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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[221.] SECTIO SEPTIMA Continens Propoſit. XVIII. & XIX.
[222.] Notæ in Propoſit. XVIII. & XIX.
[223.] SECTIO OCTAVA Continens Propoſit. XX. & XXI. Apollonij. PROPOSITIO XX.
[224.] PROPOSITIO XXI.
[225.] PROPOSITIO XXII.
[226.] PROPOSITIO XXIII.
[227.] PROPOSITIO XXIV.
[228.] Notæ in Propoſit. XX.
[229.] Notæ in Propoſit. XXI.
[230.] Notæ in Propoſit. XXII.
[231.] Notæ in Propoſit. XXIII.
[232.] Notæ in Propoſit. XXIV.
[233.] SECTIO NONA Continens Propoſit. XXV.
[234.] Notæ in Propoſit. XXV.
[235.] LEMMA IX.
[236.] SECTIO DECIMA Continens Propoſit. XXVI. XXVII. & XXVIII. PROPOSITIO XXVI.
[237.] PROPOSITIO XXVII.
[238.] PROPOSITIO XXVIII.
[239.] Notæ in Propoſit. XXVI.
[240.] Notæ in Propoſit. XXVII.
[241.] Notæ in Propoſit. XXVIII.
[242.] LEMMAX.
[243.] SECTIO VNDECIMA Continens Propoſit. XXIX. XXX. & XXXI. PROPOSTIO XXIX.
[244.] PROPOSITIO XXX.
[245.] PROPOSITIO XXXI.
[246.] Notæ in Propoſit. XXIX.
[247.] Notæ in Propoſit. XXX.
[248.] Notæ in Propoſit. XXXI.
[249.] LIBRI SEXTI FINIS.
[250.] DEFINITIONES. I.
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          <head xml:id="echoid-head284" xml:space="preserve">PROPOSITIO XXI.</head>
          <p>
            <s xml:id="echoid-s7376" xml:space="preserve">SInt poſtea duæ illæ ſectiones hyperbolicæ, & </s>
            <s xml:id="echoid-s7377" xml:space="preserve">ellipticæ ſi-
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            miles, & </s>
            <s xml:id="echoid-s7378" xml:space="preserve">earum centra T, X (remanentibus lineis, & </s>
            <s xml:id="echoid-s7379" xml:space="preserve">ſi-
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            gnis, vt prius) & </s>
            <s xml:id="echoid-s7380" xml:space="preserve">ducantur duæ contingentes V e, & </s>
            <s xml:id="echoid-s7381" xml:space="preserve">Y f.</s>
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            <s xml:id="echoid-s7383" xml:space="preserve">Quoniam B G ad B I ſuppoſita eſt, vt H E ad E K, & </s>
            <s xml:id="echoid-s7384" xml:space="preserve">pariter G B ad
              <lb/>
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            B L, vt H E ad E M; </s>
            <s xml:id="echoid-s7385" xml:space="preserve">ergo ex æqualitate, & </s>
            <s xml:id="echoid-s7386" xml:space="preserve">per conuerſionem rationis
              <lb/>
            B L ad L I eſt vt E M ad M K; </s>
            <s xml:id="echoid-s7387" xml:space="preserve">& </s>
            <s xml:id="echoid-s7388" xml:space="preserve">propter ſimilitudinem duarum ſectio-
              <lb/>
              <note position="left" xlink:label="note-0233-02" xlink:href="note-0233-02a" xml:space="preserve">b</note>
            num N L ad A I nempe L O ad O I eſt, vt M P ad D K, nempe M Q
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            ad Q K, & </s>
            <s xml:id="echoid-s7389" xml:space="preserve">antecedentes ad ſummas vel differentias terminorum, ſcilicet
              <lb/>
              <note position="right" xlink:label="note-0233-03" xlink:href="note-0233-03a" xml:space="preserve">Lem. 1.
                <lb/>
              lib. 5.</note>
            O L ad L I eandem proportionem habebit, quàm Q M ad M K, & </s>
            <s xml:id="echoid-s7390" xml:space="preserve">ex
              <lb/>
              <note position="left" xlink:label="note-0233-04" xlink:href="note-0233-04a" xml:space="preserve">c</note>
            æqualitate O L ad L B erit, vt Q M ad M E, ſed B L ad L N eſt, vt E
              <lb/>
            M ad M P, cum ex ſuppoſitione ſectiones ſint ſimiles; </s>
            <s xml:id="echoid-s7391" xml:space="preserve">ergo O L ad L N
              <lb/>
            eſt, vt Q M ad M P; </s>
            <s xml:id="echoid-s7392" xml:space="preserve">ſuntque L, M duo anguli recti: </s>
            <s xml:id="echoid-s7393" xml:space="preserve">ergo anguli O, </s>
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