Fibonacci's "De Practica Geometrie":
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
2008
|
| Schriftenreihe: | Sources and studies in the history of mathematics and physical sciences
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXXV, 406 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387729305 9780387729312 |
Internformat
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| 300 | |a XXXV, 406 S. |b graph. Darst. |c 235 mm x 155 mm | ||
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| 490 | 0 | |a Sources and studies in the history of mathematics and physical sciences | |
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Datensatz im Suchindex
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| adam_text | Table of Contents
Foreword............................................ vii
Preface.............................................. ix
Notation............................................. xv
Background......................................... xvii
Fibonacci s Knowledge of Arabic......................... xviii
Fibonacci s Schooling................................. xxi
Fibonacci s Basic Resources............................ xxii
Sources for the Translation............................. xxvi
The Translation.....................................xxviii
Italian Translations.................................. xxx
Conclusion.........................................xxxiv
Prologue and Introduction............................... 1
Commentary and Sources................................ 1
Text............................................... 4
Definitions [1]...................................... 5
Properties of Figures [2]............................... 5
Geometric Constructions [3]............................ 6
Axioms [4]......................................... 6
Pisan Measures [5]................................... 7
Computing with Measures [6-8].......................... 7
1 Measuring Areas of Rectangular Fields................... 11
Commentary and Sources................................ 11
Text............................................... 14
1.1 Area of Squares [1]................................ 14
1.2 Areas of Rectangles............................... 14
Method 1 [2-30].................................. 14
Method 2 [31-45]................................. 26
1.2 Keeping Count with Feet [13]........................ 17
2 Finding Roots of Numbers............................ 35
Commentary and Sources................................ 35
Text............................................... 38
2.1 Finding Square Roots.............................. 38
xii Table of Contents
Integral Roots [1-22]............................... 38
Irrational Roots [23-24]............................. 48
Fractional Roots [40-42]............................ 55
2.2 Operating with Roots.............................. 49
Multiplication [25-27].............................. 49
Addition [28-32].................................. 50
Subtraction [33-37]................................ 53
Division [38-39].................................. 54
3 Measuring All Kinds of Fields.......................... 57
Commentary and Sources................................ 57
Text............................................... 65
3.1 Measuring Triangles............................... 65
General [1-6].................................... 65
Pythagorean Theorem [7-8].......................... 68
Right Triangles [9-13].............................. 69
Acute Triangles [14-25]............................. 71
Oblique Triangles [26-41]........................... 77
Hero s Theorem [31]............................... 80
Surveyors Method [42-43]........................... 87
Ratios/Properties of Triangles [44]..................... 88
Lines Falling Within a Single Triangle [44-49]............ 88
Lines Falling Outside a Single Triangle [50-67]............ 90
Composition of Ratios [68].......................... 99
Excision of Ratios [69].............................. 100
Conjunction of Ratios [70-78]........................ 100
Combination of Ratios [79-82]........................ 104
3.2 Measuring Quadrilaterals........................... 106
General [83]..................................... 106
Algebraic/Geometric Model [84-94].................... 106
Squares [95-96]................................... 112
Algebraic Method [97-106].......................... 113
Rectangles [107-138]............................... 116
Multiple Solutions [139-146]......................... 128
Other Quadrilaterals [147]........................... 131
Rhombus [148-164]................................ 131
Rhomboids [165-168].............................. 137
Trapezoids...................................... 139
Concave Quadrilaterals [182]......................... 147
Convex Quadrilaterals [182].......................... 147
3.3 Measuring Multisided Fields [183-187].................. 147
3.4 Measuring the Circle and Its Parts..................... 151
Areas [188-193].................................. 151
