A treatise on the geometrical representation of the square roots of negative quantities

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Page 1 - There is no Preface or Introduction ; the first Chapter is entitled Definitions, Addition, Subtraction, Proportion, Multiplication, Division, Fractions, and Raising of Powers. I quote certain articles as follows: (1) All straight lines drawn in a given direction from a given point are represented in length and direction by algebraic quantities; and in the following treatise whenever the word quantity is used it is to be understood as signifying a line. (2) DEF.
Page 11 - ... to the second the same ratio which the third has in length to the fourth, according to Euclid's definition ; and also the angle at which the fourth is inclined to the third is equal to the angle at which the second is inclined to the first, and is measured in the same direction. Unity is a positive quantity arbitrarily assumed from a comparison with •which the values of other quantities are determined. If there be three quantities such...
Page 138 - The velocity of a body, revolving in any conic section, is to the velocity of a body revolving in a circle, at the distance of half the...
Page 11 - ... the first, and is measured in the same direction. (17) DEF. Unity is a positive quantity arbitrarily assumed, from a comparison of which the values of other quantities are obtained. (18) DEF. If there be three quantities such that unity is to the first as the second is to the third, then the third is called the product which arises from the multiplication of the second by the first. 23. The signification of these definitions may be thus expressed. Let the line drawn from an origin 0 to the point...
Page 12 - If three quantities be multiplied together, the product will be the same, whatever be the order in which they are multiplied together.

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