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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[161.] IV.
[163.] VI.
[164.] VII.
[165.] VIII.
[166.] IX.
[167.] NOTÆ.
[168.] MONITVM.
[169.] SECTIO PRIMA Continens Propoſit. I. II. IV. & X. PROPOSITIO I.
[170.] PROPOSITIO II.
[171.] PROPOSITIO IV.
[172.] PROPOSITIO X.
[173.] Notæ in Propoſit. I.
[174.] Notæ in Propoſit. II.
[175.] Notæ in Propoſit. IV.
[176.] Notæ in Propoſit. X.
[177.] SECTIO SECVNDA Continens Propoſit. III. VI. VII. & IX. PROPOSITIO III.
[178.] PROPOSITIO VI.
[179.] PROPOSITIO VII.
[180.] PROPOSITIO IX.
[181.] Notæ in Propoſit. III.
[182.] Notæ in Propoſit. VI.
[183.] Notæ in Propoſit. VII.
[184.] Notæ in Propoſit. IX.
[185.] LEMMAI.
[186.] SECTIO TERTIA Continens Propoſit. V. & VIII. PROPOSITIO V.
[187.] PROPOSITIO VIII.
[188.] Notæ in Propoſit. V.
[189.] Notæ in Propoſit. VIII.
[190.] SECTIO QVARTA Continens Propoſit. XI. XII. XIII. & XIV. PROPOSITIO XI.
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            <s xml:id="echoid-s8728" xml:space="preserve">
              <pb o="233" file="0271" n="271" rhead="Conicor. Lib. VI."/>
            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
              <lb/>
            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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              addit.</note>
            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.
                <lb/>
              13.
                <lb/>
              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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            tentus ſit acutus.</s>
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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>
            <s xml:id="echoid-s8744" xml:space="preserve">baſis hyperb l@ X; </s>
            <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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            cta linea B d C perpendicularis ad O d G, & </s>
            <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>
            <s xml:id="echoid-s8748" xml:space="preserve">b deſcribantur </s>
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