Multiplication and Division
June 12, 2010:In trade and construction multiplication and division
are essential prerequisites.People early found solutions for fast and
reliable execution of these needs.In China the abacus, able to
add, subtract, multiply and divide was known four or five thousand
years ago.
Later cultures like the ancient Greek, Roman and Japanese culture all
had their own brand of abacuses differing according to the numeral
system in use.
In Florence in Italy trade blossomed in the middle ages, and in 1343,
under the wealthy merchant family of Medici six abacus schools existed
teaching over a thousand pupils arithmetic and geometry.
In 1617 the Scottish nobleman John Napier of Edinburgh invented a new twist of the abacus, the Napier Bones.These bones (or rods) consist of 10 strips of wood enclosed in a carrying case vith the numbers 1 to 9 marked at the left side of the case.The rods are three dimensional, square in cross section, with four different rods engraved on each one.A complete set is seen beside the painting of Napier.
When multiplying the rods are picked and arranged so the
multiplicand figure at the top row of the carrying case.Multiplying are,
when the multiplicator is in the span between 1 and 9, performed just
by reading (or »transcribing«) the product by adding the diagonals
(from the right side) on the row corresponding to the multiplicator.
Multiplication with higher multiplicators and division also are not
that hard if studying these examples from Edward Wells »The Young
Gentleman`s Arithmetick and Geometry« published in London 1723 (Google
books).Multiplication is to the left.
Napier also in an effort to simplify computing
discovered the logarithmic function which was carefully tabulated by
interpolations.Precise complex calculations could now be done by
looking up in tables and using the simpler, faster and not so error
prone art of addition and subtraction.
Each number has a corresponding logarithm which can be read from the
tables, and to get the logarithm of a product you simply add the
logarithms of the multiplicand and multiplicator.With division you
subtract the logarithms of the divider and the divisor to get the
logarithm of the quotient.
The value of the product (respective quotient) can then be extrapolated
form the log table, or read directly from an antilog table.
Final thoughts: When reading in “The Young Gentleman´s...” indeed it was strange to find how clear and understandable Edward Wells wrote, and how timeless this nearly 300 year old text feel.Also - a contemporary of Napier,the Oxford mathematician Henry Briggs to Napier expressed his astonishment over the finding of logarithms:”why nobody else found it out before, when, now being known, it appears so easy”.It was a true enlightening of a void.
