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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[61.] LEMMA VII.
Page: 69 (31)
[62.] SECTIO OCTAVA Continens Prop. IL. L. LI. LII. LIII. Apoll.
Page: 70 (32)
[63.] PROPOSITIO IL. & L.
Page: 71 (33)
[64.] PROPOSITIO LI.
Page: 72 (34)
[65.] PROPOSITIO LII. LIII.
Page: 73 (35)
[66.] PROPOSITIO LIV. LV.
Page: 77 (39)
[67.] PROPOSITIO LVI.
Page: 77 (39)
[68.] PROPOSITIO LVII.
Page: 78 (40)
[69.] Notæ in Propoſit. IL. L.
Page: 78 (40)
[70.] Notæ in Propoſit. LI.
Page: 79 (41)
[71.] Demonſtratio ſecundæ partis. PROPOSITIONIS LI.
Page: 81 (43)
[72.] Notæ in Propoſ. LII. LIII.
Page: 83 (45)
[73.] Secunda pars buius propoſitionis, quam Apollonius non expoſuit hac ratione ſuppleri poteſt.
Page: 87 (49)
[74.] Notæ in Propoſ. LIV. LV.
Page: 92 (54)
[75.] Notæ in Propoſit. LVI.
Page: 93 (55)
[76.] LEMMA VIII.
Page: 95 (57)
[77.] Notæ in Propoſ. LVII.
Page: 96 (58)
[78.] SECTIO NONA Continens Propoſ. LVIII. LIX. LX. LXI. LXII. & LXIII.
Page: 98 (60)
[79.] PROPOSITIO LVIII.
Page: 98 (60)
[80.] PROPOSITIO LIX. LXII. & LXIII.
Page: 98 (60)
[81.] PROPOSITIO LX.
Page: 100 (62)
[82.] PROPOSITIO LXI.
Page: 100 (62)
[83.] Notæ in Propoſit. LVIII.
Page: 101 (63)
[84.] Notæ in Propoſit. LIX. LXII. & LXIII.
Page: 102 (64)
[85.] Notæ in Propoſit. LX.
Page: 103 (65)
[86.] Notæ in Propoſit. LXI.
Page: 103 (65)
[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.
Page: 105 (67)
[88.] PROPOSITIO XXXXIV.
Page: 105 (67)
[89.] PROPOSITIO XXXXV.
Page: 106 (68)
[90.] Notæ in Propoſ. XXXXIV.
Page: 106 (68)
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            aggregato differentiali ab-
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            ſciſſarum ramorum I L, I
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            M ab abſciſſa rami breuiſ-
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            ſimi.</s>
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          <p style="it">
            <s xml:id="echoid-s1470" xml:space="preserve">Pari modo in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s1471" xml:space="preserve">ellipſi quadratum I L ſu-
              <lb/>
            perat quadratum I M eodẽ
              <lb/>
            exceſſu, quo exemplar ap-
              <lb/>
              <note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">Ex 9. 10. h.</note>
            plicatum ad H P ſuperat
              <lb/>
            exemplar applicatum ad H
              <lb/>
            L; </s>
            <s xml:id="echoid-s1472" xml:space="preserve">ſed differentia exem-
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            plarium applicatorum ad H
              <lb/>
            P, & </s>
            <s xml:id="echoid-s1473" xml:space="preserve">H Q æqualis eſt re-
              <lb/>
            ctangulo ſub P Q exceſſu
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            differentiali, & </s>
            <s xml:id="echoid-s1474" xml:space="preserve">recta linea
              <lb/>
            compoſita ex X m, & </s>
            <s xml:id="echoid-s1475" xml:space="preserve">u l, ad quam ſumma
              <lb/>
            differentialis P H Q eandem proportionem
              <lb/>
              <figure xlink:label="fig-0062-02" xlink:href="fig-0062-02a" number="36">
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            habet, quam latus trãſuerſum ad ſummam
              <lb/>
            in hyperbola, & </s>
            <s xml:id="echoid-s1476" xml:space="preserve">ad differentiam in ellipſi
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            laterum tranſuerſi, & </s>
            <s xml:id="echoid-s1477" xml:space="preserve">recti, vt in nota
              <lb/>
            propoſitionis 5. </s>
            <s xml:id="echoid-s1478" xml:space="preserve">oſtenſum eſt; </s>
            <s xml:id="echoid-s1479" xml:space="preserve">igitur quadra-
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            tum I L ſuperat quadratum I M iam dicto
              <lb/>
            rectangulo ſub P Q, & </s>
            <s xml:id="echoid-s1480" xml:space="preserve">ſub X m, & </s>
            <s xml:id="echoid-s1481" xml:space="preserve">u l,
              <lb/>
            quod erat oſtendendum.</s>
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          <head xml:id="echoid-head76" xml:space="preserve">SECTIO IV.</head>
          <head xml:id="echoid-head77" xml:space="preserve">Continens Propoſit. VII.
            <lb/>
          & XII. Apollonij.</head>
          <p>
            <s xml:id="echoid-s1483" xml:space="preserve">SIfuerit menſura A
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            D minor com-
              <lb/>
              <note position="right" xlink:label="note-0062-02" xlink:href="note-0062-02a" xml:space="preserve">a</note>
            parata A E, (12.) </s>
            <s xml:id="echoid-s1484" xml:space="preserve">aut
              <lb/>
            ſit pars lineæ breuiſſi-
              <lb/>
            mæ, & </s>
            <s xml:id="echoid-s1485" xml:space="preserve">axis in ellipſi
              <lb/>
            ſit maior, erit A D
              <lb/>
            breuiſſimus ramorum
              <lb/>
            egredientium ex ori-
              <lb/>
            gine eius in omnibus
              <lb/>
            ſectionibus, vt ſunt F
              <lb/>
            D, G D, B D, C D,
              <lb/>
            & </s>
            <s xml:id="echoid-s1486" xml:space="preserve">proximior illi minor eſt remotiore, nempe F D quam G D, & </s>
            <s xml:id="echoid-s1487" xml:space="preserve">G
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            D, quàm B D.</s>
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