When Were Exponents First Used?
An exponent is a symbolic way of showing how many times a number is multiplied by itself. Exponents were not used in the raised position to the right of the number until 1636. René Descartes is believed to have been the first, one year later, to use it in the exact notation generally used today. Exponents have subsequently been introduced with many other meanings: the inverse of a function, the order of a derivative and even for mappings in set theory.
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Early Starts
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In the 14th century, Nicole Oresme used numbers to indicate power but the numbers were not raised.
In the 15th century, Nicolas Chuquet used raised numbers in "Le Triparty en la Science des Nombres," but 12^3 actually meant 12x^3.
In 1634, Pierre Hérigone wrote powers as a, a2, a3, etc., in "Cursus Mathematicus" without raising them.
The Raised Exponent
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In 1636, raised exponents were finally used in the meaning of power that we use today. They appeared in James Hume's "L'Algèbre de Viète d'une Methode Novelle, Claire et Facile." They differed in appearance a little from today, in that he used Roman numerals as the raised exponent, to accentuate the difference between base and exponent.
The following year, René Descartes used Arabic numerals, the numerals most commonly used today, in raised exponents in his "Geometrie."
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Negative Integers as Exponents
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John Wallis was the first to suggest the use of negative raised exponents. Isaac Newton is the first known to use it, in a letter in1676 to Henry Oldenburg on the subject of the binomial theorem.
Fractions as Exponents
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Again, John Wallis spoke, in "Arithmetica Infinitorum," of fractions to be used as exponents but did not actually demonstrate it. Newton used fractions as exponents in the letter mentioned above.
Scientific Notation
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Electromagnetism is the first field known to use scientific notation in the form of a product of a decimal form and a power of 10. James Clerk Maxwell is known to have used powers of 10. Johann Balmer is the first known to have combined a decimal form and power of 10 as a product, in 1885. Michelson and Morley, of special relativity fame, were using the notation in 1887.
Euler's Number
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Leonard Euler introduced the notation for the base for continuously compounded interest, calling it "e." (This number is also referred to today as "Euler's number.") He also is first to discuss complex exponents (exponents with the square root of -1), noting an important property of them today known as "Euler's formula."
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References
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