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The opening chapter of the books tells what is known of
Diophantus and his contemporaries, and surveys the problems published by Diophantus. The second chapter reviews the mathematics known to Diophantus, including his development of negative numbers, rational numbers, and powers of numbers, and his
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has written of the works of
Diophantus that "not the slightest trace of a general, comprehensive method is discernible; each problem calls for some special method which refuses to work even for the most closely related problems". In contrast, the thesis of Bashmakova's book is that Diophantus indeed
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Very little mathematical background is needed to read this book. Despite "qualms about
Bashmakova's historical claims", reviewer David Graves writes that "a wealth of material, both mathematical and historical, is crammed into this remarkable little book", and he recommends it to any
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of
Alexandria studied equations of this type in the second century AD. Scholarly opinion has generally held that Diophantus only found solutions to specific equations, and had no methods for solving general families of equations. For instance,
92:. These equations are to be solved by finding rational-number values for the variables that, when plugged into the equation, make it become true. Although there is also a well-developed theory of
199:. Reviewer Alan Osborne is also positive, writing that it is "well-crafted, ... offering considerable historical information while inviting the reader to explore a great deal of mathematics."
167:, and the possibility that Diophantus may have known of some form of this theorem. The remaining four chapters trace the influence of Diophantus and his works through
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and into 19th-century Europe, particularly concentrating on the development of the theory of elliptic curves and their group law.
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had general methods, which can be inferred from the surviving record of his solutions to these problems.
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96:(rather than rational) solutions to polynomial equations, it is not included in this book.
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The German edition adds supplementary material including a report by
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Zur
Geschichte der Mathematik in Alterthum und Mittelalter
155:, considered in modern mathematics as an example of the
120:. The third chapter brings in more modern concepts of
397:(in German), Leipzig: Teubner, pp. 164–165
112:philosophy of mathematics treating numbers as
404:Chinese Mathematics in the Thirteenth Century
64:, 1974) and into English by Abe Shenitzer as
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140:and birational equivalences between curves.
36:of Alexandria. It was originally written in
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151:to generate infinitely many points on a
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165:Fermat's theorem on sums of two squares
80:In the sense considered in the book, a
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439:Books about the history of mathematics
264:Diophant und diophantische Gleichungen
58:Diophant und diophantische Gleichungen
7:
363:Diophantus and Diophantine Equations
332:Diophantus and Diophantine Equations
305:Diophantus and Diophantine Equations
66:Diophantus and Diophantine Equations
21:Diophantus and Diophantine Equations
315:Mathematical Association of America
70:Mathematical Association of America
52:. It was translated into German by
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301:Graves, David (February 1999),
178:on progress towards a proof of
143:Chapters four and five concern
221:Диофант и диофантовы уравнения
50:Диофант и диофантовы уравнения
1:
84:is an equation written using
330:Gundlach, K.-B., "Review of
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401:Libbrecht, Ulrich (2005),
163:. Chapter seven concerns
118:inhomogeneous polynomials
391:Hankel, Hermann (1874),
262:Steiner, R., "Review of
219:Bolling, R., "Review of
114:dimensionless quantities
48:in 1972 under the title
367:The Mathematics Teacher
88:whose coefficients are
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449:1974 non-fiction books
444:1972 non-fiction books
407:, Dover, p. 218,
197:history of mathematics
186:Audience and reception
32:and their solution by
26:history of mathematics
434:Diophantine equations
180:Fermat's Last Theorem
30:Diophantine equations
269:Mathematical Reviews
226:Mathematical Reviews
82:Diophantine equation
28:, on the history of
399:. As translated in
176:Joseph H. Silverman
44:, and published by
42:Isabella Bashmakova
195:or scholar of the
122:algebraic geometry
153:cubic plane curve
138:rational mappings
24:is a book in the
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311:MAA Reviews
303:"Review of
86:polynomials
54:Ludwig Boll
428:Categories
346:0883.11001
247:0241.01003
203:References
100:Diophantus
62:Birkhäuser
34:Diophantus
373:(1): 70,
157:group law
72:, 1997).
379:27970826
278:0485648
239:0414483
169:Hypatia
94:integer
38:Russian
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136:, and
132:of an
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76:Topics
375:JSTOR
130:genus
46:Nauka
409:ISBN
228:and
128:and
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342:Zbl
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243:Zbl
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159:of
56:as
40:by
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371:92
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274:MR
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235:MR
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