The History of Mathematics: A Brief Course
402 13. PROBLEMS LEADING TO ALGEBRA area width length - width^1 + length 1 FIGURE 1. Reduction of a problem to standard form. di ...
MESOPOTAMIA 403 t y t xy = A 1 1 1 A 1 1 I FIGURE 2. A scenario that may "fit" a text from cuneiform tablet AO 6670. reciproca ...
404 13. PROBLEMS LEADING TO ALGEBRA This recipe is equivalent to the modern formula for the sum of the squares of the first ç in ...
CHINA^405 performed. Srinivasiengar (1967, p. 39) gives the solution using symbols for the unknown values of the animals, but ...
406 13. PROBLEMS LEADING TO ALGEBRA and whose length is 1 \ bu. This problem amounts to one linear equation in one unknown. Divi ...
QUESTIONS AND PROBLEMS^407 xy=A Ô 2 A- FIGURE 3. Another scenario to "fit" a text on cuneiform tablet AO 6670. Questions and pro ...
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Chapter 14. Equations and Algorithms In this chapter we take up the history of algebra from the point at which equa- tions appea ...
410 14. EQUATIONS AND ALGORITHMS could provide satisfactory proofs. If this was the opinion of a lead- ing mathematician of the ...
THE ARl ÔÇ Ì Ε TIG A OF DIOPHANTUS 411 to indicate addition, each term followed by the corresponding number symbol (for which ...
412 14. EQUATIONS AND ALGORITHMS If x > 0 and a > b, then 1 < rn = (x + a)/(x + b) < a/6. That is, the given ratio m ...
CHINA 413 numbers in the abstract and illustrating them geometrically with lines. It does seem strange that Euclid clings to w ...
414 14. EQUATIONS AND ALGORITHMS distance d of the tree from the gate. For that kind of data, the problem is the linear equation ...
CHINA^415 0 á a á Í Í - a^3 Í-a^3 Í - a^3 0 -- á^2 —> 3á^2 -- 3á^2 0 a 2á 3á 1 1 1 1 Next, given any approximation á, the a ...
416 14. EQUATIONS AND ALGORITHMS We see that we need to make the following conversion of the coefficients (reading from bottom t ...
JAPAN 417 9 FIGURE 1. A quartic equation problem. This problem is obviously concocted so as to lead to an equation of higher d ...
418 14. EQUATIONS AND ALGORITHMS LM = rx Ì Í — r 3 - Ãé Ê Í = r 3 - r 2 KM = ri + r 2 LN = v^f - 2r 3 r, FIGURE 2. Sawaguchi Kaz ...
JAPAN 419 that he also solved the fourteenth problem (see Section 4 of Chapter 9), which involved an equation of degree 1458. ...
420 14. EQUATIONS AND ALGORITHMS Europe around the same time (1693, by Leibniz), but in a comparatively limited context. As Smit ...
HINDU ALGEBRA 421 4.2. Bhaskara II. In the five centuries between Brahmagupta and Bhaskara II (who will henceforth be referred ...
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