Page:The Algebra of Mohammed Ben Musa (1831).djvu/84

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ON MERCANTILE TRANSACTIONS.

You know that all mercantile transactions of people, such as buying and selling, exchange and hire, comprehend always two notions and four numbers, which are stated by the enquirer; namely, measure and price, and quantity and sum. The number which expresses the measure is inversely proportionate to the number which expresses the sum, and the number of the price inversely proportionate to that of the quantity. Three of these four numbers are always known, one is unknown, and this is implied when the person inquiring says how much? and it is the object of the question. The computation in such instances is this, that you try the three given numbers; two of them must necessarily. be inversely proportionate the one to the other. Then you multiply these two proportionate numbers by each other, and you divide the product by the third given number, the proportionate of which is unknown. The quotient of this division is the unknown number, which the inquirer asked for; and it is inversely proportionate to the divisor.^[1]

Examples.— For the first case: If you are told, “ten (49) for six, how much for four?” then ten is the measure;

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1. If $a$ is given for $b$, and $A$ for $B$, then $a:b::A:B$ or $aB=bA\;\therefore \;a={\tfrac {bA}{B}}$ and $b={\tfrac {aB}{A}}$.