If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If we are to believe the list of titles printed in Malraux's latest book, La Metamorphose Des Dieux, Vol. 1 ( ( 1957 ), he is still engaged in writing a large novel under his original title.

If the original word was capitalised, then the first letter of its abbreviation should retain the capital, for example Lev.

If Acorn had thought to include this small modification in the original Electron design it is likely the machine would have had a much greater impact as it would have nearly doubled the amount of motion possible in games and saved modes 0 – 3 ( including the only 16 colour mode ) from being nearly useless due to contended memory timings.

* Split ( only available as first decision of a hand ): If the first two cards have the same value, the player can split them into two hands, by moving a second bet equal to the first into an area outside the betting box of the original bet.

If all four players pass in the first round, the deal is not played ; in rubber bridge the deal is not scored and the hand is redealt by the original dealer, while in duplicate the score is recorded as zero for each pair and returned to the board.

If you admired a necklace worn by Bette Davis in The Private Lives of Elizabeth and Essex, you could buy a copy from Joseff of Hollywood, who made the original.

If preserving the original quality of the stream is more important than eliminating the correspondingly larger data sizes, lossless codecs are preferred.

If later characters are stereotypes, it's because they are from the same original mould.

If the original penalty yardage would have resulted in a first down or moving the ball past the goal line, a first down is awarded.

To make a figure larger or smaller is equivalent to multiplying the Cartesian coordinates of every point by the same positive number m. If ( x, y ) are the coordinates of a point on the original figure, the corresponding point on the scaled figure has coordinates

If the earlier completion procedure is applied to a normed vector space, the result is a Banach space containing the original space as a dense subspace, and if it is applied to an inner product space, the result is a Hilbert space containing the original space as a dense subspace.

If Wisda's Landscaping breaks the contract, and Neal Townsend is forced to hire another service for $ 60 an hour, expectation ( direct ) damages paid to Neal Townsend would equal $ 100 ($ 10 an hour, the difference in price between the original contract and the new contract ).

To avoid debates about the possibility of in-vitro fertilization, artificial insemination, or cloning, the original Darwin Awards book applied the following " deserted island " test to potential winners: If the person were unable to reproduce when stranded on a deserted island with a fertile member of the opposite sex, he or she would be considered sterile.

If the polar reciprocal of the canonical form in the sphere is congruent to the original, then the figure is self-dual.

If an aftershock is larger than the main shock, the aftershock is redesignated as the main shock and the original main shock is redesignated as a foreshock.

If this triangulated graph is colorable using four colors or less, so is the original graph since the same coloring is valid if edges are removed.

If we study the Four Noble Truths with the help of these references and explanations, we get a fairly good and accurate account of the essential teachings of the Buddha according to the original texts.

If, supposing it turns out that the original Ship of Theseus, S1, was actually stolen property, and the rightful owner demands its return, should the police give him S2 or S3?

If a compression scheme is lossless — that is, you can always recover the entire original message by uncompressing — then a compressed message has the same quantity of information as the original, but communicated in fewer bits.

If any other person has put in the eye and eyebrow of a face, I can perceive whose work the original face is, and who has painted the eye and eyebrow.

If Joe answers Jim, saying " That may be true for you, but it is not true for me ," he has given an answer which is fallacious as well as being somewhat meaningless in the context of Jim's original statement.

It features the band members ' favorite original songs plus three new tracks, " If I Die Tomorrow ", " Sick Love Song " ( co-written by Sixx and James Michael ), and a cover of The Rolling Stones ' classic " Street Fighting Man ".

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If Af denotes the space of N times continuously differentiable functions, then the space V of solutions of this differential equation is a subspace of Af.

If D denotes the differentiation operator and P is the polynomial Af then V is the null space of the operator p (, ), because Af simply says Af.

If Af is the null space of Af, then Theorem 12 says that Af.

If the argument is accepted as essentially sound up to this point, it remains for us to consider whether the patient's difficulties in orienting himself spatially and in locating objects in space with the sense of touch can be explained by his defective visual condition.

If, on the other hand, they opted for representation, it had to be representation per se -- representation as image pure and simple, without connotations ( at least, without more than schematic ones ) of the three-dimensional space in which the objects represented originally existed.

If a child loses a molar at the age of two, the adjoining teeth may shift toward the empty space, thus narrowing the place intended for the permanent ones and producing a jumble.

If elements in the sample space increase arithmetically, when placed in some order, then the median and arithmetic average are equal.

If antimatter-dominated regions of space existed, the gamma rays produced in annihilation reactions along the boundary between matter and antimatter regions would be detectable.

If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.

* Theorem If X is a normed space, then X ′ is a Banach space.

If F is also surjective, then the Banach space X is called reflexive.

* Corollary If X is a Banach space, then X is reflexive if and only if X ′ is reflexive, which is the case if and only if its unit ball is compact in the weak topology.

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

If the norm of a Banach space satisfies this identity, the associated inner product which makes it into a Hilbert space is given by the polarization identity.

If X is a real Banach space, then the polarization identity is

If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.