+612 9045 4394
Fibonacci's de Practica Geometrie : Sources and Studies in the History of Mathematics and Physical Sciences - Barnabas Hughes

Fibonacci's de Practica Geometrie

Sources and Studies in the History of Mathematics and Physical Sciences

Hardcover Published: 1st November 2007
ISBN: 9780387729305
Number Of Pages: 408

Share This Book:


or 4 easy payments of $59.22 with Learn more
Ships in 5 to 9 business days

Other Available Editions (Hide)

  • Paperback View Product Published: 29th November 2010
    Ships in 5 to 9 business days

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 prior Italian translations. A bibliography of primary and secondary resources follows the translation, completed by an index of names and special words.

Industry Reviews

From the reviews:

"This is a translation of a book written in 1223. It was designed for those who had to solve practical problems such as finding areas and roots, measuring fields of all kinds, dividing fields among partners, measuring dimensions of bodies and heights, depths, longitude of planets, etc. It's a joy to read. The translation is charming. ... De practica geometrie belongs in every library that supports graduate mathematics programs and also those that support programs in education." (Donald Cook, Mathematical Reviews, Issue 2008 k)

"In this book Fibonacci not only collected the plane geometry of Euclid but went far beyond. He included the use of trigonometry and algebra to solve geometrical problems ... . Each chapter is accompanied by comments which serve as guidelines through the book. The book can be read with much pleasure. ... Hughes has certainly presented a major scholarly work and ... his translation will be read by many interested mathematicians and historians of science." (Thomas Sonar, Zentralblatt MATH, Vol. 1145, 2008)

Forewordp. vii
Prefacep. ix
Notationp. xv
Backgroundp. xvii
Fibonacci's Knowledge of Arabicp. xviii
Fibonacci's Schoolingp. xxi
Fibonacci's Basic Resourcesp. xxii
Sources for the Translationp. xxvi
The Translationp. xxviii
Italian Translationsp. xxx
Conclusionp. xxxiv
Prologue and Introductionp. 1
Commentary and Sourcesp. 1
Textp. 4
Definitions [1]p. 5
Properties of Figures [2]p. 5
Geometric Constructions [3]p. 6
Axioms [4]p. 6
Pisan Measures [5]p. 7
Computing with Measures [6-8]p. 7
Measuring Areas of Rectangular Fieldsp. 11
Commentary and Sourcesp. 11
Textp. 14
Area of Squares [1]p. 14
Areas of Rectanglesp. 14
Method 1 [2-30]p. 14
Method 2 [31-45]p. 26
Keeping Count with Feet [13]p. 17
Finding Roots of Numbersp. 35
Commentary and Sourcesp. 35
Textp. 38
Finding Square Rootsp. 38
Integral Roots [1-22]p. 38
Irrational Roots [23-24]p. 48
Fractional Roots [40-42]p. 55
Operating with Rootsp. 49
Multiplication [25-27]p. 49
Addition [28-32]p. 50
Subtraction [33-37]p. 53
Division [38-39]p. 54
Measuring All Kinds of Fieldsp. 57
Commentary and Sourcesp. 57
Textp. 65
Measuring Trianglesp. 65
General [1-6]p. 65
Pythagorean Theorem [7-8]p. 68
Right Triangles [9-13]p. 69
Acute Triangles [14-25]p. 71
Oblique Triangles [26-41]p. 77
Hero's Theorem [31]p. 80
Surveyors' Method [42-43]p. 87
Ratios/Properties of Triangles [44]p. 88
Lines Falling Within a Single Triangle [44-49]p. 88
Lines Falling Outside a Single Triangle [50-67]p. 90
Composition of Ratios [68]p. 99
Excision of Ratios [69]p. 100
Conjunction of Ratios [70-78]p. 100
Combination of Ratios [79-82]p. 104
Measuring Quadrilateralsp. 106
General [83]p. 106
Algebraic/Geometric Model [84-94]p. 106
Squares [95-96]p. 112
Algebraic Method [97-106]p. 113
Rectangles [107-138]p. 116
Multiple Solutions [139-146]p. 128
Other Quadrilaterals [147]p. 131
Rhombus [148-164]p. 131
Rhomboids [165-168]p. 137
Trapezoidsp. 139
Concave Quadrilaterals [182]p. 147
Convex Quadrilaterals [182]p. 147
Measuring Multisided Fields [183-187]p. 147
Measuring the Circle and Its Partsp. 151
Areas [188-193]p. 151
[pi] [194-200]p. 154
Arc Lengths and Chords [201-207, 210]p. 158
Ptolemy's Theorem [208-209, 232]p. 162
Sectors and Segments [220-226]p. 163
Inscribed Figures [227-231, 233-239]p. 166
Measuring Fields on Mountain Sides [240-247]p. 174
Archipendium [242]p. 174
Dividing Fields Among Partnersp. 181
Commentary and Sourcesp. 181
Textp. 185
Multisided Figuresp. 186
Triangles [1-26]p. 186
Parallelograms [27-31]p. 205
Trapezoids [32-56]p. 211
Quadrilaterals With Unequal Sides [57-64, 66-69]p. 230
Squares [65]p. 237
Pentagons [70-75]p. 242
Circlesp. 246
General [76-81]p. 246
Semicircles [82-83, 85]p. 250
Segments [84, 86]p. 251
Finding Cube Rootsp. 255
Commentary and Sourcesp. 255
Textp. 259
Finding Cube Roots [1-11]p. 259
Finding Numbers in Continued Proportionsp. 265
Archytas' Method [12]p. 265
Philo's Method [13]p. 267
Plato's Method [14-15]p. 268
Computing with Cube Rootsp. 270
Multiplication [16]p. 270
Division [17]p. 271
Addition and Subtraction [18-23]p. 271
Finding Dimensions of Bodiesp. 275
Commentary and Sourcesp. 275
Textp. 277
Definitions [1-3]p. 277
Euclidean Resources [4-10]p. 278
Various Areas and Volumesp. 282
Parallelepipeds [11-18]p. 282
Wedge [19-20]p. 287
Column [21-25]p. 289
Pyramids [26-41, 44]p. 292
Cones [42-43]p. 305
Spheres [45-53]p. 308
Surface Area and Volume [54-60]p. 319
Inscribed Cube [61-67]p. 324
Ratios of Volumes [68-73]p. 330
Other Solids [74. 76-84]p. 333
Divide a Line in Mean and Extreme Ratio [75]p. 335
Measuring Heights, Depths, and Longitude of Planetsp. 343
Commentary and Sourcesp. 343
Textp. 346
Different Heights [1-3]p. 346
Tools: Triangle [4]p. 348
Quadrant [5-9]p. 349
Table of Arcs and Chords [211-219]p. 354
Geometric Subtletiesp. 361
Commentary and Sourcesp. 361
Textp. 365
Pentagons [1-2], [6-7], [10-12], [16-18], [21-22], [25-26]p. 365
Decagons [3-5], [8-9], [13-15], [19], [23-24[, [27]p. 367
Triangles [20-33*]p. 377
Problem with Many Solutionsp. 395
Commentary and Sourcesp. 395
Textp. 396
Bibliographyp. 399
Indexp. 407
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780387729305
ISBN-10: 0387729305
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 408
Published: 1st November 2007
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.67 x 16.38  x 2.49
Weight (kg): 0.74

This product is categorised by