If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.

If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.

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 no specific organization plan exists limiting the number of scientists at each salary level, the result is a department top-heavy with high-level, high-salaried personnel ''.

If we thus spent our very first day in the midst of a large number of your people honoring a new hero and a great national achievement, our last day, to us at least, was equally impressive and very moving, even though the crowds were absent and there was almost complete silence.

If a wedge-shaped coating of increasing thickness is removed from a substrate by an instrument like the Hesiometer with a knife of constant rake angle, a number of removal mechanisms are often observed which depend upon the thickness of the coating.

If all the operating variables were varied simultaneously, Af operations would be required to do the same job, and as R increases this increases very much more rapidly than the number of operations required by the dynamic program.

If Rock shows up during the number -- or you hear anything -- give me the signal ''.

If one takes the middle number, 5, and multiplies it by 3 ( the base number of the magic square of three ), the result is 15, which is also the constant sum of all the rows, columns, and two main diagonals.

If so, it might be worth while to assign a future jazz show to a different department -- one with enough confidence in the musical material to cut down on the number of performers and give them a little room to display their talents.

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

If its minimal polynomial has degree, then the algebraic number is said to be of degree.

If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.

* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )

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 a ) testimonies conflict one another, b ) there are a small number of witnesses, c ) the speaker has no integrity, d ) the speaker is overly hesitant or bold, or e ) the speaker is known to have motives for lying, then the epistemologist has reason to be skeptical of the speaker's claims.

If we take in our hand any volume ; of divinity or school metaphysics, for instance ; let us ask, Does it contain any abstract reasoning concerning quantity or number?

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

If the two carbon atoms at the double bond are linked to a different number of hydrogen atoms, the halogen is found preferentially at the carbon with fewer hydrogen substituents ( Markovnikov's rule ).

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

If there is no number to its left, simply look at the column headed " 1 " in the previous row.

If the game has been scored correctly, the total number of plate appearances for a team should equal the total of that team's runs, men left on base, and men put out.

If the other player also knows to offer sacrifices, the expert also has to manipulate the number of available sacrifices through earlier play.

If we let them go, they won't stay away, they'll find men to ride with them and they'll be back.

If the hardships of the winter at Valley Forge were trying for healthy men, they were, of course, much more so for those not in good health.

If goodness and badness lie in attitudes only and hence are brought into being by them, those men who greeted death and misery with childishly merry laughter are taking the only sensible line.

If she runs around with other men, and if you hate her as you say, why not just divorce her ''??

`` If asked to choose between a terrible probability and a more terrible possibility, most men will choose the latter ''.

If this entailed transforming the West Saxon fyrd from a sporadic levy of king's men and their retinues into a mounted standing army, so be it.

If women attended, they were often isolated to a section away from the men, supposedly to distance them from any vulgarities that the male spectators ( or players ) might speak.

If left untreated, it is possible for chlamydia in men to spread to the testicles causing epididymitis, which in rare cases can cause sterility if not treated within 6 to 8 weeks.

Criticism of other officials was allowed during these meetings, for instance, Karl Radek said to Lenin ( criticising his position of supporting peace with the Germans ), " If there were five hundred courageous men in Petrograd, we would put you in prison.

If the late queen would have believed her men of war as she did her scribes, we had in her time beaten that great empire in pieces and made their kings of figs and oranges as in old times.

If, for example, eight men line up on the line of scrimmage, the team loses an eligible receiver.

If many men settled in the Faroes in the reign of Harald Hårfagre, people must have known about the Faroes.

In Christ stilling the Storm he wrote: " If a man believe in Christ, and make a point of his belief, then the promise that God hath made to come into the land of light shall be given by virtue of Christ, to all men that make this the chief matter.

If there was a separate class of warriors, it probably consisted of single young men.

On 11 June 1304, with both of them having witnessed the heroic efforts of their countrymen during King Edward's siege of Stirling Castle, Bruce and William Lamberton made a pact that bound them, each to the other, in “ friendship and alliance against all men .” If one should break the secret pact, he would forfeit to the other the sum of ten thousand pounds.

If all else failed, a besieger could claim the booty of his conquest undamaged, and retain his men and equipment intact, for the price of a well-placed bribe to a disgruntled gate-keeper.

If the old have sinned, why should the young suffer ; and if men have been guilty, why should the cattle be destroyed?

# If it were not for God's restraints, there are, in the souls of wicked men, hellish principles reigning which, presently, would kindle and flame out into hellfire.

If the decision is not properly discussed, men and women may view moving in together in different ways.

If I fulfill this path and do not violate it, may it be granted to me to enjoy life and art, being honored with fame among all men for all time to come ; if I transgress it and swear falsely.

If similar amounts of land have been lost on other parts of the Solent shore, the Solent was likely much narrower in Roman times, and it is possible to believe Diodorus Siculus's report that in his time men could wade to the Isle of Wight at low tide.

In 2006, in an interview about The L Word she said more than once that she was " turned on " by the woman-woman sex scenes: " If you look at what we know about men, women and our sexuality, a great majority of people are bisexual.

If that is the position, the decision you have to reach, on all the evidence, is whether you are sure that it was the Defendant who left that stain or whether it is possible that it was one of that other small group of men who share the same DNA characteristics.