Ji [194-200]..................................... 154
Arc Lengths and Chords [201-207, 210]................. 158
Ptolemy s Theorem [208-209, 232]..................... 162
Table of Contents xiii
Sectors and Segments [220-226]....................... 163
Inscribed Figures [227-231, 233-239]................... 166
3.5 Measuring Fields on Mountain Sides [240-247]............ 174
Archipendium [242]................................ 174
4 Dividing Fields Among Partners........................ 181
Commentary and Sources................................ 181
Text................................................ 185
4.1 Multisided Figures................................ 186
Triangles [1-26].................................. 186
Parallelograms [27-31]............................. 205
Trapezoids [32-56]................................ 211
Quadrilaterals With Unequal Sides [57-64, 66-69].......... 230
Squares [65]..................................... 237
Pentagons [70-75]................................. 242
4.2 Circles......................................... 246
General [76-81].................................. 246
Semicircles [82-83, 85].............................. 250
Segments [84, 86]................................. 251
5 Finding Cube Roots................................. 255
Commentary and Sources................................ 255
Text............................................... 259
5.1 Finding Cube Roots [1-11].......................... 259
5.2 Finding Numbers in Continued Proportions.............. 265
Archytas Method [12].............................. 265
Philo s Method [13]................................ 267
Plato s Method [14-15]............................. 268
5.3 Computing with Cube Roots......................... 270
Multiplication [16]................................ 270
Division [17]..................................... 271
Addition and Subtraction [18-23]...................... 271
6 Finding Dimensions of Bodies.......................... 275
Commentary and Sources................................ 275
Text............................................... 277
6.1 Definitions [1-3].................................. 277
Euclidean Resources [4-10].......................... 278
Various Areas and Volumes.......................... 282
Parallelepipeds [11-18]............................. 282
Wedge [19-20]................................... 287
Column [21-25].................................. 289
6.2 Pyramids [26-41, 44]............................... 292
Cones [42-43].................................... 305
6.3 Spheres [45-53]................................... 308
xiv Table of Contents
Surface Area and Volume [54-60]...................... 319
Inscribed Cube [61-67]............................. 324
Ratios of Volumes [68-73]........................... 330
Other Solids [74. 76-84]............................ 333
6.4 Divide a Line in Mean and Extreme Ratio [75]............ 335
7 Measuring Heights, Depths, and Longitude of Planets......... 343
Commentary and Sources................................ 343
Text.............................................. . 346
7.1 Different Heights [1-3].............................. 346
7.2 Tools: Triangle [4]................................ 348
Quadrant [5-9]................................... 349
7.3 Table of Arcs and Chords [211-219].................... 354
8 Geometric Subtleties................................ 361
Commentary and Sources................................ 361
Text............................................... 365
8.1 Pentagons [1-2], [6-7], [10-12], [16-18], [21-22], [25-26]...... 365
8.2 Decagons [3-5], [8-9], [13-15], [19], [23-24[, [27] . .......... 367
8.3 Triangles [20-33*]................................. 377
Appendix Problem with Many Solutions.................... 395
Commentary and Sources................................ 395
Text............................................... 396
Bibliography......................................... 399
Index.............................................. 407
|
| adam_txt |
Table of Contents
Foreword. vii
Preface. ix
Notation. xv
Background. xvii
Fibonacci's Knowledge of Arabic. xviii
Fibonacci's Schooling. xxi
Fibonacci's Basic Resources. xxii
Sources for the Translation. xxvi
The Translation.xxviii
Italian Translations. xxx
Conclusion.xxxiv
Prologue and Introduction. 1
Commentary and Sources. 1
Text. 4
Definitions [1]. 5
Properties of Figures [2]. 5
Geometric Constructions [3]. 6
Axioms [4]. 6
Pisan Measures [5]. 7
Computing with Measures [6-8]. 7
1 Measuring Areas of Rectangular Fields. 11
Commentary and Sources. 11
Text. 14
1.1 Area of Squares [1]. 14
1.2 Areas of Rectangles. 14
Method 1 [2-30]. 14
Method 2 [31-45]. 26
1.2 Keeping Count with Feet [13]. 17
2 Finding Roots of Numbers. 35
Commentary and Sources. 35
Text. 38
2.1 Finding Square Roots. 38
xii Table of Contents
Integral Roots [1-22]. 38
Irrational Roots [23-24]. 48
Fractional Roots [40-42]. 55
2.2 Operating with Roots. 49
Multiplication [25-27]. 49
Addition [28-32]. 50
