Editor's Foreword |
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xiii | |
Preface |
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xix | |
Note |
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xxiv | |
Chapter I Banu Musa And The Calculation Of The Volume Of The Sphere And The Cylinder |
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1 | (37) |
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1.1.1 The Banu Masa: dignitaries and learned |
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1 | (6) |
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1.1.2 The mathematical works of the Banu Musa |
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7 | (3) |
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1.1.3 Treatise on the measurement of plane and spherical figures: a Latin translation and a rewritten version by al-Tusi |
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10 | (24) |
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1.1.4 Title and date of the Banu Musa treatise |
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34 | (4) |
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1.2 Mathematical Commentary |
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38 | (35) |
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1.2.1 Organization and structure of the Banfi Musa book |
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38 | (2) |
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1.2.2 The area of the circle |
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40 | (6) |
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1.2.3 The area of the triangle and Hero's formula |
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46 | (1) |
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1.2.4 The surface area of a sphere and its volume |
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47 | (13) |
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1.2.5 The two-means problem and its mechanical construction |
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60 | (6) |
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1.2.6a The trisection of angles and Pascal's Limacon |
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66 | (3) |
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1.2.6b Approximating cubic roots |
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69 | (4) |
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1.3 Translated Text: On the Knowledge of the Measurement of Plane and Spherical Figures |
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73 | (40) |
Chapter II Thabit Ibn Qurra And His Works In Infinitesimal Mathematics |
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113 | (17) |
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2.1.1 Thabit ibn Qurra: from Harran to Baghdad |
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113 | (9) |
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2.1.2 The works of Thabit ibn Qurra in infinitesimal mathematics |
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122 | (2) |
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2.1.3 History of the texts and their translations |
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124 | (6) |
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2.2 Measuring The Parabola |
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130 | (79) |
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2.2.1 Organization and structure of Ibn Qurra's treatise |
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130 | (3) |
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2.2.2 Mathematical commentary |
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133 | (36) |
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2.2.2.1 Arithmetical propositions |
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133 | (9) |
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2.2.2.2 Sequence of segments and bounding |
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142 | (12) |
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2.2.2.3 Calculation of the area of a portion of a parabola |
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154 | (15) |
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2.2.3 Translated text: On the Measurement of the Conic Section Called Parabola |
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169 | (40) |
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2.3 Measuring The Paraboloid |
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209 | (124) |
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2.3.1 Organization and structure of Ibn Qurra's treatise |
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209 | (5) |
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2.3.2 Mathematical commentary |
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214 | (47) |
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2.3.2.1 Arithmetical propositions |
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214 | (4) |
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2.3.2.2 Extension to sequences of segments |
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218 | (5) |
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2.3.2.3 Volumes of cones, rhombuses and other solids |
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223 | (7) |
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2.3.2.4 Property of four segments |
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230 | (1) |
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2.3.2.5 Arithmetical propositions |
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231 | (2) |
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2.3.2.6 Sequence of segments and bounding |
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233 | (11) |
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2.3.2.7 Calculation of the volumes of paraboloids |
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244 | (12) |
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2.3.2.8 Parallel between the treatise on the area of the parabola and the treatise on the volume of the paraboloid |
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256 | (5) |
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2.3.3 Translated text: On the Measurement of the Paraboloids |
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261 | (72) |
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2.4 On The Sections Of The Cylinder And Its Lateral Surface |
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333 | (126) |
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333 | (4) |
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2.4.2 Mathematical commentary |
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337 | (44) |
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2.4.2.1 Plane sections of the cylinder |
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337 | (4) |
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2.4.2.2 Area of an ellipse and elliptical sections |
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341 | (15) |
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2.4.2.3 Concerning the maximal section of the cylinder and concerning its minimal sections |
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356 | (7) |
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2.4.2.4 Concerning the lateral area of the cylinder and the lateral area of portions of the cylinder lying between the plane sections touching all sides |
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363 | (18) |
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2.4.3 Translated text: On the Sections of the Cylinder and its Lateral Surface |
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381 | (78) |
Chapter III Ibn Sinan, Critique Of Al-Mahani: The Area Of The Parabola |
