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In mathematics, the regula falsi, method of false position, or false position method is a very old method for solving an equation with one unknown; this method, ...
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This means that the false position method always converges; however, only with a linear order of convergence. Bracketing with a super-linear order of convergence as the secant method can be attained with improvements to the false position method (see Regula falsi § Improvements in regula falsi) such as the ITP method or the Illinois method.
False position is similar to the secant method, except that, instead of retaining the last two points, it makes sure to keep one point on either side of the root. The false position method can be faster than the bisection method and will never diverge like the secant method.
False position and regula falsi are often treated as names for the same algorithm or class of algorithms. Yes, I don't deny that, and I concede that Wikipedia's policy is not to promote new usages. But, as you said, both names are widely-used and well-established. That means that Wikipedia isn't compelled to use one instead of the other.
Solving these Aha problems involves a technique called method of false position. The technique is also called the method of false assumption. The scribe would substitute an initial guess of the answer into the problem.
Usage on de.wikipedia.org Regula falsi; Usage on de.wikibooks.org Ing Mathematik: Numerisches Lösen nichtlinearer Gleichungen; Usage on en.wikibooks.org Introduction to Numerical Methods/Roots of Equations; Usage on es.wikipedia.org Método de la regla falsa; Usage on fa.wikipedia.org روش نابجایی; Usage on fi.wikipedia.org Regula ...