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

Table of contents

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[201.] COROLLARIVM I.
[202.] COROLLARIVM II.
[203.] Notæ in Propoſit. XI.
[204.] Notæ in Propoſit. XII.
[205.] Notæ in Propoſit. XIII.
[206.] Notæ in Propoſit. XIV.
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
[208.] PROPOSITIO Præmiſſa VI.
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
[210.] Notæ in Propoſit. Præmiſſ. VI.
[211.] SECTIO SEXTA Continens Propoſit. XV. XVI. & XVII. PROPOSITIO XV.
[212.] PROPOSITIO XVI.
[213.] PROPOSITIO XVII.
[214.] Notæ in Propoſit. XV.
[215.] MONITVM.
[216.] LEMMA VI.
[217.] LEMMA VII.
[218.] LEMMA VIII.
[219.] Notæ in Propoſit. XVI.
[220.] Notæ in Propoſit. XVII.
[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.
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            vel hyperbolæ, nec habent baſes, à quibus circumſcribantur, igitur in ſectionibus
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            ſimilibus A B, & </s>
            <s xml:id="echoid-s6398" xml:space="preserve">G F homolegæ axium abſciſſæ B C, F H non ſupponuntur iam
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            dißectæ, & </s>
            <s xml:id="echoid-s6399" xml:space="preserve">determinatæ; </s>
            <s xml:id="echoid-s6400" xml:space="preserve">quare poßunt eße cuiuſcunque menſuræ, & </s>
            <s xml:id="echoid-s6401" xml:space="preserve">habere poſ-
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            ſunt eandem, & </s>
            <s xml:id="echoid-s6402" xml:space="preserve">non eandem proportionem ad conterminas potentiales; </s>
            <s xml:id="echoid-s6403" xml:space="preserve">& </s>
            <s xml:id="echoid-s6404" xml:space="preserve">ideo
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            ad vitandam incertitudinem adiungi debet determinatio, quod prædictæ homo-
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            logæ abſcißæ B C, F H proportionales ſint lateribus rectis B D, F I, at in ſeg-
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            mentis, ſeu portionibus ſectionum conicarum ſimilium inutilis omnino eßet illa
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            determinatio. </s>
            <s xml:id="echoid-s6405" xml:space="preserve">An verò hæc mea ſententia omninò reijci debeat alijs iudicandũ
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            relinquo.</s>
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          <head xml:id="echoid-head257" xml:space="preserve">Notæ in Propoſit. XI.</head>
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            <s xml:id="echoid-s6407" xml:space="preserve">CVmque B C ad B L poſita ſit vt H F ad F N, &</s>
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            <s xml:id="echoid-s6409" xml:space="preserve">Quia inuertendo
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            D B ad B C eandem proportionem habet quàm I F ad F H, & </s>
            <s xml:id="echoid-s6410" xml:space="preserve">C B ad B
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            L eſt vt H F ad F N; </s>
            <s xml:id="echoid-s6411" xml:space="preserve">ergo ex æquali ordinata D B ad B L eandem proportio-
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            nem habebit, quàm I F ad F N; </s>
            <s xml:id="echoid-s6412" xml:space="preserve">eſtque ordinatim applicata Q L media pro.
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            portionatis inter abſciſſam B L, & </s>
            <s xml:id="echoid-s6414" xml:space="preserve">latus rectum B D ( cum in parabola quadra-
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            tum Q L æquale ſit rectangulo L B D ) pariterque X N media proportionalis eſt
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              <note position="right" xlink:label="note-0203-02" xlink:href="note-0203-02a" xml:space="preserve">11. lib. I.</note>
            inter F N, & </s>
            <s xml:id="echoid-s6415" xml:space="preserve">I F; </s>
            <s xml:id="echoid-s6416" xml:space="preserve">ergo Q L ad L B eſt vt X N ad N F, & </s>
            <s xml:id="echoid-s6417" xml:space="preserve">antecedentium,
              <lb/>
            duplæ, ſcilicet Q R ad L B, atque X r
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            ad N F in eadem ratione erunt. </s>
            <s xml:id="echoid-s6418" xml:space="preserve">Non
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            ſecus oſtendetur O P ad K B vt T V ad M F.</s>
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