Great Moments in Mathematics Before 1650American Mathematical Soc., 1983 M12 31 - 270 pages Great Moments in Mathematics: Before 1650 is the product of a series of lectures on the history of mathematics given by Howard Eves. He presents here, in chronological order, 20 ``great moments in mathematics before 1650'', which can be appreciated by anyone who enjoys mathematics. These wonderful lectures could be used as the basis of a course on the history of mathematics but can also serve as enrichment to any mathematics course. Included are lectures on the Pythagorean Theorem, Euclid's Elements, Archimedes (on the sphere), Diophantus, Omar Khayyam, and Fibonacci. |
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Page 9
... equal to four times the area of one of its great circles - a fact that was first rigorously established by Archimedes in the third century B.c. With such experiments , geometry became a laboratory study . The laboratory stage in ...
... equal to four times the area of one of its great circles - a fact that was first rigorously established by Archimedes in the third century B.c. With such experiments , geometry became a laboratory study . The laboratory stage in ...
Page 10
... equal to half of s , our eyes tell us that the circular segment is approximately equal in area to the isosceles triangle formed by the line of c and the two secant lines . Assuming the areas are actually equal , we find the old Chinese ...
... equal to half of s , our eyes tell us that the circular segment is approximately equal in area to the isosceles triangle formed by the line of c and the two secant lines . Assuming the areas are actually equal , we find the old Chinese ...
Page 15
... equal parts each of altitude h / 3 and designate one of these slices by U. Combine A , B , C , D into a rectangular parallelepiped of base b ( a - b ) and altitude h , and horizontally slice Q into three equal parts of altitude h / 3 ...
... equal parts each of altitude h / 3 and designate one of these slices by U. Combine A , B , C , D into a rectangular parallelepiped of base b ( a - b ) and altitude h , and horizontally slice Q into three equal parts of altitude h / 3 ...
Page 17
... equal to the same thing are equal to one another , it follows that angle x = angle y . The desired result has been obtained by a small chain of deductive reasoning , stemming from a more fundamental result . This type of geometry is ...
... equal to the same thing are equal to one another , it follows that angle x = angle y . The desired result has been obtained by a small chain of deductive reasoning , stemming from a more fundamental result . This type of geometry is ...
Page 22
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Contents
8 | |
16 | |
Lecture 4 The first great theorem | 26 |
Lecture 5 Precipitation of the first crisis | 43 |
Lecture 6 Resolution of the crisis | 53 |
Lecture 7 First step in organizing mathematic | 62 |
Lecture 8 The mathematicians bible | 70 |
Lecture 9 The thinker and the thug | 83 |
Lecture 14 The poetmathematician of khorasan | 148 |
Lecture 15 The blockhead | 160 |
Lecture 16 An extraordinary and bizarre story | 172 |
Lecture 17 Doubling the life of the astronomer | 182 |
Lecture 18 The stimulating of science | 194 |
Lecture 19 Slicing it thin | 206 |
Lecture 20 The transformsolveinvert technique | 215 |
Hints of the solution of some of the exercises | 229 |
Lecture 10 A boost from astronomy | 96 |
Lecture 11 the first great number theorist | 110 |
Lecture 12 The syncopation of algebra | 126 |
Lecture 13 Two early computing inventions | 135 |
Index | 261 |
Back cover | 271 |
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