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 a translation memory system is used consistently on appropriate texts over a period of time, it can save translators considerable work.

# Contingency: If a consequence does not contingently ( reliably, or consistently ) follow the target response, its effectiveness upon the response is reduced.

If all instances are running at the same frame rate consistently, it is possible to get tight synchronization between displays.

If the figure 20px can be consistently positioned at all points of the surface without turning into its mirror image, then this will induce an orientation in the above sense on each of the triangles of the triangulation by selecting the direction of each of the triangles based on the order red-green-blue of colors of any of the figures in the interior of the triangle.

If deadlines are consistently maintained instead of arbitrarily moved up, proofreaders can manage their own time by putting proofs aside at their own discretion for re-reading later.

If the scale consistently reads " 150 ", then it is reliable, but not valid.

Koch consistently demonstrated a fierce love for New York City, which some observers felt he carried to extremes on occasion: In 1984 he had gone on record as opposing the creation of a second telephone area code for the city, claiming that this would divide the city's population ; and when the National Football League's New York Giants won Super Bowl XXI in January 1987, he refused to grant a permit for the team to hold their traditional victory parade in the city, quipping famously, " If they want a parade, let them parade in front of the oil drums in Moonachie " ( the latter being a town in New Jersey adjacent to East Rutherford, site of the Meadowlands Sports Complex, where the Giants play their home games ).

If only a handful of dominant teams are able to win consistently and challenge for the championship, many of the contests will be blowouts by the superior team, reducing the sport's attractiveness for spectators both at the ground and viewing on television.

If the judge cannot consistently tell which is which, then the computer wins the game.

If the usual resting pulse pressure is consistently greater than 100 mmHg, the most likely basis is stiffness of the major arteries, aortic regurgitation ( a leak in the aortic valve ), arteriovenous malformation ( an extra path for blood to travel from a high pressure artery to a low pressure vein without the gradient of a capillary bed ), hyperthyroidism or some combination.

If bad pivots are consistently chosen, this degrades to the minimum-based selection described previously, and so can require as much as O ( n < sup > 2 </ sup >) time.

If milliliters are used consistently for volume measurements, the result of the COD calculation is given in mg / L.

If you can explain that fact consistently with the two men having faithfully and honestly discharged their duties you should acquit them.

If you cannot explain the staggering fact consistently with the men having faithfully discharged their duties then you must convict them.

If a set of edges contains a cycle, then the corresponding columns ( multiplied by if necessary to reorient the edges consistently around the cycle ) sum to zero, and is not independent.

If a data model is used consistently across systems then compatibility of data can be achieved.

If a Kapre befriends any human, especially because of love, the Kapre will consistently follow its " love interest " throughout life.

If the amount of water ingested consistently falls below the amount of water lost, the serum sodium level will begin to rise, leading to hypernatremia.

However, having failed to consistently achieve blue dye from the Murex trunculus, he wrote: “ If for the present all hope is to be abandoned of rediscovering the hillazon shel tekhelet in some species of the genera Murex and Purpura we could do worse than suggest the Janthina as a not improbable identification ”.

If the zero reading is consistently above or below zero, a systematic error is present.

If they are not worn consistently, treatment time will increase.

* " If you consistently and persistently do the things that other successful people do, nothing in the world can stop you from being a big success also.

If executed properly and consistently this technique would be able to change the game's long-term odds from the house's favor to the player's favor.

If one acts " in good faith ", one assumes that relevant principles will be honored in practice, and if that faith is disappointed, that is because in practice the principles were not applied consistently or appropriately.