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="197" file="0235" n="235" rhead="Conicor. Lib. VI."/>
            T B ad T e erit, vt E X ad X f; </s>
            <s xml:id="echoid-s7417" xml:space="preserve">& </s>
            <s xml:id="echoid-s7418" xml:space="preserve">iam oſtendimus, quod B T ad T O
              <lb/>
            eſt, vt E X ad X Q; </s>
            <s xml:id="echoid-s7419" xml:space="preserve">igitur ex æqualitate, & </s>
            <s xml:id="echoid-s7420" xml:space="preserve">comparando terminorum
              <lb/>
            differentias ad conſequentes erit O e ad e T, vt Q f ad f X; </s>
            <s xml:id="echoid-s7421" xml:space="preserve">ſed T e ad e
              <lb/>
              <note position="right" xlink:label="note-0235-01" xlink:href="note-0235-01a" xml:space="preserve">Lem. 1.
                <lb/>
              lib. 5.</note>
            V eandem proportionem habet quam X f ad f Y, eo quod oſtenſa ſunt
              <lb/>
            ſimilia triangula V T e, Y X f; </s>
            <s xml:id="echoid-s7422" xml:space="preserve">quare O e ad e V eſt vt Q f ad f Y; </s>
            <s xml:id="echoid-s7423" xml:space="preserve">& </s>
            <s xml:id="echoid-s7424" xml:space="preserve">
              <lb/>
            iam oſtendimus, quod O e ad R V eandem proportionem habet, quàm
              <lb/>
            Q f ad S Y; </s>
            <s xml:id="echoid-s7425" xml:space="preserve">ergo R V ad V e eſt, vt S Y ad Y f, & </s>
            <s xml:id="echoid-s7426" xml:space="preserve">angulus e æqualis
              <lb/>
            eſt angulo f; </s>
            <s xml:id="echoid-s7427" xml:space="preserve">igitur duo ſegmenta N V A, P Y D ſimilia ſunt inter ſe
              <lb/>
            (17. </s>
            <s xml:id="echoid-s7428" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s7429" xml:space="preserve">& </s>
            <s xml:id="echoid-s7430" xml:space="preserve">ſimiliter poſita. </s>
            <s xml:id="echoid-s7431" xml:space="preserve">Inſuper dico, non eſſe ſimilia alicui alte-
              <lb/>
            ri ſegmento; </s>
            <s xml:id="echoid-s7432" xml:space="preserve">quia non abſcinduntur ab vna ordinatione, aut duabus, & </s>
            <s xml:id="echoid-s7433" xml:space="preserve">
              <lb/>
            earum diſtantia in ellipſi à centro non eſt æqualis (18. </s>
            <s xml:id="echoid-s7434" xml:space="preserve">ex 6.)</s>
            <s xml:id="echoid-s7435" xml:space="preserve">, & </s>
            <s xml:id="echoid-s7436" xml:space="preserve">hoc erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s7437" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div677" type="section" level="1" n="225">
          <head xml:id="echoid-head285" xml:space="preserve">PROPOSITIO XXII.</head>
          <p>
            <s xml:id="echoid-s7438" xml:space="preserve">SEctionum non ſimilium A B C, D E F vnum ſegmentum
              <lb/>
            vnius non eſt ſimile alicui ſegmento alterius.</s>
            <s xml:id="echoid-s7439" xml:space="preserve"/>
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          <figure number="267">
            <image file="0235-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0235-01"/>
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            <s xml:id="echoid-s7440" xml:space="preserve">Si enim hoc verum non eſt, ſit ſegmentum G C ſectionis A B C (ſi
              <lb/>
            fieri poteſt) ſimile ipſi H F alterius ſectionis D E F, & </s>
            <s xml:id="echoid-s7441" xml:space="preserve">iungamus G C,
              <lb/>
            H F, eaſdẽq; </s>
            <s xml:id="echoid-s7442" xml:space="preserve">bifariam ſecemus in I, K; </s>
            <s xml:id="echoid-s7443" xml:space="preserve">iungamuſque L I, M K; </s>
            <s xml:id="echoid-s7444" xml:space="preserve">quæ ſint
              <lb/>
              <note position="right" xlink:label="note-0235-02" xlink:href="note-0235-02a" xml:space="preserve">44. lib. 2.</note>
            duæ diametri, & </s>
            <s xml:id="echoid-s7445" xml:space="preserve">ſecent ſegmenta in B, E: </s>
            <s xml:id="echoid-s7446" xml:space="preserve">ſi itaque fuerint duo axes, cũ
              <lb/>
            duo ſegmenta ſint ſimilia, vtique egrederentur in eorum ſingulis ordina-
              <lb/>
              <note position="right" xlink:label="note-0235-03" xlink:href="note-0235-03a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            tiones ad duos axes, numero æquales, continentes cum axibus angulos
              <lb/>
            rectos, & </s>
            <s xml:id="echoid-s7447" xml:space="preserve">proportiones ordinationum ad ſua abſciſſa in qualibet earum
              <lb/>
            eſſent æedem, ac abſciſſæ ad abſciſſas proportionales quoque eſſent. </s>
            <s xml:id="echoid-s7448" xml:space="preserve">Et
              <lb/>
              <note position="right" xlink:label="note-0235-04" xlink:href="note-0235-04a" xml:space="preserve">Defin. 2.
                <lb/>
              huius.</note>
              <note position="left" xlink:label="note-0235-05" xlink:href="note-0235-05a" xml:space="preserve">a</note>
            propterea duæ ſectiones A B C, D E F ſimiles erunt, ſed iam ſuppoſitæ
              <lb/>
            fuerunt non ſimiles; </s>
            <s xml:id="echoid-s7449" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s7450" xml:space="preserve">Si verò I L, M K non fuerint
              <lb/>
            axes, educamus ex B, E ad duos axes L P, M Q duas perpendiculares
              <lb/>
            B P, E Q, & </s>
            <s xml:id="echoid-s7451" xml:space="preserve">duas tangentes B N, & </s>
            <s xml:id="echoid-s7452" xml:space="preserve">E O: </s>
            <s xml:id="echoid-s7453" xml:space="preserve">itaque (propter ſimilitudinẽ
              <lb/>
              <note position="left" xlink:label="note-0235-06" xlink:href="note-0235-06a" xml:space="preserve">b</note>
            duorum ſegmentorum) ſimilia erunt B N L, E O M; </s>
            <s xml:id="echoid-s7454" xml:space="preserve">& </s>
            <s xml:id="echoid-s7455" xml:space="preserve">pariter L B P,
              <lb/>
            M E Q; </s>
            <s xml:id="echoid-s7456" xml:space="preserve">atque quadratum B P ad L B in P N, nempe in eadem </s>
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