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.
Page: 199 (161)
[202.] COROLLARIVM II.
Page: 199 (161)
[203.] Notæ in Propoſit. XI.
Page: 203 (165)
[204.] Notæ in Propoſit. XII.
Page: 204 (166)
[205.] Notæ in Propoſit. XIII.
Page: 205 (167)
[206.] Notæ in Propoſit. XIV.
Page: 206 (168)
[207.] SECTIO QVINTA Continens ſex Propoſitiones Præmiſſas, PROPOSITIO I. II. III. IV. & V.
Page: 206 (168)
[208.] PROPOSITIO Præmiſſa VI.
Page: 209 (171)
[209.] Notæ in Propoſit. Præmiſſas I. II. III. IV. & V.
Page: 209 (171)
[210.] Notæ in Propoſit. Præmiſſ. VI.
Page: 212 (174)
[211.] SECTIO SEXTA Continens Propoſit. XV. XVI. & XVII. PROPOSITIO XV.
Page: 213 (175)
[212.] PROPOSITIO XVI.
Page: 215 (177)
[213.] PROPOSITIO XVII.
Page: 216 (178)
[214.] Notæ in Propoſit. XV.
Page: 219 (181)
[215.] MONITVM.
Page: 221 (183)
[216.] LEMMA VI.
Page: 221 (183)
[217.] LEMMA VII.
Page: 222 (184)
[218.] LEMMA VIII.
Page: 224 (186)
[219.] Notæ in Propoſit. XVI.
Page: 225 (187)
[220.] Notæ in Propoſit. XVII.
Page: 226 (188)
[221.] SECTIO SEPTIMA Continens Propoſit. XVIII. & XIX.
Page: 229 (191)
[222.] Notæ in Propoſit. XVIII. & XIX.
Page: 230 (192)
[223.] SECTIO OCTAVA Continens Propoſit. XX. & XXI. Apollonij. PROPOSITIO XX.
Page: 231 (193)
[224.] PROPOSITIO XXI.
Page: 233 (195)
[225.] PROPOSITIO XXII.
Page: 235 (197)
[226.] PROPOSITIO XXIII.
Page: 236 (198)
[227.] PROPOSITIO XXIV.
Page: 236 (198)
[228.] Notæ in Propoſit. XX.
Page: 237 (199)
[229.] Notæ in Propoſit. XXI.
Page: 241 (203)
[230.] Notæ in Propoſit. XXII.
Page: 243 (205)
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            perpendicularis eſt ad circuli diametrum C A, & </s>
            <s xml:id="echoid-s9905" xml:space="preserve">propterea A D, planorum
              <lb/>
            H A I, & </s>
            <s xml:id="echoid-s9906" xml:space="preserve">A C M communis ſectio, tanget circulum A C, & </s>
            <s xml:id="echoid-s9907" xml:space="preserve">ideo ſuperficiem
              <lb/>
            ipſam conicam, & </s>
            <s xml:id="echoid-s9908" xml:space="preserve">ſectionem in ea exiſtentem continget; </s>
            <s xml:id="echoid-s9909" xml:space="preserve">& </s>
            <s xml:id="echoid-s9910" xml:space="preserve">diameter A L non
              <lb/>
            erit perpendicularis ad tangentem, ſeu ordinatim applicatam A D per verticem
              <lb/>
            A, alias A L eſſet axis, quod non ponitur. </s>
            <s xml:id="echoid-s9911" xml:space="preserve">Deinde in plano D A B ex A du-
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            catur recta linea A E perpendicularis ad A D ſupra, vel infra circulum, & </s>
            <s xml:id="echoid-s9912" xml:space="preserve">
              <lb/>
            vertice quolibet puncto E ſumpto in recta linea A E, & </s>
            <s xml:id="echoid-s9913" xml:space="preserve">baſi circulo A C M fiat
              <lb/>
            alter conus E A C, in cuius ſuperficie planũ D A H I deſignet ſectionẽ F A G, & </s>
            <s xml:id="echoid-s9914" xml:space="preserve">
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            in ea triangulum per axim E A C efficiat diametrum A K: </s>
            <s xml:id="echoid-s9915" xml:space="preserve">Et quia eadem re-
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            cta linea D A perpendicularis eſt ad A C, atque ad A E ſe ſecantes in A; </s>
            <s xml:id="echoid-s9916" xml:space="preserve">ergo
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            D A perpendicularis eſt ad planum C E A, atque planum D A C extenſum
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            per perpendicularem D A, erit quoque perpendiculare ad planum trianguli per
              <lb/>
            axim C E A, quare triangulum per axim efficiet diametrum A K, quæ erit
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            axis ſectionis F A G, atque D A perpendicularis erit ad axim A K exiſtentem
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            in plano C E A, ad quod D A eſt perpendicularis, & </s>
            <s xml:id="echoid-s9917" xml:space="preserve">cum ea conuenit: </s>
            <s xml:id="echoid-s9918" xml:space="preserve">quare
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            D A ordinatim ad axim applicata perverticem A tanget ſectionem F A G, quæ
              <lb/>
              <note position="right" xlink:label="note-0301-01" xlink:href="note-0301-01a" xml:space="preserve">32. lib. I.</note>
            prius in eodem puncto A tangebat ſectionem H A I in eodem plano exiſtentem;
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            <s xml:id="echoid-s9919" xml:space="preserve">& </s>
            <s xml:id="echoid-s9920" xml:space="preserve">propterea eadem recta A D vtramque ſectionem tangit in puncto A. </s>
            <s xml:id="echoid-s9921" xml:space="preserve">Poſtea
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            coniungatur recta linea B E, & </s>
            <s xml:id="echoid-s9922" xml:space="preserve">quia rectæ lineæ B A, A D, A E ſunt in eo-
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            dem plano tangente vtrumque conum (cum per vertices B, & </s>
            <s xml:id="echoid-s9923" xml:space="preserve">E, atque per D
              <lb/>
            A contingentem circulum baſis communis ducatur) & </s>
            <s xml:id="echoid-s9924" xml:space="preserve">E A, & </s>
            <s xml:id="echoid-s9925" xml:space="preserve">B A angulum
              <lb/>
            conſtituunt, cum E A poſita ſit perpendicularis ad D A, at B A ad eandem ſit
              <lb/>
            inclinata, & </s>
            <s xml:id="echoid-s9926" xml:space="preserve">exiſtunt in eodem plano; </s>
            <s xml:id="echoid-s9927" xml:space="preserve">ergo recta B E parallela eſt, aut ſecat
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            contingentem D A extra circulum vt in D. </s>
            <s xml:id="echoid-s9928" xml:space="preserve">Poterit igitur ex propoſ. </s>
            <s xml:id="echoid-s9929" xml:space="preserve">15. </s>
            <s xml:id="echoid-s9930" xml:space="preserve">addi-
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            tarum duci per rectam B E planum aliud B E M V vtrumq; </s>
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