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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[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.
[251.] II.
[252.] III.
[253.] IV.
[255.] VI.
[256.] VII.
[257.] VIII.
[258.] NOTÆ.
[259.] SECTIO PRIMA Continens Propoſit. I. V. & XXIII. Apollonij. PROPOSITIO I.
[260.] PROPOSITIO V. & XXIII.
[261.] Notæ in Propoſit. I.
[262.] Notæ in Propoſit. V. & XXIII.
[263.] SECTIO SECVNDA Continens Propoſit. II. III. IV. VI. & VII. Apollonij. PROPOSITIO II. & III.
[264.] PROPOSITIO IV.
[265.] PROPOSITIO VI. & VII.
[266.] Notæ in Propoſit. II. III.
[267.] Notæ in Propoſit. IV.
[268.] Notæ in Propoſit. VI. & VII.
[269.] SECTIO TERTIA Continens Propoſit. Apollonij VIII. IX. X. XI. XV. XIX. XVI. XVIII. XVII. & XX.
[270.] Notæ in Propoſit. VIII.
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          <head xml:id="echoid-head347" xml:space="preserve">Notæ in Propoſit. XVII.</head>
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            <s xml:id="echoid-s10595" xml:space="preserve">SIue ad duo quadrata ex I L, & </s>
            <s xml:id="echoid-s10596" xml:space="preserve">I P erit, vt C G in E H ad duo qua-
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            drata E G, & </s>
            <s xml:id="echoid-s10597" xml:space="preserve">E H, &</s>
            <s xml:id="echoid-s10598" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10599" xml:space="preserve">Quoniam I L ad I P erat vt H E ad E G,
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            & </s>
            <s xml:id="echoid-s10600" xml:space="preserve">quadratum I L ad quadratum I P erit vt quadratum H E ad quadratum
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            E G: </s>
            <s xml:id="echoid-s10601" xml:space="preserve">& </s>
            <s xml:id="echoid-s10602" xml:space="preserve">comparando antecedentes ad terminorũ ſummas quadratum I L ad qua-
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            dratum I L vna cum quadrato I P habebit eandem proportionem, quàm qua-
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            dratum H E ad ſummam quadrati H E cum quadrato E G: </s>
            <s xml:id="echoid-s10603" xml:space="preserve">ſed prius quadra-
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            tum A C ad quadratum I L erat vt rectangulum A H E ad quadratum H E;
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            <s xml:id="echoid-s10604" xml:space="preserve">igitur quadratum A C ad ſummam quadrati I L cum quadrato I P eãdem pro-
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            portionem babebit quàm rectangulum A H E ad quadratum E G vna cum qua-
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            drato E H.</s>
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          <head xml:id="echoid-head348" xml:space="preserve">Notæ in Propoſit. XX.</head>
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            <s xml:id="echoid-s10606" xml:space="preserve">SIue ad differentiam duorum quadratorum I L, I P erit, vt C G in H
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            E ad differentiam duorum quadratorum ex H E, & </s>
            <s xml:id="echoid-s10607" xml:space="preserve">ex E G, &</s>
            <s xml:id="echoid-s10608" xml:space="preserve">c.
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            <s xml:id="echoid-s10609" xml:space="preserve">Quoniam vt dictum eſt quadratum I L ad quadratum I P eandem proportionẽ
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            habet, quàm quadratum H E ad quadratum G E, & </s>
            <s xml:id="echoid-s10610" xml:space="preserve">comparando anteceden-
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            tes ad terminorum differentias quadratum I P ad differentiam quadrati I L à
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            quadrato I P eandem proportionem habebit, quàm quadratum H E ad diffe-
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            rentiam inter quadratum H E, & </s>
            <s xml:id="echoid-s10611" xml:space="preserve">quadratum E G: </s>
            <s xml:id="echoid-s10612" xml:space="preserve">eſtque quadratum C A
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            ad quadratum I L, vt rectangulum A H E ad quadratũ H E; </s>
            <s xml:id="echoid-s10613" xml:space="preserve">ergo ex æquali
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            quadratum A C ad quadratorum ex I L, & </s>
            <s xml:id="echoid-s10614" xml:space="preserve">ex I P differentiam eandem pro-
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            portionem habebit, quàm rectangulum A H E ad quadratorum ex E G, & </s>
            <s xml:id="echoid-s10615" xml:space="preserve">ex
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            E H differentiam.</s>
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