Geometry and Algebra in Ancient CivilizationsSpringer Science & Business Media, 6. pro 2012. - Broj stranica: 226 Originally, my intention was to write a "History of Algebra", in two or three volumes. In preparing the first volume I saw that in ancient civiliza tions geometry and algebra cannot well be separated: more and more sec tions on ancient geometry were added. Hence the new title of the book: "Geometry and Algebra in Ancient Civilizations". A subsequent volume on the history of modem algebra is in preparation. It will deal mainly with field theory, Galois theory and theory of groups. I want to express my deeply felt gratitude to all those who helped me in shaping this volume. In particular, I want to thank Donald Blackmore Wagner (Berkeley) who put at my disposal his English translation of the most interesting parts of the Chinese "Nine Chapters of the Art of Arith metic" and of Liu Hui's commentary to this classic, and also Jacques Se siano (Geneva), who kindly allowed me to use his translation of the re cently discovered Arabic text of four books of Diophantos not extant in Greek. Warm thanks are also due to Wyllis Bandler (Colchester, England) who read my English text very carefully and suggested several improve ments, and to Annemarie Fellmann (Frankfurt) and Erwin Neuenschwan der (Zurich) who helped me in correcting the proof sheets. Miss Fellmann also typed the manuscript and drew the figures. I also want to thank the editorial staff and production department of Springer-Verlag for their nice cooperation. |
Sadržaj
1 | |
Methods Ascribed to Pythagoras and Plato | 8 |
Pythagoras and the | 14 |
Megalith Architecture in Egypt | 22 |
Euclids Proof | 28 |
Chinese and Babylonian Mathematics | 36 |
Areas of Plane Figures | 38 |
The Moscow Papyrus | 44 |
Aryabhatas Method | 117 |
Brahmaguptas System | 124 |
The Motion of the Apogees and Nodes | 130 |
Part B Babylonian Egyptian and Early Greek Problems | 158 |
Mathematical Papyri from Hellenistic Egypt | 164 |
Part E Squaring the Circle and Circling the Square | 170 |
Area of the Circumscribed Circle of a Square | 176 |
The Date of Heron | 182 |
The Broken Bamboo | 53 |
Quadratic Equations in Babylonian Texts | 60 |
The Historical Development | 66 |
Three Kinds of Algebra | 72 |
The Application of Areas | 80 |
An Application of II10 to Sides and Diagonals | 86 |
The Sum of a Geometrical Progression | 94 |
From Book | 100 |
Indeterminate Equations in the Heronic Collections | 109 |
Part G The Mishnat haMiddot | 188 |
Height of a Tree | 194 |
The Volume of a Pyramid | 200 |
Liu Hui and Euclid | 202 |
97 | 214 |
Square Roots and Cube Roots | 216 |
218 | |
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Uobičajeni izrazi i fraze
Algebra ancient apogee Apollonios approximation Archimedes arithmetic Aryabhata Aryabhatiya astronomical Babylonian texts base Bhaskara Bhaskara II box-lid Brahmagupta Cairo papyrus calculation century A. D. ch'ih Chinese text chord circle segment circumference commentary computed constructions correct cube cubits diagonal diameter difference Diophantos divided divisor Egyptian epicycle equal estimate Euclid Euclid's Elements Euclidean algorithm formula fractions Geometric Algebra geometrical given numbers Greek height Heron Hindu Hipparchos hypotenuse Iamblichos inscribed Kaliyuga Kalpa line segments linear Diophantine equations linear equations Liu Hui longitudes mathematical mathematician means multiplied numbers of revolution obtains pair Pell's equation planets polygon problem Proklos proof proposition pyramid Pythagoras Pythagorean triples quadratic equation radius ratio rectangle remainder result Rhind papyrus right-angled triangle rule says scribe setat sexagesimal Shen Kua side similar Sines solve square root subtract Sulvasūtras Theorem of Pythagoras theory tion translation treatise ts'un unknown volume yang-ma