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459 | (7) |
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3.1.1 Ibrahim ibn Sian: 'heir' and 'critic' |
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459 | (4) |
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3.1.2 The two versions of The Measurement of the Parabola: texts and translations |
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463 | (3) |
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3.2 Mathematical Commentary |
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466 | (17) |
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3.3.1 On the Measurement of the Parabola |
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483 | (12) |
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3.3.2 On the Measurement of a Portion of the Parabola |
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495 | (8) |
Chapter IV Abu Ja'far Al-Khazin: Isoperimetrics And Isepiphanics |
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503 | (4) |
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4.1.1 Al-Khazin: his name, life and works |
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503 | (3) |
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4.1.2 The treatises of al-Khazin on isoperimeters and isepiphanics |
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506 | (1) |
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4.2 Mathematical Commentary |
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507 | (44) |
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507 | (2) |
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509 | (15) |
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524 | (22) |
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4.2.4 The opuscule of al-Sumaysati |
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546 | (5) |
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4.3.1 Commentary on the First Book of the Almagest |
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551 | (26) |
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4.3.2 The Surface of any Circle is Greater than the Surface of any Regular Polygon with the Same Perimeter (al-Sumaysati) |
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577 | (2) |
Chapter V Al-Quhi, Critique Of Thabit: Volume Of The Paraboloid Of Revolution |
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579 | (9) |
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5.1.1 The mathematician and the artisan |
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579 | (4) |
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5.1.2 The versions of the volume of a paraboloid |
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583 | (5) |
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5.2 Mathematical Commentary |
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588 | (11) |
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5.3.1 On the Determination of the Volume of a Paraboloid |
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599 | (10) |
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5.3.2 On the Volume of a Paraboloid |
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609 | (6) |
Chapter VI Ibn Al-Samh: The Plane Sections Of A Cylinder And The Determination Of Their Areas |
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615 | (8) |
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6.1.1 Ibn al-Samh and Ibn Qurra, successors to al-Hasan ibn Musa |
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615 | (3) |
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6.1.2 Serenus of Antinoupolis, al-Hasan ibn Musa, Thabit ibn Qurra and Ibn al-Sant |
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618 | (4) |
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6.1.3 The structure of the study by Ibn al-Samh |
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622 | (1) |
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6.2 Mathematical Commentary |
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623 | (44) |
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6.2.1 Definitions and accepted results |
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623 | (3) |
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626 | (1) |
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6.2.3 The plane sections of a cylinder |
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627 | (1) |
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6.2.4 The properties of a circle |
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628 | (4) |
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6.2.5 Elliptical sections of a right cylinder |
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632 | (7) |
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6.2.6 The ellipse as a plane section of a right cylinder |
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639 | (6) |
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6.2.7 The area of an ellipse |
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645 | (8) |
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6.2.8 Chords and sagittas of the ellipse |
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653 | (14) |
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6.3 Translated Text: On the Cylinder and its Plane Section |
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667 | (54) |
Chapter VII Ibn Hud: The Measurement Of The Parabola And The Isoperimetric Problem |
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721 | (8) |
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7.1.1 Kitab al-Istikmal, a mathematical compendium |
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721 | (6) |
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7.1.2 Manuscript transmission of the texts |
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727 | (2) |
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7.2 The Measurement Of The Parabola |
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729 | (26) |
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7.2.1 Infinitesimal property or conic property |
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729 | (4) |
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7.2.2 Mathematical commentary on Propositions 18-21 |
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733 | (16) |
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7.2.3 Translation: Kitab al-Istikmal |
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749 | (6) |
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7.3 The Isoperimetric Problem |
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755 | (12) |
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7.3.1 An extremal property or a geometric property |
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755 | (3) |
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7.3.2 Mathematical commentary on Propositions 16 and 19 |
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758 | (6) |
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7.3.3 Translation: Kitab al-Istikmal |
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764 | |
Supplementary Notes |
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The Formula of Hero of Alexandria according to Thabit ibn Qurra |
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767 | (1) |
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Commentary of Ibn Abi Jarrada on The Sections of the Cylinder by Thabit ibn Qurra |
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767 | (12) |
Bibliography |
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779 | (14) |
Indexes |
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793 | (4) |
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797 | (8) |
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805 | |