Monday, 6 September 2010

Robert Recorde

I'm not sure what the force is behind certain blog posts popularity. In the last two months my second most popular "hit" has been "Math Symbols Are NOT All Created Equal". What makes that seem unusual to me is that I wrote it in the summer of 2008. The blog is about the equal sign and how it came to be the most ubiquitous of mathematical symbols. I suspect that it is the start of school year that has driven many of these searches by students driven to find the creator of the symbol. If that is true, then here is a little more interesting history for them (or their teachers) to share.

The symbol was, as you know if you read the blog, created by Robert Recorde in his "Whetstone of Witte", and published in London just before Recorde's death in 1558.

Recorde died in the King's Bench Prison at Southwark in London, most likely for being unable to pay his debts. Then, as now, teaching was not an economically rewarding position. Along the way, he had been a very successful writer of mathematics textbooks. His first arithmetic, "The Ground of Artes," was published around 1540-43. It became a very popular arithmetic and was reprinted over a dozen times. After his death, other mathematicians would use it as the base of their own books, making minor adaptations and keeping Recorde's well known name. One such edition by Edward Hatton bears the date 1699, almost 150 years after Recorde's death. Algebra, it seems, was a less popular topic. The "Whetstone of Witte", in which he introduced the "gemowye" lines of equality, never made it to a second edition.
If you remember that most publications in mathematics were in Latin, then the task of creating an English language Geometry or Algebra required the introduction of English terms for some of the technical terms needed. Recorde's "Pathway to Knowledge" was two decades ahead of Billingsly's translation of Euclid. In it he introduced many Saxon-English words for the Latin terms. A "poynt or prycke" was used for the point. One-hundred years later Newton would write that he used "pricked letters" to indicate a fluxion. "Sharp" and "blunt" corners were the translations from the Latin acute, and obtuse, to the detriment of many geometry students who would better remember and understand the Saxon terms. Recorde allowed that his "gemowe" or parallel lines (he used both terms) need not be straight. Those crooked copies of each other, like ss, he called "tortuous parallels".

Tangent lines were called "touche lynes" in an Anglo-Saxon translation. Vertical angles were referred to as "matche corners", and rectangles were "losenges or diamondes". If the parallelogram was oblique, it was called "diamonde-like".

None of these became popular terminology, most likely because the language of scholars continued to be Latin for over a century after his death. Although the terms "long square" for a rectangle and "diamonde" for rhombus appeared in the Billingsly translation of Euclid, little other evidence of Recorde's language inovations seem to appear.

Recorde was not totally adverse to using existing or foreign terms. He referred to "cooslike" numbers for variables, which had been introduced by Pacioli (1494) from the Latin "cosa" for thing, which had become very popular in Germany. The German algebraists were sometimes called cossists, and the study of algebra as "die cost."

Also, we should keep in mind that it was Recorde who first used the word sine in print in English.


Anonymous said...

Your link to your old post is broken.

It may be posts like
that are driving blog readers to look for more posts about equals signs.

Pat's Blog said...

Thanks Gas, It seems to be working now...That's true, there have been a couple about the research last year...You just keep them coming my way, need all the traffic I can get...

Anonymous said...

Did you know that all Robert Recorde's books are back in print? Go to for more details.