The Philosophy of Arithmetic Considered As a Branch of Mathematical Science
The Philosophy of Arithmetic Considered As a Branch of Mathematical Science
John Walker
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But performing the same operation al- gebraically, and comparing the product a;* ^xy-\-y^ with Uie factors, we at once observe that the square of ^ y consists of the sum of the squares of >: and y {j?*4-2A?2/-f^^, or is equal to the sum of their squares plv^ twice their product ; as we have before ob- served. ( 34. ) Again if we multiply ^+3/ by x y, we shall find the product at* y^ ; for of the four products which compose it x^-\-xy xy 3/^, the second and third when added together disappear. B...ut this presents to us the general principle that the product of the sum and dif- ference of any two numbers is equal to the difference of their squares.
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