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="250" file="0288" n="288" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0288-01" xlink:href="fig-0288-01a" number="336">
                <image file="0288-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0288-01"/>
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            E I eandem proportionẽ habet, quàm quadratum B Q ad C Q in Q A
              <lb/>
            eſtq; </s>
            <s xml:id="echoid-s9361" xml:space="preserve">C Q æqualis Q A, atq; </s>
            <s xml:id="echoid-s9362" xml:space="preserve">T S æqualis S E, & </s>
            <s xml:id="echoid-s9363" xml:space="preserve">T S ad S E eandẽ pro-
              <lb/>
              <note position="right" xlink:label="note-0288-01" xlink:href="note-0288-01a" xml:space="preserve">e</note>
            portionẽ habet, quã T R ad R H, ſeu quàm E V ad V H; </s>
            <s xml:id="echoid-s9364" xml:space="preserve">igitur E V æqua-
              <lb/>
            lis eſt V H; </s>
            <s xml:id="echoid-s9365" xml:space="preserve">quod eſt abſurdum; </s>
            <s xml:id="echoid-s9366" xml:space="preserve">propterea quo L O diameter, quæ ad illã
              <lb/>
            perpendicularis eſt, bifariam ſecat eam in N. </s>
            <s xml:id="echoid-s9367" xml:space="preserve">Oſtenſum igitur eſt, non repe-
              <lb/>
            riri conum alium continentem ſectionem D E F, præter ſuperius expoſi-
              <lb/>
            tum. </s>
            <s xml:id="echoid-s9368" xml:space="preserve">Tandem ſupponamus, quadratum B Q ad quadratum Q A habere
              <lb/>
            minorem proportionem, quàm E H ad E I. </s>
            <s xml:id="echoid-s9369" xml:space="preserve">Patet quadratum L P, nẽ-
              <lb/>
              <note position="right" xlink:label="note-0288-02" xlink:href="note-0288-02a" xml:space="preserve">f</note>
            pe N E, ſeu O N in N L ad quadratum E P, nempe ad quadratum N
              <lb/>
            L, ſcilicet O N ad N L habere minorem proportionem, quàm H E ad
              <lb/>
            E I: </s>
            <s xml:id="echoid-s9370" xml:space="preserve">ponamus iam O N ad N X, vt H E ad E I, & </s>
            <s xml:id="echoid-s9371" xml:space="preserve">per X ducamus R
              <lb/>
            X Y parallelam H E, & </s>
            <s xml:id="echoid-s9372" xml:space="preserve">iungamus E R, O R, & </s>
            <s xml:id="echoid-s9373" xml:space="preserve">H R producatur ad T
              <lb/>
            quouſque ſecet E T parallelam ipſi O R. </s>
            <s xml:id="echoid-s9374" xml:space="preserve">Oſtendetur (quemadmodum
              <lb/>
              <note position="right" xlink:label="note-0288-03" xlink:href="note-0288-03a" xml:space="preserve">g</note>
            ſupra dictum eſt) quod E T R, B A C ſunt iſoſcelia, & </s>
            <s xml:id="echoid-s9375" xml:space="preserve">ſimilia. </s>
            <s xml:id="echoid-s9376" xml:space="preserve">Et quia
              <lb/>
            E H ad E I eſt vt O N ad N X; </s>
            <s xml:id="echoid-s9377" xml:space="preserve">nempe vt O V ad V R, nempe vt O V
              <lb/>
            in V R, quod eſt æquale ipſi E V in V H ad quadratum V R; </s>
            <s xml:id="echoid-s9378" xml:space="preserve">hæc au-
              <lb/>
            tem proportio componitur ex E V, nempe S R ad V R, nempe ad E S,
              <lb/>
            & </s>
            <s xml:id="echoid-s9379" xml:space="preserve">ex proportione V H ad V R, nempe S R ad S T, ex quibus compo-
              <lb/>
            nitur proportio quadrati R S ad S T in S E; </s>
            <s xml:id="echoid-s9380" xml:space="preserve">igitur quadratum R S ad E
              <lb/>
            S in S T eandẽ proportionem habet, quàm H E ad E I; </s>
            <s xml:id="echoid-s9381" xml:space="preserve">& </s>
            <s xml:id="echoid-s9382" xml:space="preserve">propterea
              <lb/>
            planum ſectionis D E F in cono, cuius vertex eſt R, & </s>
            <s xml:id="echoid-s9383" xml:space="preserve">illius trianguli
              <lb/>
            latera R E, R T, producit ſectionem hyperbolicam, cuius inclinatus eſt
              <lb/>
            E H, & </s>
            <s xml:id="echoid-s9384" xml:space="preserve">erectus E I; </s>
            <s xml:id="echoid-s9385" xml:space="preserve">quare conus cuius vertex eſt R, continet ſectionẽ D E
              <lb/>
            F, nec non continet illam alius conus, huic cono ſimilis, cuius vertex
              <lb/>
            eſt Y; </s>
            <s xml:id="echoid-s9386" xml:space="preserve">& </s>
            <s xml:id="echoid-s9387" xml:space="preserve">hi duo coni ſunt ſimiles cono A B C, nec continet illam ter-
              <lb/>
            tius alius conus, qui ſimilis ſit cono A B C, nam (ſi hoc ſieri poſſibile
              <lb/>
            eſt) contineat illam alius conus, cuius vertex Z, & </s>
            <s xml:id="echoid-s9388" xml:space="preserve">punctum verticis
              <lb/>
            illius incidet in arcum E L H, & </s>
            <s xml:id="echoid-s9389" xml:space="preserve">iungamus O Z, quæ ſecet H E in e:
              <lb/>
            </s>
            <s xml:id="echoid-s9390" xml:space="preserve">
              <note position="right" xlink:label="note-0288-04" xlink:href="note-0288-04a" xml:space="preserve">h</note>
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