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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            parallela conſeruantur; </s>
            <s xml:id="echoid-s8729" xml:space="preserve">igitur duæ ſectiones K H M, & </s>
            <s xml:id="echoid-s8730" xml:space="preserve">L X S, exiſtentes in
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            eodem plano ſecante duas ſuperficies, quæ licet in infinitum producantur vbique
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            ſeparatæ ſunt, erunt aſymptoticæ. </s>
            <s xml:id="echoid-s8731" xml:space="preserve">Quartò, quia duæ hyperbolæ H K M, & </s>
            <s xml:id="echoid-s8732" xml:space="preserve">L
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            X S ſunt æquales, ſimiles, & </s>
            <s xml:id="echoid-s8733" xml:space="preserve">ſimiliter poſitæ circa communem diametrum H X
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              <note position="right" xlink:label="note-0271-01" xlink:href="note-0271-01a" xml:space="preserve">Prop. 7.
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            I, earum diſtantiæ ſemper magis, ac magis diminuuntur; </s>
            <s xml:id="echoid-s8734" xml:space="preserve">nunquam tamen mi-
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            nores efſici poſſunt interuallo duarum æquidiſtantium, hyperbolas continentium.
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            <s xml:id="echoid-s8735" xml:space="preserve">Et hoc erat propoſitum.</s>
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            <s xml:id="echoid-s8737" xml:space="preserve">Data hyperbola X duos conos ſimiles exhibere vt idem planum in eis
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              <note position="right" xlink:label="note-0271-02" xlink:href="note-0271-02a" xml:space="preserve">PROP.
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              13.
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              Addit.</note>
            efficiat duas hyperbolas ſimiles, & </s>
            <s xml:id="echoid-s8738" xml:space="preserve">æquales datæ, quæ aſymptoticæ ſint,
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            & </s>
            <s xml:id="echoid-s8739" xml:space="preserve">ex vna parte ſibi ipſis viciniores fiant interuallo minori quolibet da-
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            to: </s>
            <s xml:id="echoid-s8740" xml:space="preserve">ex altera verò parte ad ſe ipſas propius accedant interuallo tamen
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            maiore dato: </s>
            <s xml:id="echoid-s8741" xml:space="preserve">oportet autem vt angulus ab aſymptotis ſectionis X con-
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            <s xml:id="echoid-s8743" xml:space="preserve">In quolibet @l@no fiat angulus A d O æqualis angulo inclinationis diametri,
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            <s xml:id="echoid-s8745" xml:space="preserve">& </s>
            <s xml:id="echoid-s8746" xml:space="preserve">per o d extenſo quolibet alio planol, ducatur in eo re-
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            <s xml:id="echoid-s8747" xml:space="preserve">ſumpto quolibet alio puncto b in
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            recta linea G O in plano per B G C O ducto, centris d, & </s>
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