Quaternions as the result of algebraic operations . p:eose-^ (-xeos0+pa Result: Same as in § 73. 37 38 QUATERNIONS 76. Into any quaternion. Let the quaternions be reduced,§ 72, to a common numerator and denominator respectively,viz.:. a ^ af Denote the arcs which de-termine the planes of the qua-ternions by c, o, h respec-tively, as shown in the effect of the quaternionwhose axis is ax-c operatingupon the quaternion whoseaxis is ax-a is to give a newquaternion whoso axis is ax ? can be analyzed as follows: Suppose we move thearc a horizontally along c, being careful not to ch
Quaternions as the result of algebraic operations . p:eose-^ (-xeos0+pa Result: Same as in § 73. 37 38 QUATERNIONS 76. Into any quaternion. Let the quaternions be reduced,§ 72, to a common numerator and denominator respectively,viz.:. a ^ af Denote the arcs which de-termine the planes of the qua-ternions by c, o, h respec-tively, as shown in the effect of the quaternionwhose axis is ax-c operatingupon the quaternion whoseaxis is ax-a is to give a newquaternion whoso axis is ax ? can be analyzed as follows: Suppose we move thearc a horizontally along c, being careful not to change itsinclination to c, until it takes the position a. The ax-awill move horizontally around ax-c (conical revolution) untilit takes the position ax-a. Then as wo turn a down tocoincidence with b around a as an axis, ax-a will move upthe arc passing through ax-c (the equator of a) until ittakes the position ax - b. That is, the multiplication of ^ into — tur7is the axis of — (X horizontally, , parallel to the plane of ^ (conical revolu-tion) through an angle equal to that between a and /?, andraises or lowers it through an angle which depends entirely upon —. Whatever the position of j- with reference to 3, the h
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