If a child watched its progress he whispered, `` Hay, hay, load of hay -- make a wish and turn away '', and then stared rigidly in the opposite direction until the sound of the horses' feet returned no more.

If `` Jack the Courtier '' is really to be taken as Swift, the following remark is obviously Steele's comment on Swift's change of parties and its effect on their friendship: `` I assure you, dear Jack, when I first found out such an Allay in you, as makes you of so malleable a Constitution, that you may be worked into any Form an Artificer pleases, I foresaw I should not enjoy your Favour much longer ''.

If art is to release us from these postulated things ( things we must think symbolically about ) and bring us back to the ineffable beauty and richness of the aesthetic component of reality in its immediacy, it must sever its connection with these common sense entities ''.

If, as Reid says, `` nearly all his poetry was produced when he was not taking opium '', there may be some reason to doubt that he was under its influence in the period from 1896 to 1900 when he was writing the poems to Katie King and making plans for another book of verse.

If there were no West Berlin problem, imperialist quarters would have invented an excuse for stepping up the armaments race to try to solve the internal and external problems besetting the United States and its NATO partners.

If you do use a cold frame be sure that its ventilation is adequate.

If the temperature is controlled properly, the avocado will delay its ripening until needed.

If the target can change its position significantly during the 30 minutes the missile is in the air on its way, the probability of the missile destroying the target is drastically reduced.

If you can't see your way clear to have summer cooling included when building, by all means make provision for its easy adding later.

If a nation wished to get a head start in physical fitness over all other nations, it would start its kindergarten students on a program of gymnastics the day they entered and thus eliminate a large number of the problems that plague American schools.

If you have a higher-quality product, how can you make it stand out -- justify its premium price -- without the spoken word??

If this seems arbitrary, its effect was to treat citizens of the District of Columbia equally with citizens of the states -- at the expense of expanding a troublesome jurisdiction.

If the transferor has substantial assets other than the claim, it seems reasonable to assume no corporation would be willing to acquire all of its properties in the dim hope of collecting a claim for refund of taxes.

If this threefold division of costs were to have its counterpart in the actual rates of charge for service, as it actually does have in some rates, there would result a three-part rate for any one class of service.

If, however, the figure to be discerned were complicated, composed of several interlocking subfigures, and so on, even the tracing process failed him, and he could not focus even relatively simple shapes among its parts.

If it failed on occasion to elect its candidates for general state offices by majorities, the failure was due to a lingering remnant of the Know-Nothing party, which called itself the American Republican party.

If T is the total `` length '' of the process, its feed state may be denoted by a vector p(T) and the product state by p(Q).

If anti-Semitism was on trial in Jerusalem, why was it not identified, and with enough emphasis to capture the notice of the world press, in its connection with the activities of Eichmann's Department of Jewish Affairs, as exemplified by the betrayal and murder of Jews by non-police and non-party anti-Semites in Germany, as well as in Poland, Czechoslovakia, Hungary??

If, as a home movie maker, you shoot the inevitable footage of your child taking its first steps, you have merely recorded an historical event.

If death receives more than its share of attention from the theologian and if sin receives less than its share, the gift of the life eternal through Christ begins to look like the divinely appointed means of rescue from temporal, i.e., created, existence.

The next traditional step then was to accept it as the authoritative textbook of the Christian faith just as one would accept a treatise on any earthly `` science '', and I submitted to its conditions according to Christ's invitation and promise that, `` If any man will do his will, he shall know of the doctrine, whether it be of God, or whether I speak of myself '' ( John 7: 17 ).

If a man totally ignorant of America were to judge our land and its civilization based on Hollywood alone, what conclusions do you think he might come to??

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 a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).

If two cofinal subsets of B have minimal cardinality ( i. e. their cardinality is the cofinality of B ), then they are order isomorphic to each other.

If there is a graph requiring 5 colors, then there is a minimal such graph, where removing any vertex makes it four-colorable.

If the field is increased past the optimum, further volume reductions are possible with minimal increase in cost.

