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of reasoning was enormously facilitated by
the invention of logarithms by Napier. He
was born at Merchistoun, near Edinburgh,
in 1550, and died in 1617. By this system
the tedious arithmetical operations neces-
sary in astronomical calculations, especially
those dealing with the trigonometrical func-
tions of angles, were so much simplified that
Laplace declared that by this invention the
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