Trigonometry And Double Algebra

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But for all other directions except ( , 0) and ( , ir), lines of the same direction have not products in that or the opposite direction.
Let AA, AAA, AAAA, &c., without any reference to ex- ponents, be called the second, third, fourth, &c. powers of A.
And let V-^> ^-4, V^, &c., be lines of which the meaning is defined by ^A x ^JA, ■\l A x ^ A x \l A, &c., being each equal to A, and they may be called the second, third, fourth, &c.
roots of A, Then we have immediately AA = (oa, 2a), AAA = (aoo,
... 3a), AAAA = {aaxm, 4a), &c..
As explained in pages 43, 44, choice of values immediately com- mences, as soon as we have occasion to take a subdivision of an angle. Thus, since a + ^mir may take the place of a, we may infer, as in the^ pages cited, that ^A has two directions whose angles differ by tt, half a revolution ; that \lA has three directions, indicated by angles differing by a third of a revo- lution; and so on. In fact that 7^ is any one of (%, - + m —V \ n nj Digitized by VjOOQIC TJBLE ALGEB^ 121 where m is any integer.


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