Analysis of information sources in references of the Wikipedia article "Inverse hyperbolic functions" in English language version.
Another form of notation, arcsinh x, arccosh x, etc., is a practice to be condemned as these functions have nothing whatever to do with arc, but with area, as is demonstrated by their full Latin names, ¶ arsinh area sinus hyperbolicus ¶ arcosh area cosinus hyperbolicus, etc.Zeidler, Eberhard; Hackbusch, Wolfgang; Schwarz, Hans Rudolf (2004). "§ 0.2.13 The inverse hyperbolic functions". Oxford Users' Guide to Mathematics. Translated by Hunt, Bruce. Oxford University Press. p. 68. ISBN 0198507631.
The Latin names for the inverse hyperbolic functions are area sinus hyperbolicus, area cosinus hyperbolicus, area tangens hyperbolicus and area cotangens hyperbolicus (of x)..... Zeidler & al. use the notations arsinh, etc.; note that the quoted Latin names are back-formations, invented long after Neo-Latin ceased to be in common use in mathematical literature. Bronshtein, Ilja N.; Semendyayev, Konstantin A.; Musiol, Gerhard; Heiner, Mühlig (2007). "§ 2.10: Area Functions". Handbook of Mathematics (5th ed.). Springer. p. 91. doi:10.1007/978-3-540-72122-2. ISBN 978-3540721215.
The area functions are the inverse functions of the hyperbolic functions, i.e., the inverse hyperbolic functions. The functions sinh x, tanh x, and coth x are strictly monotone, so they have unique inverses without any restriction; the function cosh x has two monotonic intervals so we can consider two inverse functions. The name area refers to the fact that the geometric definition of the functions is the area of certain hyperbolic sectors ...Bacon, Harold Maile (1942). Differential and Integral Calculus. McGraw-Hill. p. 203.
Another form of notation, arcsinh x, arccosh x, etc., is a practice to be condemned as these functions have nothing whatever to do with arc, but with area, as is demonstrated by their full Latin names, ¶ arsinh area sinus hyperbolicus ¶ arcosh area cosinus hyperbolicus, etc.Zeidler, Eberhard; Hackbusch, Wolfgang; Schwarz, Hans Rudolf (2004). "§ 0.2.13 The inverse hyperbolic functions". Oxford Users' Guide to Mathematics. Translated by Hunt, Bruce. Oxford University Press. p. 68. ISBN 0198507631.
The Latin names for the inverse hyperbolic functions are area sinus hyperbolicus, area cosinus hyperbolicus, area tangens hyperbolicus and area cotangens hyperbolicus (of x)..... Zeidler & al. use the notations arsinh, etc.; note that the quoted Latin names are back-formations, invented long after Neo-Latin ceased to be in common use in mathematical literature. Bronshtein, Ilja N.; Semendyayev, Konstantin A.; Musiol, Gerhard; Heiner, Mühlig (2007). "§ 2.10: Area Functions". Handbook of Mathematics (5th ed.). Springer. p. 91. doi:10.1007/978-3-540-72122-2. ISBN 978-3540721215.
The area functions are the inverse functions of the hyperbolic functions, i.e., the inverse hyperbolic functions. The functions sinh x, tanh x, and coth x are strictly monotone, so they have unique inverses without any restriction; the function cosh x has two monotonic intervals so we can consider two inverse functions. The name area refers to the fact that the geometric definition of the functions is the area of certain hyperbolic sectors ...Bacon, Harold Maile (1942). Differential and Integral Calculus. McGraw-Hill. p. 203.
