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How did the ancient Egyptian method of false position solve arithmetic problems?
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arithmetic
A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”
The method of false position, also known as the method of false assumption, was a technique used by ancient Egyptian scribes to solve linear equations, such as finding a quantity (aha) when given a specific relationship involving its parts.1
To solve a problem using this method, the scribe would perform the following steps:
- Assume a trial value: Instead of solving for the unknown directly, the scribe would choose a convenient "false" number for the quantity to see how it behaved in the given equation.21
- Calculate the discrepancy: The scribe would apply the conditions of the problem to the trial value. If the result did not match the target value, the scribe would determine the ratio between the target result and the result obtained from the trial value.1
- Adjust the result: The scribe would then multiply the initial trial value by that ratio to find the correct answer.1
For example, to solve "a quantity and its 7th together make 19," a scribe might assume the quantity is 7. Since 7 plus its 7th (1) equals 8, and 8 is not 19, the scribe would multiply 7 by the ratio of 19/8 to arrive at the correct solution.1