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 the differential equations are nonlinear and have a known solution, it may be possible to linearize the nonlinear differential equations at that solution.

If the resulting linear differential equations have constant coefficients one can take their Laplace transform to obtain a transfer function.

If the density of the chain is variable then the analysis above can be adapted to produce equations for the curve given the density, or given the curve to find the density.

If is continuous in an open set Ω and the partial derivatives of ƒ with respect to x and y exist in Ω, and satisfies the Cauchy – Riemann equations throughout Ω, then ƒ is holomorphic ( and thus analytic ).

* If ƒ ( z ) is locally integrable in an open domain Ω ⊂ C, and satisfies the Cauchy – Riemann equations weakly, then ƒ agrees almost everywhere with an analytic function in Ω.

Linear Diophantine equations take the form ax + by = c. If c is the greatest common divisor of a and b then this is Bézout's identity, and the equation has an infinite number of solutions.

The evidence was compiled by W de Sitter ( 1927 ) who wrote " If we accept this hypothesis, then the ' astronomical time ', given by the earth's rotation, and used in all practical astronomical computations, differs from the ' uniform ' or ' Newtonian ' time, which is defined as the independent variable of the equations of celestial mechanics ".

If interstellar colonization is possible, then this assumption is invalid, and the equations of population dynamics would apply instead.

If a complex function = is holomorphic, then u and v have first partial derivatives with respect to x and y, and satisfy the Cauchy – Riemann equations:

If one identifies C with R < sup > 2 </ sup >, then the holomorphic functions coincide with those functions of two real variables with continuous first derivatives which solve the Cauchy-Riemann equations, a set of two partial differential equations.

If they did exist, both Gauss's law for magnetism and Faraday's law would need to be modified, and the resulting four equations would be fully symmetric under the interchange of electric and magnetic fields ; see magnetic monopoles for details.

If the velocities are and before the collision and and after, the equations expressing conservation of momentum and kinetic energy are:

If the generalized coordinates are represented as a vector and time differentiation is represented by a dot over the variable, then the equations of motion ( known as the Lagrange or Euler – Lagrange equations ) are a set of equations:

If the Euler-Lagrange equations are solved for this system, it is found that the motion depends on two constants and ( each related to a constant of motion ).

If λ represents wavelength and f represents frequency ( note, λf = c where c is the speed of light ), then z is defined by the equations:

If the string is approximated with 100 discrete mass points one gets the 100 coupled second order differential equations (), () and () or equivalently 200 coupled first order differential equations.

If and are not neglected, the Telegrapher's equations become:

If f = u + iv, then the Cauchy – Riemann equations state that

If the dynamics of a system is known, the equations are the solutions to the differential equations describing the motion of the dynamics.