theorem

It was gravely said by some of the prelates in the Council of Trent, where the doctrine of the Schoolmen bare great sway, that the Schoolmen were like astronomers, which did feign eccentrics and epicycles, and such engines of orbs, to save the phenomena; though they knew there were no such things; and in like manner, that the Schoolmen had framed a number of subtle and intricate axioms, and theorems, to save the practice of the church.

The objects of geometrical inquiry are so entirely abstracted from those pursuits which stir up and put in motion the unruly passions of the human heart, that mankind, without difficulty, adopt not only the more simple theorems of the science, but even those abstruse paradoxes which, however they may appear susceptible of demonstration, are at variance with the natural conceptions which the mind, without the aid of philosophy, would be led to entertain upon the subject.

The theorem that the square of the diagonal is double the square of the side--that famous discovery of primitive mathematics, in honour of which the legendary Pythagoras is said to have sacrificed a hecatomb--is elicited from him.

"Most decidedly," said he, "men are not equal, and I must beg my father to develop this theorem in the Chamber of Peers."

Most people, in thinking about punishment, have had no more need to hide their vindictive impulses from themselves than they have had to hide the exponential theorem. Our impulses are not patent to a casual observation, but are only to be discovered by a scientific study of our actions, in the course of which we must regard ourselves as objectively as we should the motions of the planets or the chemical reactions of a new element.

At the age of twenty-one he wrote a treatise upon the Binomial Theorem, which has had a European vogue.

what I've got to do," said Tom, drawing Maggie toward him and showing her his theorem, while she pushed her hair behind her ears, and prepared herself to prove her capability of helping him in Euclid.

By Theorems 14, 16, and 27 and the dominated convergence theorem, we have the following two theorems.

Samet [18] proved coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces.

By the theory of quasi-log schemes discussed in [7, Chapter 6] and Theorem 1.1, the fundamental theorems of the minimal model program hold for [Z, [v.sup.*][omega]].

They illustrate them with fundamental theorems such as Gromov's Theorem on groups of polynomial growth, Tits' Alternative Theorem, Mostow's Rigidity Theorem, Stallings' Theorem on ends of groups, and theorems of Tukia and Schwartz on quasi-isometric rigidity for lattices in real-hyperbolic spaces.

Recently, Dalal and Govil [15] unified the above theorems and proved the following theorem.