Alligation Alternate and the Composition of Medicines: Arithmetic and Medicine in Early Modern England

Abstract

Practical mathematics in the early modern period was applied to such fields as astronomy and navigation; cartography and surveying; engineering and military arts, including gunnery; and especially banking and mercantile trade. Those who have written about practical mathematics make no mention of medical applications in their surveys, although there were many cases where physicians set up as mathematical practitioners. 1 This article examines medical applications found in practical mathematical literature up to the end of the seventeenth century in England.While instruction in the medical applications of mathematics are scarcely to be found in earlier English publications, we shall see that a sudden minor outburst occurred in the 1650s, when three separate arithmetics appeared with chapters on ''the composition of medicines''. These chapters were each associated with a mathematical operation called ''alligation'', a term which means ''tying together''. There are two main types of alligation: ''alligation medial'' for simple problems and ''alligation alternate'' for use when varied quantities and elements are to be mixed. It was the technique called alligation alternate that was adapted specifically to the composition of medicines in these arithmetics.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 # Alvan Bregman 2005

Review of periodical literature published in 2005

“…Using a sample of 1,392 almanacs she illustrates how their pages disseminated the rudiments of Galenic medicine, astrology, and newer understandings of medical (often herbal) materialism, to up to 400,000 readers per annum. Bregman examines the composition of more elevated forms of treatment, explaining contemporary understandings of the principles of ‘alligation’—determining the mathematical ratios in which medical ingredients should be mixed. He situates these understandings in relation to the main mathematical texts concerned with this process, from Robert Record (1543) to William Salmon (1671).…”