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Line 33: By [[Lindemann–Weierstrass theorem]], the hyperbolic functions have a [[transcendental number\|transcendental value]] for every non-zero [[algebraic number\|algebraic value]] of the argument.<ref>{{Cite book \| jstor=10.4169/j.ctt5hh8zn\| title=Irrational Numbers \| volume=11\| last1=Niven\| first1=Ivan\| year=1985\| publisher=Mathematical Association of America\| isbn=9780883850381}}</ref> Hyperbolic functions were introduced in the 1760s independently by [[Vincenzo Riccati]] and [[Johann Heinrich Lambert]].<ref>Bradley, Robert E.; D'Antonio, Lawrence A.; Sandifer, Charles Edward. ''Euler at 300: an appreciation.'' Mathematical Association of America, 2007. Page 100.</ref> Riccati used {{math\|''Sc.''}} and {{math\|''Cc.''}} ({{lang\|la\|sinus/cosinus circulare}}) to refer to circular functions and {{math\|''Sh.''}} and {{math\|''Ch.''}} ({{lang\|la\|sinus/cosinus hyperbolico}}) to refer to hyperbolic functions. Lambert adopted the names, but altered the abbreviations to those used today.<ref>Becker, Georg F~~. Becker~~. ''Hyperbolic functions.'' Read Books, 1931. Page xlviii.</ref> The abbreviations {{math\|sh}}, {{math\|ch}}, {{math\|th}}, {{math\|cth}} are also currently used, depending on personal preference. == Notation ==

Hyperbolic functions: Difference between revisions