Hyperbolic functions: Difference between revisions

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The first to suggest a similarity between the sector of the circle and that of the hyperbola was [[Isaac Newton]] in his 1687 [[Philosophiæ Naturalis Principia Mathematica|''Principia Mathematica'']].<ref name=":0">{{Cite book |last=McMahon |first=James |url=https://archive.org/details/hyperbolicfuncti031883mbp/page/n75/mode/2up |title=Hyperbolic Functions |date=1896 |publisher=John Wiley And Sons |others=Osmania University, Digital Library Of India}}</ref>

In 17721722, [[Roger Cotes]] suggested to modify the trigonometric functions using the [[imaginary unit]] <math>i=\sqrt{-1} </math> to obtain an oblate [[spheroid]] from a prolate one.<ref name=":0" />

Hyperbolic functions were formally introduced in 1757 by [[Vincenzo Riccati]].<ref name=":0" /><ref name=":3" /><ref name=":4" /> 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.<ref name=":0" /> As early as 1759, [[François Daviet de Foncenex|Daviet de Foncenex]] showed the interchangeability of the trigonometric and hyperbolic functions using the imaginary unit and extended [[de Moivre's formula]] to hyperbolic functions.<ref name=":4" /><ref name=":0" />