Subtraction [33-37]. 53
Division [38-39]. 54
3 Measuring All Kinds of Fields. 57
Commentary and Sources. 57
Text. 65
3.1 Measuring Triangles. 65
General [1-6]. 65
Pythagorean Theorem [7-8]. 68
Right Triangles [9-13]. 69
Acute Triangles [14-25]. 71
Oblique Triangles [26-41]. 77
Hero's Theorem [31]. 80
Surveyors' Method [42-43]. 87
Ratios/Properties of Triangles [44]. 88
Lines Falling Within a Single Triangle [44-49]. 88
Lines Falling Outside a Single Triangle [50-67]. 90
Composition of Ratios [68]. 99
Excision of Ratios [69]. 100
Conjunction of Ratios [70-78]. 100
Combination of Ratios [79-82]. 104
3.2 Measuring Quadrilaterals. 106
General [83]. 106
Algebraic/Geometric Model [84-94]. 106
Squares [95-96]. 112
Algebraic Method [97-106]. 113
Rectangles [107-138]. 116
Multiple Solutions [139-146]. 128
Other Quadrilaterals [147]. 131
Rhombus [148-164]. 131
Rhomboids [165-168]. 137
Trapezoids. 139
Concave Quadrilaterals [182]. 147
Convex Quadrilaterals [182]. 147
3.3 Measuring Multisided Fields [183-187]. 147
3.4 Measuring the Circle and Its Parts. 151
Areas [188-193]. 151
Ji [194-200]. 154
Arc Lengths and Chords [201-207, 210]. 158
Ptolemy's Theorem [208-209, 232]. 162
Table of Contents xiii
Sectors and Segments [220-226]. 163
Inscribed Figures [227-231, 233-239]. 166
3.5 Measuring Fields on Mountain Sides [240-247]. 174
Archipendium [242]. 174
4 Dividing Fields Among Partners. 181
Commentary and Sources. 181
Text. 185
4.1 Multisided Figures. 186
Triangles [1-26]. 186
Parallelograms [27-31]. 205
Trapezoids [32-56]. 211
Quadrilaterals With Unequal Sides [57-64, 66-69]. 230
Squares [65]. 237
Pentagons [70-75]. 242
4.2 Circles. 246
General [76-81]. 246
Semicircles [82-83, 85]. 250
Segments [84, 86]. 251
5 Finding Cube Roots. 255
Commentary and Sources. 255
Text. 259
5.1 Finding Cube Roots [1-11]. 259
5.2 Finding Numbers in Continued Proportions. 265
Archytas' Method [12]. 265
Philo's Method [13]. 267
Plato's Method [14-15]. 268
5.3 Computing with Cube Roots. 270
Multiplication [16]. 270
Division [17]. 271
Addition and Subtraction [18-23]. 271
6 Finding Dimensions of Bodies. 275
Commentary and Sources. 275
Text. 277
6.1 Definitions [1-3]. 277
Euclidean Resources [4-10]. 278
Various Areas and Volumes. 282
Parallelepipeds [11-18]. 282
Wedge [19-20]. 287
Column [21-25]. 289
6.2 Pyramids [26-41, 44]. 292
Cones [42-43]. 305
6.3 Spheres [45-53]. 308
xiv Table of Contents
Surface Area and Volume [54-60]. 319
Inscribed Cube [61-67]. 324
Ratios of Volumes [68-73]. 330
Other Solids [74. 76-84]. 333
6.4 Divide a Line in Mean and Extreme Ratio [75]. 335
7 Measuring Heights, Depths, and Longitude of Planets. 343
Commentary and Sources. 343
Text. . 346
7.1 Different Heights [1-3]. 346
7.2 Tools: Triangle [4]. 348
Quadrant [5-9]. 349
7.3 Table of Arcs and Chords [211-219]. 354
8 Geometric Subtleties. 361
Commentary and Sources. 361
Text. 365
8.1 Pentagons [1-2], [6-7], [10-12], [16-18], [21-22], [25-26]. 365
8.2 Decagons [3-5], [8-9], [13-15], [19], [23-24[, [27] . . 367
8.3 Triangles [20-33*]. 377
Appendix Problem with Many Solutions. 395
Commentary and Sources. 395
Text. 396
Bibliography. 399
Index. 407 |
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| index_date | 2024-07-02T19:43:30Z |
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| spelling | Hughes, Barnabas B. Verfasser aut Fibonacci's "De Practica Geometrie" Barnabas Hughes New York Springer 2008 XXXV, 406 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Sources and studies in the history of mathematics and physical sciences Geschichte 1200-1240 gnd rswk-swf Geometry Early works to 1800 Mathematics, Medieval Geometrie (DE-588)4020236-7 gnd rswk-swf Geodäsie (DE-588)4020202-1 gnd rswk-swf (DE-588)4135952-5 Quelle gnd-content Geodäsie (DE-588)4020202-1 s Geometrie (DE-588)4020236-7 s Geschichte 1200-1240 z b DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016300248&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hughes, Barnabas B. Fibonacci's "De Practica Geometrie" Geometry Early works to 1800 Mathematics, Medieval Geometrie (DE-588)4020236-7 gnd Geodäsie (DE-588)4020202-1 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4020202-1 (DE-588)4135952-5 |
| title | Fibonacci's "De Practica Geometrie" |
| title_auth | Fibonacci's "De Practica Geometrie" |
| title_exact_search | Fibonacci's "De Practica Geometrie" |
| title_exact_search_txtP | Fibonacci's "De Practica Geometrie" |
| title_full | Fibonacci's "De Practica Geometrie" Barnabas Hughes |
| title_fullStr | Fibonacci's "De Practica Geometrie" Barnabas Hughes |
| title_full_unstemmed | Fibonacci's "De Practica Geometrie" Barnabas Hughes |
| title_short | Fibonacci's "De Practica Geometrie" |
| title_sort | fibonacci s de practica geometrie |
| topic | Geometry Early works to 1800 Mathematics, Medieval Geometrie (DE-588)4020236-7 gnd Geodäsie (DE-588)4020202-1 gnd |
| topic_facet | Geometry Early works to 1800 Mathematics, Medieval Geometrie Geodäsie Quelle |
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