Alligation alternate and the composition of medicines: arithmetic and medicine in early modern England.

Bregman A - Med Hist (2005)

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f1: Calculation using alligation alternate.
Mentions: Alligation was a relatively advanced arithmetical operation, presupposing a knowledge of the rules of proportion. As such, alligation was usually presented near the end of arithmetical texts. Most commonly the examples used to explain alligation involved grains, metals, wines or spices. A typical use of alligation alternate would be to determine the appropriate quantities to mix of various elements each having a different price in order to concoct a mixture destined to sell at a desired unit price. For example, say you are a grocer and you have ample quantities of wheat, rye, barley and oats, which sell respectively for 28, 20, 14 and 10 pence a bushel. For whatever reason, you wish to sell a mixture of these grains at 16 pence a bushel. What quantities of each grain should you mix? The solution of the problem, using alligation alternate, looks like Figure 1.

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Affiliation: University of Illinois at Urbana-Champaign, University Library, 1408 W. Gregory Drive, Urbana, IL 61801, USA. abregman@uiuc.edu

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