Quote: solving a proportional equation with one unknown

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history of mathematics


A Problem of the First Type Ten for six, how many for four? Observe now in what manner the given numbers are related, according to what we have said. For when you say "ten," you give the measure, and when you say "for six," you state the price. When you ask, "how much?" you give the unknown, called Almuhen or Magul, and saying "for four," you mention the cost. You note further that three of these, that is, 10, 6, and 4, are known and definite numbers, and the question is concerning the fourth or unknown number. If now you take account of the rule given, you multiply the first by the last, that is, 10 by 4, for they are the known and definite numbers which are inversely proportional to each other. It is necessary to divide the product, that is, 40, by the other known and definite number, that is, the measure, which is 6. This give 6 2/3, designating the unknown number. This number is inversely proportional to the number 6, which in Arabic is called Alszarar.   Google-1   Google-2

Published before 1923

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