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As well as arithmetical calculations, Babylonian mathematicians also developed algebraic methods of solving equations. Once again, these were based on pre-calculated tables. To solve a quadratic equation, the Babylonians essentially used the standard quadratic formula. They considered quadratic equations of the form:
Completing the square is the oldest method of solving general quadratic equations, used in Old Babylonian clay tablets dating from 1800–1600 BCE, and is still taught in elementary algebra courses today.
In stage 2, the well-attested Old Babylonian method of completing the square is used to solve what is effectively the system of equations b − a = 0.25, ab = 0.75. [6] Geometrically this is the problem of computing the lengths of the sides of a rectangle whose area A and side-length difference b − a are known, which was a recurring problem ...
The Egyptian Berlin Papyrus, dating back to the Middle Kingdom (2050 BC to 1650 BC), contains the solution to a two-term quadratic equation. [21] Babylonian mathematicians from circa 400 BC and Chinese mathematicians from circa 200 BC used geometric methods of dissection to solve quadratic equations with positive roots.
The earliest methods for solving quadratic equations were geometric. Babylonian cuneiform tablets contain problems reducible to solving quadratic equations. [23] The Egyptian Berlin Papyrus, dating back to the Middle Kingdom (2050 BC to 1650 BC), contains the solution to a two-term quadratic equation. [24]
Plimpton 322 is a Babylonian clay tablet, believed to have been written around 1800 BC, that contains a mathematical table written in cuneiform script.Each row of the table relates to a Pythagorean triple, that is, a triple of integers (,,) that satisfies the Pythagorean theorem, + =, the rule that equates the sum of the squares of the legs of a right triangle to the square of the hypotenuse.
Babylonian algebra was much more advanced than the Egyptian algebra of the time; whereas the Egyptians were mainly concerned with linear equations the Babylonians were more concerned with quadratic and cubic equations. [7]
An Old Babylonian tablet (Strasbourg 363) seeks the solution of a quadratic equation. [1] c. 1800 BC: The Plimpton 322 tablet gives a table of Pythagorean triples in Babylonian Cuneiform script. [2] 1800 BC: Berlin Papyrus 6619 (19th dynasty) contains a quadratic equation and its solution. [3] [4] 800 BC
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