s xml:id="echoid-s9427" xml:space="preserve">& </s>
            <s xml:id="echoid-s9428" xml:space="preserve">quia angulus H K C, nempe A O K æ-
              <lb/>
              <note position="right" xlink:label="note-0290-02" xlink:href="note-0290-02a" xml:space="preserve">c</note>
            qualis eſt H A C, & </s>
            <s xml:id="echoid-s9429" xml:space="preserve">angulus C H A æqualis eſt C K A, remanet angu-
              <lb/>
            lus H C A æqualis O A K; </s>
            <s xml:id="echoid-s9430" xml:space="preserve">eritque H C A, quod ſimile eſt F E G, ſi-
              <lb/>
            mile quoque O K A; </s>
            <s xml:id="echoid-s9431" xml:space="preserve">quapropter O K A iſoſceleum, & </s>
            <s xml:id="echoid-s9432" xml:space="preserve">ſimile eſt ipſi
              <lb/>
            F E G; </s>
            <s xml:id="echoid-s9433" xml:space="preserve">igitur conus, cuius vertex eſt K, ſimilis eſt dato cono F E G,
              <lb/>
              <note position="left" xlink:label="note-0290-03" xlink:href="note-0290-03a" xml:space="preserve">Defin. 8.
                <lb/>
              huus.</note>
            & </s>
            <s xml:id="echoid-s9434" xml:space="preserve">quidem continet ſectionem A B C, vti diximus. </s>
            <s xml:id="echoid-s9435" xml:space="preserve">Similiter quoque
              <lb/>
            oſtendemus, quod eandem ſectionem continebit alius conus, cuius ver-
              <lb/>
            tex eſt L, ſi educantur A L, L C. </s>
            <s xml:id="echoid-s9436" xml:space="preserve">Et alius conus, præter hos duos,
              <lb/>
            iuxta hanc hypotheſin non continebit illam: </s>
            <s xml:id="echoid-s9437" xml:space="preserve">Alioquin contineat illam,
              <lb/>
              <note position="right" xlink:label="note-0290-04" xlink:href="note-0290-04a" xml:space="preserve">d</note>
            alius conus, cuius vertex ſit Q, & </s>
            <s xml:id="echoid-s9438" xml:space="preserve">triangulum A Q P: </s>
            <s xml:id="echoid-s9439" xml:space="preserve">& </s>
            <s xml:id="echoid-s9440" xml:space="preserve">oſtendetur,
              <lb/>
            quemadmodum ſupra dictum eſt, quod communis ſectio plani, per axim
              <lb/>
            illius coni ducti, erecti ad planum ſectionis A B C, & </s>
            <s xml:id="echoid-s9441" xml:space="preserve">plani ſectionis
              <lb/>
            eſt A C, & </s>
            <s xml:id="echoid-s9442" xml:space="preserve">quod punctum verticis illius coni ſit in circumferentia ſeg-
              <lb/>
            menti A H C, & </s>
            <s xml:id="echoid-s9443" xml:space="preserve">ſit Q, ducamus per H Q rectam H R, & </s>
            <s xml:id="echoid-s9444" xml:space="preserve">iungamus
              <lb/>
            C Q, A Q, & </s>
            <s xml:id="echoid-s9445" xml:space="preserve">educamus A S parallelam H Q R, & </s>
            <s xml:id="echoid-s9446" xml:space="preserve">Q S parallelam A
              <lb/>
            C, erit Q A P triangulum illius coni, & </s>
            <s xml:id="echoid-s9447" xml:space="preserve">eſt iſoſceleum, erit quadratum
              <lb/>
            Q S ad A S in S P, vt C R in R A; </s>
            <s xml:id="echoid-s9448" xml:space="preserve">quod eſt æquale ipſi H R in R Q
              <lb/>
            ad quadratum R Q, nempe H R ad R Q; </s>
            <s xml:id="echoid-s9449" xml:space="preserve">ergo H R ad R Q eſt, vt A C
              <lb/>
              <note position="right" xlink:label="note-0290-05" xlink:href="note-0290-05a" xml:space="preserve">e</note>
            ad A D, quæ eſt, vt H I ad I K; </s>
            <s xml:id="echoid-s9450" xml:space="preserve">ergo diuidendo permutandoq; </s>
            <s xml:id="echoid-s9451" xml:space="preserve">H K
              <lb/>
            maior ad H Q minorem, eandem proportionem habebit, quàm K I mi-
              <lb/>
            nor ad R Q maiorem: </s>
            <s xml:id="echoid-s9452" xml:space="preserve">& </s>
            <s xml:id="echoid-s9453" xml:space="preserve">hoc eſt abſurdum. </s>
            <s xml:id="echoid-s9454" xml:space="preserve">Non ergo reperiri poteſt
              <lb/>
            tertius conus, continens ſectionem B A C. </s>
            <s xml:id="echoid-s9455" xml:space="preserve">Et hoc erat oſtendendum,</s>
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