{"id":6391,"date":"2011-08-08T13:33:07","date_gmt":"2011-08-08T05:33:07","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=6391"},"modified":"2016-09-19T11:14:10","modified_gmt":"2016-09-19T03:14:10","slug":"the-signs-used-in-arithmetic","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/the-signs-used-in-arithmetic-6391","title":{"rendered":"The signs used in arithmetic"},"content":{"rendered":"

Reader Lemmie sent me an interesting excerpt from a book The Children's Treasure House Vol 5 How and Why<\/em>, by Arthur Mee, printed in 1926. <\/p>\n

It contains an interesting passage about the origin of signs used in arithmetic.<\/p>\n

Lemmie is a "mature" reader and said "This is from an old set of books in the bookshelf of my late mum. It was my 'TV' back in the late 40s". <\/p>\n

I've mostly quoted directly from the excerpt, but added extra information in square brackets and some links to more information. Some of the notation explanations are somewhat speculative, I suspect. <\/p>\n

THE SIGNS USED IN ARITHMETIC <\/h2>\n

The signs that we use in arithmetic are known to all, but their origin is not so familiar. <\/p>\n

The sign =, meaning equal to<\/strong>, was first used by [Welshman] Robert Recorde<\/a>, of All Souls' College, Oxford, in 1531. To save himself the trouble of writing the words "equal to" again and again, he drew two little lines equal to one another. [He said "Noe 2 thynges can be moare equalle” than parallel lines. His symbol appears to be 5 times the current length of the equal sign, as we can see in The Whetstone of Witte<\/em> by Recorde, below.] <\/p>\n

\n

\"Recorde
\n Image source with text<\/a> <\/p>\n<\/div>\n

The sign for addition<\/strong> (+) is really a carelessly made p<\/em>, from plus<\/em>, the Latin word for more<\/em>. <\/p>\n

The —, for subtraction<\/strong>, also comes from a shortened Latin word, minus<\/em>, meaning "less than", which was written m n s<\/em>, with a horizontal stroke on top to show that it had been shortened. Then the letters were omitted, and the stroke only written. <\/p>\n

<\/ins><\/div>\n

The multiplication sign<\/strong> (×) was invented early in the seventeenth century by Oughtred Etonensis, the most famous mathematician then in Europe [aka William Oughtred<\/a>, who contributed to inventing the slide rule, and gave us "sin" and "cos" in trigonometry]. It was simply the + sign turned round, multiplication being a short way of doing addition. [There is some debate about this notion. See Devlin's Angle where he argues It Ain't No Repeated Addition - unfortunately this is no longer available.]<\/p>\n

In division<\/strong> the Hindus used to put the dividend [the number you divide into] above the divisor [the number you are dividing by] with a horizontal line between, and from this plan the Arabians developed the sign ÷, placing it between the dividend and divisor. [This "divide" sign is often hard to read, since it can look a lot like a plus sign, depending on the font used and font size.] <\/p>\n

The sign % for per cent<\/strong> has developed from ÷, once used for per cent as well as for division. <\/p>\n

The radical sign (√), meaning that the square root<\/strong> of a number is to be taken, is really the first letter (r<\/em>), of the Latin word radix<\/em>, meaning root. [The radical sign was introduced by Christoff Rudolff (Polish, 1499 - 1545).]<\/p>\n

The • (dot) as used in decimal fractions<\/strong> was invented by John Napier<\/a> [1550 - 1617], the man who also invented logarithms. <\/p>\n

The n<\/em> used in algebra to signify any indefinite number<\/strong> is the initial letter of the Latin word numerus<\/em>, meaning a number. <\/p>\n

OTHER SIGNS [also used in math] <\/h2>\n

The present question mark (?) and the exclamation mark (!) have a similar and an interesting origin. <\/p>\n

The ! (exclamation mark) represents the Latin exclamation lo<\/em>, which was used to signify a cry of joy. When the Latin writers wished to signify joy they wrote this word, then, so that it might not be read as a part of the verse or line, they wrote the letters one above the other, thus 1<\/sup>0<\/sub>, and this, in rapid writing, soon developed into "!". <\/p>\n

[Interestingly, you often hear in Asia the word "aiyoh<\/em>" to mean surprise or frustration. This could be linguistically related to the Latin Io<\/em>.] <\/p>\n

The ? (question mark) came similarly from the first and last letters of the Latin word questio<\/em>, meaning question, written one above the other in the same way Q<\/sup>0<\/sub>. The Q written quickly became [the top of the question mark symbol] and the o became a point.<\/p>\n

Concluding remark<\/h2>\n

Much of our math notation is relatively quite recent and was introduced as Europe emerged from the Dark Ages. We act as though the notation is fixed an unchangeable, but I think we are overdue for math notation reform. See: Toward more meaningful math notation<\/a>.<\/p>\n

See the 2 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"

\"math<\/a>Where do our math symbols come from? Here's a short background on the common ones.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[129],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/6391"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=6391"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/6391\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=6391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=6391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=6391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}