> as lemmas

1873 P. Kelland & P. G. Tait Introd. Quaternions iii. 32 (heading) Vector multiplication and division.

1881 A. S. Hardy Elem. Quaternions i. 3 The operation of vector addition is commutative.

1881 J. W. Gibbs Sci. Papers (1906) II. 17 An algebra or analytical method in which a single letter or other expression is used to specify a vector may be called a vector algebra or vector analysis.

1897 C. E. Curry Theory Electr. & Magnetism 361 If we replace the vector-equation by its three component-equations and the vector-integrals of the latter by the above values.

1904 Rep. Brit. Assoc. Advancem. Sci. 1903 53 I cannot help thinking that he would have used vector methods throughout if he had found ready to hand a vector analysis instead of a theory of quaternions.

1955 A. Huxley Genius & Goddess 38 The great man would get bored and quietly fade away, leaving me to solve Timmy's problem by some method a little simpler than vector analysis.

1964 J. W. Linnett Electronic Struct. Molecules i. 7 The resultant angular momentum is, therefore, by vector addition..√2h/2π.

1968 E. T. Copson Metric Spaces ix. 138 This is ordinary vector algebra without scalar and vector products.

1969 Jane's Freight Containers 1968–9 147/2 It has been assumed..that the vector sum (the actual value of the lashing tension) will not exceed 30 400 kgf.

1972 M. Kline Math. Thought xxxii. 786 By Maxwell's time a great deal of vector analysis was created by treating the scalar and vector parts of quaternions separately.

1973 H. M. Schey Div, Grad, Curl, & All That i. 1 Much of vector calculus was invented for use in electromagnetic theory and is ideally suited to it.

1982 Sci. Amer. Jan. 117/3 For any operation that can be applied to a single operand (such as the extraction of the square root) there is a corresponding vector operation that consists of applying the same operation to every element of a vector.