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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[91.] Notæ in Propoſ. XLV.
Page: 107 (69)
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
Page: 108 (70)
[93.] PROPOSITIO LXX.
Page: 109 (71)
[94.] PROPOSITIO LXXI.
Page: 109 (71)
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
Page: 109 (71)
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
Page: 110 (72)
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
Page: 111 (73)
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
Page: 112 (74)
[99.] PROPOSITIO LXVI.
Page: 113 (75)
[100.] PROPOSITIO LXVII.
Page: 114 (76)
[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)
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              <pb o="349" file="0387" n="388" rhead="Conicor. Lib. VII."/>
            tri figuræ P Q minus eſt quadrato diametri figuræ I L, & </s>
            <s xml:id="echoid-s12126" xml:space="preserve">quadratum
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            diametri figuræ I L minus eſt quadrato diametri figuræ A C. </s>
            <s xml:id="echoid-s12127" xml:space="preserve">Ponãtur
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            poſtea diametri S T, & </s>
            <s xml:id="echoid-s12128" xml:space="preserve">γ O vltra diametrum P Q, ſitque A X ordinatim
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            applicata ad diametrum S T, & </s>
            <s xml:id="echoid-s12129" xml:space="preserve">V X ad axim perpendicularis ſit, oſten-
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            detur (quemadmodum in præcedentibus dictum eſt) quod diameter fi-
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            guræ P Q minor ſit diametro figuræ S T, & </s>
            <s xml:id="echoid-s12130" xml:space="preserve">diameter figuræ S T minor
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            ſit diametro figuræ γ O, vbicunque ſecet ad axim perpendicularis X V
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            ipſam A C. </s>
            <s xml:id="echoid-s12131" xml:space="preserve">Et hoc erat oſtendendum.</s>
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        <div xml:id="echoid-div1041" type="section" level="1" n="330">
          <head xml:id="echoid-head408" xml:space="preserve">In Sectionem IX. Propoſit. XXXXI.
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          XXXXVII. & XXXXVIII.</head>
          <head xml:id="echoid-head409" xml:space="preserve">LEMMA. XIII.</head>
          <p style="it">
            <s xml:id="echoid-s12133" xml:space="preserve">Sl recta linea G H ſecetur bifariam in D, & </s>
            <s xml:id="echoid-s12134" xml:space="preserve">non bifariam in O,
              <lb/>
            E, atque fiat G a æqualis H E; </s>
            <s xml:id="echoid-s12135" xml:space="preserve">ſi quidem proportio dupli O H
              <lb/>
            ad H G eadem fuerit proportioni G H ad H E, erit duplum rectan-
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            guli ex differentia ipſarum E H, G O in H O æquale quadratis ex G
              <lb/>
            O, & </s>
            <s xml:id="echoid-s12136" xml:space="preserve">ex O H: </s>
            <s xml:id="echoid-s12137" xml:space="preserve">ſi verò proportio illa maior fueri erit rectangulum ma-
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            ius quadratis; </s>
            <s xml:id="echoid-s12138" xml:space="preserve">& </s>
            <s xml:id="echoid-s12139" xml:space="preserve">ſi eadem proportio fuerit minor, idipſum rectangulum
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            quadratis minus erit.</s>
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            <s xml:id="echoid-s12141" xml:space="preserve">Et primo quia duplum O H
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            ad H G eſt vt G H ad H E,
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            ergo duplum rectanguli O H
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            E æquale erit quadrato ex G
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            H; </s>
            <s xml:id="echoid-s12142" xml:space="preserve">auferatur cõmuniter du-
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            plum rectanguli H O G, quia
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            H O eſt communis rectangulo-
              <lb/>
            rum altitudo, remanet duplũ
              <lb/>
            rectanguli ex differentia ipſa-
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            rum E H, G O, ſeu ex diffe-
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            rentia ipſarum G a, & </s>
            <s xml:id="echoid-s12143" xml:space="preserve">G O
              <lb/>
            in H O, ſeu remanet duplum rectanguli a O H æquale quaàrato H G minus
              <lb/>
            duplo rectanguli G O H: </s>
            <s xml:id="echoid-s12144" xml:space="preserve">huic verò differentiæ æqualia ſunt duo quadrata ex
              <lb/>
            G O, & </s>
            <s xml:id="echoid-s12145" xml:space="preserve">ex H O, ergo duplum rectanguli a O H æquale eſt ſummæ quadrato-
              <lb/>
            rum ex G O, & </s>
            <s xml:id="echoid-s12146" xml:space="preserve">ex O H.</s>
            <s xml:id="echoid-s12147" xml:space="preserve"/>
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            <s xml:id="echoid-s12148" xml:space="preserve">Secundo, quia duplum O H ad H G maiorem proportionem habet, quàm
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            G H ad H E, ergo duplum rectanguli O H E maius erit quadrato G H, & </s>
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              <lb/>
            ablato communiter duplo rectanguli G O H erit duplum rectanguli ex differen-
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            tia ipſarum E H, & </s>
            <s xml:id="echoid-s12150" xml:space="preserve">G O in H O maius, quàm ſumma quadratorum ex G O,
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            & </s>
            <s xml:id="echoid-s12151" xml:space="preserve">ex H O.</s>
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