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"First edition of Byrne's invention of a new method of solving problems of importance without the aid of tables, formulae, or methods of approximation. He sets forth his rules which, according to the preface, 'unfolds the capabilities of numbers in an original manner, extending the boundaries of mathematical science.' He applies the numerical operations of his dual arithmetic to a variety of developments, so that in each investigation the best method to connect actual calculation with algebraic language and symbolical expression may be applied. Byrne (1810-1880), well-known for his Euclid and the use of colors instead of numbers, establishes modern analysis on a purely mathematical basis, rejecting the reasoning of the differential and other methods. this invention was followed by his 'Dual logarithms' in 1867 and other works." -- Antiquarian bookseller's description, 2018.