Fibonacci's De practica geometrie / edited by Barnabas Hughes.

Format:

Book

Author/Creator:

Fibonacci, Leonardo, approximately 1170-approximately 1240.

Contributor:

Hughes, Barnabas, 1926-

Series:

Sources and studies in the history of mathematics and physical sciences

Standardized Title:

De practica geometrie. English

Language:

English

Latin

Subjects (All):

Geometry--Early works to 1800.

Geometry.

Mathematics, Medieval.

Physical Description:

xxxv, 408 pages : illustrations ; 25 cm.

Place of Publication:

New York : Springer, [2008]

Summary:

Leonardo da Pisa, perhaps better known as Fibonacci (ca. 1170 - ca. 1240), selected the most useful parts of Greco-Arabic geometry for the book known as De practica geometrie. Beginning with the definitions and constructions found early on in Euclid's Elements, Fibonacci instructed his reader how to compute with Pisan units of measure, find square and cube roots, determine dimensions of both rectilinear and curved surfaces and solids, work with tables for indirect measurement, and perhaps finally fire the imagination of builders with analyses of pentagons and decagons. His work exceeded what readers would expect for the topic.

Practical geometry is the name of the craft for medieval landmeasurers, otherwise known as surveyors in modern times. Fibonacci wrote De practica geometrie for these artisans, a fitting complement to Liber abbaci. He had been at work on the geometry project for some time when a friend encouraged him to complete the task, which he did, going beyond the merely practical, as he remarked, "Some parts are presented according to geometric demonstrations, other parts in dimensions after a lay fashion, with which they wish to engage according to the more common practice."

This translation offers a reconstruction of De practica geometrie as the author judges Fibonacci wrote it. In order to appreciate what Fibonacci created, the author considers his command of Arabic, his schooling, and the resources available to him. To these are added the authors own views on translation and remarks about early Renaissance Italian translations. A bibliography of primary and secondary resources follows the translation, completed by an index of names and special words.

Contents:

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

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

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

[pi] [194-200] 154

Arc Lengths and Chords [201-207, 210] 158

Ptolemy's Theorem [208-209, 232] 162

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

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.

Notes:

Includes bibliographical references (pages [399]-406) and index.

ISBN:

0387729305

9780387729305

OCLC:

166357939