Sentence examples for discovered the same theorem from inspiring English sources
However, he failed to publish his work, and in Germany Leibniz independently discovered the same theorem and published it in 1686.
Interestingly, nearly the same theorem was proven under two phylogenomic models that addressed horizontal gene transfer (HGT)!
By Theorem 2.6, Q is precisely the set of minimal separators of H. Furthermore, because H is also a minimal triangulation of G(M), the same theorem states that Q is a subset of the minimal separators of G M).
Saito et al. [34] also discover the same conclusions for the two-species predator-prey systems.
It has the same theorems as the local lΛ, namely the elements of Λ.
Call two definitions equivalent iff they yield the same theorems in the expanded language.
However, if Pythagoras had not lived, someone else would have discovered exactly the same Pythagoras theorem.
In connection with his studies of the work of Hilbert, he discovered the plane translation theorem, which characterizes topological mappings of the Cartesian plane, and the first of his fixed-point theorems, which later became important in the establishment of some fundamental theorems in branches of mathematics such as differential equations and game theory.
In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus.
Mesopotamian, Indian and Chinese mathematicians are all known to have discovered the theorem independently and, in some cases, provide proofs for special cases.
