Atnaujinkite slapukų nuostatas

El. knyga: Fibonacci's De Practica Geometrie

4.00/5 (2 ratings by Goodreads)
Kitos knygos pagal šią temą:
Fibonacci's De Practica GeometrieDidesnis paveikslėlis
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

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.

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. This high quality 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 author's 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.

Recenzijos

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. Its 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)

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
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
π [ 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 [ 20-331
377
Appendix Problem with Many Solutions 395
Commentary and Sources
395
Text
396
Bibliography 399
Index 407


Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97803877293122e.html
Raktažodžiai: