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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[101.] PROPOSITIO LXXII.
Page: 115 (77)
[102.] MONITVM.
Page: 116 (78)
[103.] LEMMA IX.
Page: 116 (78)
[104.] LEMMA X.
Page: 116 (78)
[105.] LEMMA XI.
Page: 117 (79)
[106.] Notæ in Propoſ. LXIV. & LXV.
Page: 117 (79)
[107.] Notæ in Propoſ. LXVI.
Page: 120 (82)
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
Page: 120 (82)
[109.] Notæ in Propoſ. LXVII.
Page: 121 (83)
[110.] COROLLARIVM PROPOSIT. LXVII.
Page: 122 (84)
[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
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            <s xml:id="echoid-s8844" xml:space="preserve">
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            nuuntur quidem; </s>
            <s xml:id="echoid-s8845" xml:space="preserve">ſed non efficiuntur minora interuallo quo parallelæ asymptoti
              <lb/>
            diſtant inter ſe; </s>
            <s xml:id="echoid-s8846" xml:space="preserve">ex altera verò parte perueniri poteſt ad interuallum minus
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            quolibet dato. </s>
            <s xml:id="echoid-s8847" xml:space="preserve">Et hoc erat faciendum.</s>
            <s xml:id="echoid-s8848" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8849" xml:space="preserve">Data hyperbola eadem X præcedentis propoſitionis deſcribere duos ſi-
              <lb/>
              <note position="left" xlink:label="note-0274-01" xlink:href="note-0274-01a" xml:space="preserve">PROP.
                <lb/>
              14. Add.</note>
            miles conos, vt idem planum in eis efficiat duas hyperbolas ſimiles da-
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            tæ ſectioni, quæ asymptoticæ ſint, & </s>
            <s xml:id="echoid-s8850" xml:space="preserve">ex vtraque parte ſibi ipſis vici-
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            niores fiant interuallo minori quolibet dato.</s>
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            <s xml:id="echoid-s8852" xml:space="preserve">In quolibet plano fiat angulus A d G æqualis angulo inclinationis diametri,
              <lb/>
            & </s>
            <s xml:id="echoid-s8853" xml:space="preserve">baſis hyperbolæ datæ X, & </s>
            <s xml:id="echoid-s8854" xml:space="preserve">per G d extenſo quolibet alio plano, ducatur in
              <lb/>
            eo recta linea B d C perpendicularis ad G d O, & </s>
            <s xml:id="echoid-s8855" xml:space="preserve">ſumpto quolibet alio puncto
              <lb/>
            b in recta linea B C in plano per B G O extenſo, centris d, & </s>
            <s xml:id="echoid-s8856" xml:space="preserve">b, deſcribãtur
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            duo circuli inter ſe æquales G C O B, & </s>
            <s xml:id="echoid-s8857" xml:space="preserve">S Q P L ſe ſe ſecantes in duobus punctis
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            R, a: </s>
            <s xml:id="echoid-s8858" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s8859" xml:space="preserve">vt latus rectum ad tranſuerſum ſectionis datæ X, ita fiat quadratũ
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            G d ad quadratũ d A, & </s>
            <s xml:id="echoid-s8860" xml:space="preserve">ducatur recta linea A N M parallela ipſi B C, quæ ſecet
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            b N æquidiſtantẽ d A in N, & </s>
            <s xml:id="echoid-s8861" xml:space="preserve">coniungantur rectæ lineæ A B, A C, N L, N Q,
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            & </s>
            <s xml:id="echoid-s8862" xml:space="preserve">fiant A, & </s>
            <s xml:id="echoid-s8863" xml:space="preserve">N vertices duorũ conorũ A B C, N L Q, & </s>
            <s xml:id="echoid-s8864" xml:space="preserve">in eorũ ſuper ficiebus
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            planum M c T æquidiſtans planis A G O, & </s>
            <s xml:id="echoid-s8865" xml:space="preserve">N S P efficiat ſectiones H I K,
              <lb/>
            & </s>
            <s xml:id="echoid-s8866" xml:space="preserve">T V c, quarum diametri D V I genitæ à triangulis A B C, & </s>
            <s xml:id="echoid-s8867" xml:space="preserve">N L Q per
              <lb/>
            axes in eodem plano exiſbentibus ſunt æquidiſtantes axibus conorum A d, N b,
              <lb/>
            propter planorum æquidiſtantiam: </s>
            <s xml:id="echoid-s8868" xml:space="preserve">Dico, eas eſſe hyperbolas quæſitas. </s>
            <s xml:id="echoid-s8869" xml:space="preserve">Qnoniam
              <lb/>
            (propter æquidiſtantiam oppoſitarum linearum) eſt ſpatium A b parallelogram-
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            mum; </s>
            <s xml:id="echoid-s8870" xml:space="preserve">igitur conorum axes A d, N b æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s8871" xml:space="preserve">æquè inclinan-
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            tur ad communem rectam lineam B C Q (propter æquidiſtantiam earundem
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            A d, N b); </s>
            <s xml:id="echoid-s8872" xml:space="preserve">ſuntque æqualium circulorum radij d B, d C, b L, b Q æqua-
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            les inter ſe; </s>
            <s xml:id="echoid-s8873" xml:space="preserve">igitur triangula A B C, N L Q ſimilia ſunt inter ſe, & </s>
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