Analysis of information sources in references of the Wikipedia article "Cis (mathematics)" in English language version.
[...] cos [...] + i sin [...] we shall occasionally abridge to the following: [...] cis [...]. As to the marks [...], they are to be considered as chiefly available for the present exposition of the system, and as not often wanted, nor employed, in the subsequent practise thereof; and the same remark applies to the recent abrigdement cis, for cos + i sin [...]([1], [2][3]) (NB. This work was published posthumously, Hamilton died in 1865.)
[...] recent abridgment cis for cos + i sin [...](NB. This edition was reprinted by Chelsea Publishing Company in 1969.)
As an abbreviation for cos θ + i sin θ it is convenient to use cis θ, which may be read: sector of θ.
It has been recognized, almost from the start, however, that the form which best combines mathematical simplicity and complete generality makes use of the exponential oscillating function ei2πft. More recently the overwhelming advantage of using this oscillating function in the discussion of sinusoidal oscillatory systems has been generally recognized. It is, therefore, plain that this oscillating function should be adopted as the basic oscillation for both of the proposed tables. A name for this oscillation, associating it with sines and cosines, rather than with the real exponential function, seems desirable. The abbreviation cis x for (cos x + i sin x) suggests that we name this function a cis or a cisoidal oscillation.(69 pages)
[...] cos [...] + i sin [...] we shall occasionally abridge to the following: [...] cis [...]. As to the marks [...], they are to be considered as chiefly available for the present exposition of the system, and as not often wanted, nor employed, in the subsequent practise thereof; and the same remark applies to the recent abrigdement cis, for cos + i sin [...]([1], [2][3]) (NB. This work was published posthumously, Hamilton died in 1865.)
Stringham denoted cos β + i sin β by "cis β", a notation also used by Harkness and Morley.(NB. ISBN and link for reprint of 2nd edition by Cosimo, Inc., New York, US, 2013.)
It has been recognized, almost from the start, however, that the form which best combines mathematical simplicity and complete generality makes use of the exponential oscillating function ei2πft. More recently the overwhelming advantage of using this oscillating function in the discussion of sinusoidal oscillatory systems has been generally recognized. It is, therefore, plain that this oscillating function should be adopted as the basic oscillation for both of the proposed tables. A name for this oscillation, associating it with sines and cosines, rather than with the real exponential function, seems desirable. The abbreviation cis x for (cos x + i sin x) suggests that we name this function a cis or a cisoidal oscillation.(69 pages)
[...] Bitte vergessen Sie aber nicht, dass eiφ für uns bisher nur eine Schreibweise für den Einheitszeiger mit Winkel φ ist. In anderen Büchern wird dafür oft der Ausdruck cis(φ) anstelle von eiφ verwendet. [...](109 pages)
It has been recognized, almost from the start, however, that the form which best combines mathematical simplicity and complete generality makes use of the exponential oscillating function ei2πft. More recently the overwhelming advantage of using this oscillating function in the discussion of sinusoidal oscillatory systems has been generally recognized. It is, therefore, plain that this oscillating function should be adopted as the basic oscillation for both of the proposed tables. A name for this oscillation, associating it with sines and cosines, rather than with the real exponential function, seems desirable. The abbreviation cis x for (cos x + i sin x) suggests that we name this function a cis or a cisoidal oscillation.(69 pages)
[...] Bitte vergessen Sie aber nicht, dass eiφ für uns bisher nur eine Schreibweise für den Einheitszeiger mit Winkel φ ist. In anderen Büchern wird dafür oft der Ausdruck cis(φ) anstelle von eiφ verwendet. [...](109 pages)
