Thursday, 4 June 2015

Just For the Recorde, More than an Equal Sign

Ask someone with a passing interest in mathematics history what Robert Recorde did, and you will probably get one most common answer: He invented the equal sign. Pushed for more information, they may recall the name of his somewhat famous book, The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing the extraction of rootes; the cossike practise, with the rule of equation; and the workes of Surde Nombers(1557), which contained the first use of the equal sign using what he called "Gemowe lines" (meaning twin lines, from the Latin gemellus). His equal signs were exceptionally long, as compared to those now used, and under the introduction of the term he uses it with a couple of foreign symbols for additions and subtraction that he didn't invent, but did introduce into English mathematics.

Recorde was one of the earliest writers of arithmetic in the English language, and his "Pathway" is the first geometry written in English. In his books he struggled to find English terms in place of the Latin and Greek terms used in more scholastic (Latin) writings. Among the many terms he introduced are perfect, commensurable, linear, square, equation and binomial. And when you mention that he introduced the equal sign, point out that he also introduced the word "sign" into mathematical language.

But far more important than the terms and symbols he used, introduced, or invented, the work is a classic because it was a continuation of The Grounde of Artes, teachings the Worke and Practise, of Arithmeticke, both in whole numbers and fractions (1543)the first Algebra book in English. The Dictionary of National Biography (1896), describes him with these words:
Recorde was practically the founder of an English school of mathematical writers. He was the first writer in English on Arithmetic, Geometry, and Astronomy and the first to introduce algebra into England. ... Recorde is superior to others, even Viete, in his perception of general results connected with the fundamental notation of algebra, and he is free from the tendency, then common, to invest simple numbers with the character of planes, solids, etc.

In between these two major works he wasn't just laying around collecting royalty checks, though perhaps he should have been, he would die in prison the year after Whetstone of Witte was published.  He was incarcerated for Debts from a slander suit for charges he made about the future Earl of Pembroke, who was almost certainly guilty but too well connected to be taken down by Recorde.

In 1556 he published the book introduced in the photo at the top of the blog, The Castle of Knowledge. The book was primarily an explanation of Ptolemaic astronomy but it also mentions the Copernican heliocentric model, the first mention of the model in English.

A couple of year earlier, 1551, he had written a geometry book, The Pathway to Knowledge, containing the First Principles of Geometry ... bothe for the use of Instrumentes Geometricall and Astronomicall, and also for Projection of Plattes. In this one he used the word Sine for the trigonometric function, a first in English. Wikipedia seems to say that the term was introduced in English in 1590 but DeMorgan says it was in Pathway. (I admit to not having the book, and if DeMorgan was wrong, we shall sink together.)
With or without the "Sine", the "Pathway" was a powerful force in English mathematics. He explains solar and lunar eclipses, demonstrates some of the elements of Euclid, gives illustrations of astronomical instruments, and estimated the circumference of the earth at 21,600 miles. The book continued to be republished almost forty years after his death. His longest lasting book, the Grounde of Artes, continued to be reprinted until 1699.

A pretty amazing mathematical achievement when you consider that between The Grounde of Artes and his death was only fifteen years. So the next time a student asks, tell them a little more about him, "Just for the Recorde."