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Babbage did not invent the typewriter - he invented the Difference Engine and the Analytical Engine: mechanical mathematical processors. His purpose in designing those was to simplify and improve the accuracy of complex, repetitive arithmetic operations.
He invented the computer
He did not invent the calculator- but was a professor of mathematics. See the link at the bottom of this page for information on him.
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Blaise Pascal invented the first calculator and Pascals triangle.