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The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz, each independently, for rational power functions in the mid 17th century, who both then used it to derive the power rule for integrals as the inverse operation. This mirrors the conventional way the related theorems are presented in modern basic ...
The elementary power rule generalizes considerably. The most general power rule is the functional power rule: for any functions f and g, ′ = () ′ = (′ + ′ ), wherever both sides are well defined. Special cases
Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .
The radical axis of two intersecting circles. The power diagram of the two circles is the partition of the plane into two halfplanes formed by this line. In the case n = 2, the power diagram consists of two halfplanes, separated by a line called the radical axis or chordale of the two circles. Along the radical axis, both circles have equal power.
Blondel's theorem (electric power) Blum's speedup theorem (computational complexity theory) Bôcher's theorem (complex analysis) Bochner's tube theorem (complex analysis) Bogoliubov–Parasyuk theorem (quantum field theory) Bohr–Mollerup theorem (gamma function) Bohr–van Leeuwen theorem ; Bolyai–Gerwien theorem (discrete geometry)
The original examples are Abel's theorem showing that if a series converges to some limit then its Abel sum is the same limit, and Tauber's theorem showing that if the Abel sum of a series exists and the coefficients are sufficiently small (o(1/n)) then the series converges to the Abel sum. More general Abelian and Tauberian theorems give ...
The theorem is named for Georg Cantor, who first stated and proved it at the end of the 19th century. Cantor's theorem had immediate and important consequences for the philosophy of mathematics. For instance, by iteratively taking the power set of an infinite set and applying Cantor's theorem, we obtain an endless hierarchy of infinite ...
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.