If I is a right ideal of R, then I is simple as a right module if and only if I is a minimal non-zero right ideal: If M is a non-zero proper submodule of I, then it is also a right ideal, so I is not minimal.

If two polarizers are placed atop one another at 90 ° angles to one another, there is minimal light transmission.

If the ordered set S is complete, then, for every Dedekind cut ( A, B ) of S, the set B must have a minimal element b,

If one performs an inversion of this parametrization centered on the triple point, one obtains a complete minimal surface with three " ends " ( that's how this parametrization was discovered naturally ).

If a given system of rights does not fully guarantee these at minimal ( or no ) cost, then the resulting distribution can be inefficient.

If a wound becomes covered with epithelial tissue within two weeks, minimal collagen will be deposited and no scar will form.

If 60 ° could be trisected, the degree of a minimal polynomial of over Q would be a power of two.

If V and W are finite-dimensional, then the space of all linear transformations from W to V, denoted Hom ( W, V ), is generated by such outer products ; in fact, the rank of a matrix is the minimal number of such outer products needed to express it as a sum ( this is the tensor rank of a matrix ).

If there exists a minimal sufficient statistic, and this is usually the case, then every complete sufficient statistic is necessarily minimal sufficient ( note that this statement does not exclude the option of a pathological case in which a complete sufficient exists while there is no minimal sufficient statistic ).

Apter also reports that Smith put in minimal effort at Notre Dame, sufficient to gain pass marks, and quotes Smith as saying: " If you were crafty enough you could convince the teachers you were special: I did virtually nothing for three years.

If the boxer is just a beginner, a minimal training routine might consist of learning how to hit the heavy bag, the speed bag, and the double end bag ( a small bag with a cord on top and bottom connecting it to the floor and ceiling ) as well as doing shadowboxing in front of a mirror, skipping rope, calisthenics and jogging every day, as well as an occasional practice bout inside the ring ( sparring ).

If these groups have N < sub > p </ sub > and N < sub > q </ sub > elements, respectively, then for any point P on the original curve, by Lagrange's theorem, k > 0 is minimal such that on the curve modulo p implies that k divides N < sub > p </ sub >; moreover,.

If shot from at least ten feet away by a gun with typical muzzle velocity, there will be minimal damage to other body parts.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

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 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 F is algebraically closed and p ( x ) is an irreducible polynomial of F, then it has some root a and therefore p ( x ) is a multiple of x − a.

If the quadratic polynomial is monic then the roots are quadratic integers.

If a polynomial time algorithm calls as a subroutine polynomially many polynomial time algorithms, the resulting algorithm is still polynomial time.

If the initial value of a polynomial ( and of its finite differences ) is calculated by some means for some value of X, the difference engine can calculate any number of nearby values, using the method generally known as the method of finite differences.

If f is a polynomial and p is big enough, then the remainder term vanishes.

* If f is an irreducible polynomial of prime degree p with rational coefficients and exactly two non-real roots, then the Galois group of f is the full symmetric group S < sub > p </ sub >.

If is a left-( respectively right -) Noetherian ring, then the polynomial ring is also a left-( respectively right -) Noetherian ring.

If a large, b-bit number is the product of two primes that are roughly the same size, then no algorithm has been published that can factor in polynomial time, i. e., that can factor it in time O ( b < sup > k </ sup >) for some constant k. There are published algorithms that are faster than O (( 1 + ε )< sup > b </ sup >) for all positive ε, i. e., sub-exponential.

A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.

If, however, the set of allowed candidates is expanded to the complex numbers, every non-constant polynomial has at least one root ; this is the fundamental theorem of algebra.

If R is commutative, then one can associate to every polynomial P in R, a polynomial function f with domain and range equal to R ( more generally one can take domain and range to be the same unital associative algebra over R ).

If R is an integral domain and f and g are polynomials in R, it is said that f divides g or f is a divisor of g if there exists a polynomial q in R such that f q = g. One can show that every zero gives rise to a linear divisor, or more formally, if f is a polynomial in R and r is an element of R such that f ( r ) = 0, then the polynomial ( X − r ) divides f. The converse is also true.