  The first major attempt among the English to clear up the foundation problems of algebra was the Treatise on Algebra, 1830, by George Peacock (1791–1858). A second edition appeared as two volumes, 1842/1845. He divided the subject into two parts, the first part being arithmetical algebra, the algebra of the positive numbers (which did not permit operations like subtraction in cases where the answer would not be a positive number). The second part was symbolical algebra, which was governed not by a specific interpretation, as was the case for arithmetical algebra, but solely by laws. In symbolical algebra there were no restrictions on using subtraction, etc.