# The Evolution of Arithmetic

This post is the second in a series; if you haven’t read the first post, on the evolution of English counting words, I’d recommend reading that one first.

As promised, this post looks at the origins of the English words for arithmetic operations. Read on, friend!

• Plus and Minus. These two are fairly straightforward—they’re the Latin words for “more” and “less”, respectively. The symbols, though, are less clear. It appears that the letters p and m were used (sometimes appearing as p and m) during the 1400s—Wikipedia claims that these first appeared in Luca Pacioli’s Summa de Arithmetica, though I’ve been unable to find a satisfactory example. In the 1500s, the modern + and – signs began to appear; Schwartzman attributes the + to an abbreviation of the Latin “et” (taking the t only) and the – to the bar from m.
• Multiply. This word comes from the Latin multiplicare, meaning “to increase.” Breaking it down a little further, we have the prefix multi– (“many”) and the suffix -plex (“fold”) so that the compound word multiplex means “many folds.” (We still use “fold” language today—when we speak of a “threefold increase,” we mean that something had been multiplied by three.) The x symbol for multiplication is attributed to William Oughtred, while Schwartzman gives credit for the dot • to Gottfried Wilhelm Leibniz.
• Divide. This word comes from Latin as well, with the origin being dividere, meaning “to separate.” (As a side note, the root videre means “to see” and gives us the modern word video, which means “I see”.) Putting di– and videre together, I suppose this means that division is literally “to see in two.”

Notice that all four of these words originate in a description of the operation itself. It turns out that exponents and roots are a little more metaphorical in their meaning:

• Exponent. Once again, we have a Latin origin: the prefix ex– and the verb ponere, roughly meaning “to put out.” Unlike the four arithmetic operations, though, the original meaning is typographical—the exponent is the number that is “put out” above and to the right of the base. In part, it’s because the exponent is a relatively new development; Schwartzman attributes the notation to Descartes, specifically La Géométrie (1637).
• Root. Finally, a non-Latin word! The word rot means “cause” or “origin”, which makes sense when you consider that since 8 = 23, its “origin” is 2. If you trace the word further back, the Proto-Indo-European root (see what I did there?) is wrad-. Thus, the Latin-based words radical and radish come from a source similar to root.

And there you have it! In the next installment, I’ll get a little more geometric and explore some words we’ve come to use for algebraic curves.