Early Uses of Mathematical Symbols

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Early Uses of Mathematical Symbols

• By Andrea Schulz

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Greek number system

• Acrophonic System
• First millennium B.C.
• Acrophonic means that the symbols for the numbers
  come from the first letter of the number name.

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Greek number system

• Here is an example of the Greek Acrophonic number
  system
• This is symbols for the numbers 5,10,100, 1000,
  10,000.

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Greek number system

• The Greek system looks a lot like Roman numerals.
• 1-10 in Greek acrophonic numbers.

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Egyptian numerals

• Based on hieroglyphs from around 3000 B.C.
• Hieroglyphs are pictures representing words.
• The Egyptians has a bases 10 system of
  hieroglyphs for numerals.

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Egyptian numerals

• Here are the numeral hieroglyphs.

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Too Much info

• I could have covered every culture and the
  symbols used in their number system. However
  that would be a very long report.
• I narrowed my search to earliest use of
  Mathematical operations.
• Plus sign
• Minus sign
• Multiplication
• Division
• Exponents
• Order of operation

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Addition and Subtraction Symbols

• Plus () and minus (-) signs
• Nicole d Oresme (1323-1382) may have used a
  figure which looks like a plus symbol as an
  abbreviation for the Latin et (meaning and)
• The plus and minus symbols only came into general
  use in England after they were used by Robert
  Recorde in 1557 in The Whetstone of Witte.
• The plus and minus symbols were in use before
  they appeared in print, for example they were
  painted on barrels to indicate whether or not the
  barrels were full.

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Multiplication Symbols

• X was used by William Oughtred (1574-1660) in the
  Clavis Mathematicae composed about 1628 and
  published in London in 1631. Cajori calls X St.
  Andrews Cross.
• The dot ( ) was advocated by Gottfried Wilhelm
  Leibniz (1646-1716) According to Cajori.

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Division Symbols

• Closed parenthesis. The arrangement 8)24 was used
  by Michael Stifel (1487-1567) in Arithmetica
  integra, which was completed in 1540 and
  published in 1544 in Nuernberg.
• The colon () was used in 1633 in a text entitled
  Johnson Arithmetik. However Johnson only used
  the symbol to indicate fractions, not for
  division.
• The obelus () was first used as a division
  symbol by Johann Rahn (1622-1676)

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Exponents

• Positive integers in exponents Nicole Oresme
  (1323-1382) used number to indicate powering in
  the fourteenth century, although he did not use
  raised numbers.
• Negative integers as exponents were used Nicolas
  Chuquet (1445-1500) in 1484 in Le Triparty en la
  Science Des Nomres.

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Scientific Notation

• The earliest use of scientific notation is not
  know. It is believed that physicist working with
  electricity in the decade or so up to 1873.
• In 1863, the Annual Encyclopedia and Register of
  Important Events of the Year 1862 the article on
  Electricity has on page 404.

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Order of Operations

• The idea that multiplication precedes addition
  and subtraction was in early algebra books in the
  16th century.
• In 1892 in Mental Arithmetic Bailey advised
  avoiding expressions containing both and X.
• In 1898 in Text Book of Algebra by Fisher and
  I.J. Schwatt, a b x b is interpreted as
• (a b) x b.

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Bibliography

• http//www-history.mcs.st-andrews.ac.uk/HistTopics
  /Greek_numbers.html
• http//www-history.mcs.st-andrews.ac.uk/HistTopics
  /Egyptian_numerals.html.
• http//jeff560.tripod.com/operation.html
• Cabillion, Julio Gonzalez A Century of
  Mathematics in America, Part 1, Vol. 1, 1988.