History of Numerals and SymbolsDate: 06/22/98 at 21:50:49 From: Melanie Edgar Subject: Symbol history We originally used the Roman system of nurmerals but the current symbols originated from the Hindo-Arabic system of numerals. Why and when did this change ocour? The symbols + and - have been commonly used in arithmetic texts since the 15th century. Can you tell us the history of symbols like =, divided by, times, etc.? Thank you. Date: 06/23/98 at 12:58:13 From: Doctor Mateo Subject: Re: Symbol history Hello Melanie, You ask some very interesting questions here. Actually there were many numeral systems in existence even before the Roman system of numerals to which you refer. The Hindu-Arabic symbols have themselves changed over the centuries into what we use today. The change on the European continent to the Hindu-Arabic system took a very long time. The Spanish used Hindu-Arabic symbols in writing as early as the late 900s A.D. The spread of the Hindu-Arabic numerals into standard usage took a long time especially in Italy, where the Roman numeral system was dominant until the middle of the 16th century A.D. In some places in Italy it was forbidden to use anything but Roman numerals in the late 1200s and early 1300s. When did the big change or acceptance of the Hindu-Arabic numeral system take place? Probably during the mid-1500s. Why? Because the printing press came into existence in the mid-1400s and the Hindu- Arabic numerals were used in printing. By the middle of the 16th century (and even later in some of the conservative parts of Italy) most of Europe had accepted Hindu-Arabic numerals. Why use Hindu-Arabic numerals instead of the Roman numerals? The transition happened after the printing press standardized the way the Hindu-Arabic numerals looked, but basically it was an issue of making good use of individuals' time. It took merchants and bookkeepers much longer to record data using Roman numerals. The Hindu-Arabic numerals made keeping records less time-consuming. The + and the - sign were originally used to show surpluses and deficits in business dealings. Johann Widmann used them in his book Mercantile Arithmetic; the book was published in 1489. The Dutch mathematician Vander Hoecke was the first person known to use the + and - symbols in writing algebraic expressions (early 1500s). The = symbol was introduced by Robert Recorde in his book The Whetstone of Witte in 1557. The first = symbol was made with much longer lines. The = symbol was chosen by Recorde because he felt that there was nothing more equal than two straight parallel lines. The multiplication symbol took a lot longer to develop. In the early 1600s Thomas Harriot used the dot to indicate multiplication in his book _Artis Analyticae_ (1631), and William Oughtred used the x as a symbol for multiplication in his book _Clavis Mathematicae_ (1631). The division symbol / was introduced into written form in 1659 by Johann Heinrich Rahn. He first used this symbol for division in his book _Teutsche Algebra_. (This division symbol was sometimes used for subtraction until symbols started becoming standardized.) The symbols were introduced to make writing faster and easier, to take up less written space, and to help the printing process. A good resource for learning more about the history of numbers and symbols is David M. Burton's _The History of Mathematics: An Introduction_. On the Web, consult "Earliest Uses of Mathematical Symbols" by Jeff Miller et al.: http://jeff560.tripod.com/mathsym.html Hope this helps you appreciate the development of mathematics as we know it today just a little more. -Doctors Mateo and Sarah, The Math Forum http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/