2. Ancient Babylonian Algebra: Around 2000 BC, the algebraic problem of written narration appeared in ancient Babylonian mathematics. For example, the clay tabletNo. 1390 1 of the British Museum records a question: "I add the area of my square to two-thirds of the side length of the square to get 35/60, and find the side length of the square." This problem is equivalent to solving an equation.
The solution given on this clay tablet is: two thirds of 1 is 40/60, and the other half is 20/60, so square.
Add 35/60 to get its square root is 50/60, subtract half of 40/60 to get 30/60, so 1/2 is the side length of a square.
This solution is equivalent to substituting the coefficients of the equation into the formula.
Note: Babylonians probably knew the root formulas of some quadratic equations with one variable at that time. Because they don't have the concept of negative numbers, they don't consider the negative roots of quadratic equations.
Quadratic equations with positive coefficients have no positive roots, so in ancient and medieval times, even in early modern times, quadratic equations have been divided into the following three categories:
(ⅰ)
(ⅱ)
(ⅲ)
These three equations can be found in ancient Babylonian clay tablets, and the correct solutions are given.
The Babylonians could also solve the problems of five unknowns and five equations.
Their algebraic equations are all described in words. They often use length, width and area to represent unknowns. They don't necessarily think that the unknown quantity they want is really these geometric quantities, but it may be because many algebraic problems come from geometry, so geometric nouns have become synonymous with the unknown quantity in algebra.