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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[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)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
[141.] PROPOSITIO XXXIII. XXXIV.
Page: 163 (125)
[142.] PROPOSITIO XXXV.
Page: 163 (125)
[143.] PROPOSITIO XXXVI.
Page: 164 (126)
[144.] PROPOSITIO XXXVII. XLVI.
Page: 164 (126)
[145.] PROPOSITIO XXXVIII.
Page: 165 (127)
[146.] PR OPOSITIO XXXIX.
Page: 166 (128)
[147.] PROPOSITIO XXXX.
Page: 166 (128)
[148.] PROPOSITIO XXXXVII.
Page: 166 (128)
[149.] PROPOSITIO XXXXVIII.
Page: 167 (129)
[150.] Notæ in Propoſit. XXXII.
Page: 167 (129)
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            C S V cum duplo trianguli F S V; </s>
            <s xml:id="echoid-s4825" xml:space="preserve">ideſt quadratum I B æquale eſt duplo trian-
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            guli I S C cum duplo trianguli F S V; </s>
            <s xml:id="echoid-s4826" xml:space="preserve">& </s>
            <s xml:id="echoid-s4827" xml:space="preserve">quoniam propter parallelas C S, & </s>
            <s xml:id="echoid-s4828" xml:space="preserve">
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            G V, triangulum I C S ſimile eſt iſoſcelio, & </s>
            <s xml:id="echoid-s4829" xml:space="preserve">rectangulo triangulo I G V, erit,
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            quadratum I C æquale duplo trianguli I C S iſoſcelei, & </s>
            <s xml:id="echoid-s4830" xml:space="preserve">rectanguli in C; </s>
            <s xml:id="echoid-s4831" xml:space="preserve">ergo
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            exceſſus quadrati I B ſupra quadratum I C æquale eſt duplo trianguli F S V;
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            <s xml:id="echoid-s4832" xml:space="preserve">eſt verò rectangulum, cuius baſis F S, altitudo verò C G æquale duplo trianguli
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            F S V; </s>
            <s xml:id="echoid-s4833" xml:space="preserve">atque buiuſmodi rectangulum eſt exemplar applicatum ad abſciſſam G
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            C, vt in notis prop. </s>
            <s xml:id="echoid-s4834" xml:space="preserve">16. </s>
            <s xml:id="echoid-s4835" xml:space="preserve">17. </s>
            <s xml:id="echoid-s4836" xml:space="preserve">& </s>
            <s xml:id="echoid-s4837" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4838" xml:space="preserve">litera c. </s>
            <s xml:id="echoid-s4839" xml:space="preserve">oſtenſum eſt igitur quadrati I B
              <lb/>
            exceßus ſupra quadratum I C eſt exemplar applicatum ad abſciſſam G C: </s>
            <s xml:id="echoid-s4840" xml:space="preserve">Simili
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            modo quadratum I K oſtendetur æquale duplo trianguli I C S vna cum duplo
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            trapezij L T S F; </s>
            <s xml:id="echoid-s4841" xml:space="preserve">atque dupli trianguli I C S cum duplo trianguli F S V ex-
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            ceſſus ſupra duplum trianguli I C S cum duplo trapezij L T S F eſt duplum
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            trianguli L T V; </s>
            <s xml:id="echoid-s4842" xml:space="preserve">ergo quadrati I B exceſſus ſupra quadratum I K eſt duplum
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            trianguli L T V, ſeu exemplar applicatum ad G P differentiam abſciſſarum.
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            <s xml:id="echoid-s4843" xml:space="preserve">Poſtea quia triangula ſimilia E C F, E D M ſunt æqualia, cum eorum bomologa
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            latera E C, E D æqualia ſint; </s>
            <s xml:id="echoid-s4844" xml:space="preserve">ergo addito communi triangulo I E V, erit trian-
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            gulum E C F cum triangulo E I V, ſeu triangulũ I C S cum triangulo F S V
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            æquale duobus triaugulis E D M, & </s>
            <s xml:id="echoid-s4845" xml:space="preserve">I E V, ſeu duobus triangulis M V N, & </s>
            <s xml:id="echoid-s4846" xml:space="preserve">
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            N I D: </s>
            <s xml:id="echoid-s4847" xml:space="preserve">erat autem quadratum I B æquale duplo trianguli I C S cum duplo tri-
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            anguli F S V; </s>
            <s xml:id="echoid-s4848" xml:space="preserve">igitur quadratum I B æquale erit duplo trianguli M N V cum
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            duplo trianguli N I D; </s>
            <s xml:id="echoid-s4849" xml:space="preserve">eſtque quadratum I D æquale duplo trianguli iſoſcelei,
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            rectanguli I D N; </s>
            <s xml:id="echoid-s4850" xml:space="preserve">igitur quadratum I B ſuperat quadratum I D, eſtque exceſ-
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            ſus duplum trianguli M N V ſeu exemplar applicatum ad G D. </s>
            <s xml:id="echoid-s4851" xml:space="preserve">Tandem quia
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            quadratum I Q æquale eſt duplo trianguli iſoſcelei rectanguli I Q X, atque
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            quadratum Q A æquale eſt duplo trapezij Q M; </s>
            <s xml:id="echoid-s4852" xml:space="preserve">igitur quadratũ bypotbenuſæ I
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            A æquale eſt duplo trianguli I D N cum duplo trapezij X N M Z; </s>
            <s xml:id="echoid-s4853" xml:space="preserve">ergo exceſ-
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            ſus quadrati I A ſupra quadratnm I D æqualis eſt duplo trapezij X N M Z; </s>
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            ſus autem trianguli N M V ſupra trapezium N Z eſt triangulum X Z V; </s>
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            erat quadrati I B exceſſus ſupra quadratum I D, triangulum ipſum M V N bis
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            ſumptum. </s>
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            <s xml:id="echoid-s4858" xml:space="preserve">Quod autem exemplaria æqualia
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