If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.

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 there was realism in the theater, there would never be a third act.

* If the third baseman fields a ball and throws it to first, it is recorded as a 5 – 3 out.

If a Committee manages to adopt a joint text, it then has to be approved in a third reading by both the Council and Parliament or the proposal is abandoned.

If the ideals A and B of R are coprime, then AB = A ∩ B ; furthermore, if C is a third ideal such that A contains BC, then A contains C. The Chinese remainder theorem is an important statement about coprime ideals.

In particular, the third anathema reads: " If anyone divides in the one Christ the hypostases after the union, joining them only by a conjunction of dignity or authority or power, and not rather by a coming together in a union by nature, let him be anathema.

If a team fails to gain ten yards in two downs they usually punt the ball on third down or try to kick a field goal ( see below ), depending on their position on the field.

If objects are seen as moving within a rotating frame, this movement results in another fictitious force, the Coriolis force ; and if the rate of rotation of the frame is changing, a third fictitious force, the Euler force is experienced.

If the third layer is placed so that its atoms are directly above those of the first layer, the stacking will be ABA — this is the hcp structure, and it continues ABABABAB.

If the panegyric detailing the ceremony implied that the true center of the Empire was not Rome, but where the Emperor sat ("... the capital of the Empire appeared to be there, where the two emperors met "), it simply echoed what had already been stated by the historian Herodian in the early third century: " Rome is where the emperor is ".

If in the third identity we take H = G, we get that the set of commutators is stable under any endomorphism of G. This is in fact a generalization of the second identity, since we can take f to be the conjugation automorphism.

If his son were guilty, he would still believe him innocent, on the basis of faith in his son ; this would violate the third subjunctive condition.

The parallel postulate: If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

If there is another functional group at a carbon, it may be named with the Greek letter, e. g., the gamma-amine in gamma-aminobutanoic acid is on the third carbon of the carbon chain attached to the carboxylic acid group.

If the team that batted second is substantially behind on first innings total, it may be required to bat again ( i. e., to immediately follow on from its first innings ) in the third innings of the match.

If anyone violates the truce of God and after the third admonition does not make satisfaction, he shall be anathematized.

If he disregards the third admonition the bishop, either with the advice of the metropolitan or with that of two or one of the neighboring bishops, shall pronounce the sentence of anathema against the violator and in writing denounce him to all the bishops.

If the Supreme Court grants certiorari and accepts the case, it will receive written briefs from each side ( and any amici curiae or friends of the court — usually interested third parties with some expertise to bear on the subject ) and schedule oral arguments.

If Language A borrowed a word from Language B, or both borrowed the word from a third language or inherited it from a common ancestor, and later the word shifted in meaning or acquired additional meanings in at least one of these languages, a native speaker of one language will face a false friend when learning the other.

If you listened very carefully, I have already stated to you what the third word is.

If you have read what I have told you, you will see that I have given you the third word.

If one carefully observes the third equation one will notice it also works for n

If the monopoly were permitted to charge individualised prices ( this is termed third degree price discrimination ), the quantity produced, and the price charged to the marginal customer, would be identical to that of a competitive company, thus eliminating the deadweight loss ; however, all gains from trade ( social welfare ) would accrue to the monopolist and none to the consumer.

If only the second and third conditions of the definition of measure above are met, and takes on at most one of the values, then is called a signed measure.

If the old fool argues about the price, tell him I shall order my husband not to treat him as a patient any longer.

If communications work, his decision would be instantly known in all command posts that would originate the actual go order.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If we grasp this opportunity to build an age of productive partnership between the less fortunate nations and those that have already achieved a high state of economic advancement, we will make brighter the outlook for a world order based upon security and freedom.

If obeyed, the law brings order and satisfaction.

If it is decided to make a small shift which may be required from military aid or special assistance funds, in order to carry out the purposes of the Mutual Security Act through this new peaceful program, this will be a hopeful sign to the world.

If not, how long to order and what is the price ''??

If possible, he should make an appointment in order that all persons involved may be present.

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

If we neglect higher than first order terms in the fluctuations, the mass balance equation becomes

If a planet is found to rotate slower than expected, then astronomers suspect that the planet is accompanied by a satellite, because the total angular momentum is shared between the planet and its satellite in order to be conserved.

If a player is one point away from winning a match, that player's opponent will always want to double as early as possible in order to catch up.

If a house or car is above a certain value, the bankrupt can buy the interest back from the estate in order to keep the asset.

If there is still a tie, each atom in each of the two lists is replaced with a sub-list of the other atoms bonded to it ( at distance 3 from the stereocenter ), the sub-lists are arranged in decreasing order of atomic number, and the entire structure is again compared atom by atom.

If a pixel-by-pixel ( image order ) approach to rendering is impractical or too slow for some task, then a primitive-by-primitive ( object order ) approach to rendering may prove useful.

If the hoop is the hoop in order for the striker ’ s ball, the striker earns a bonus stroke.

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, after that, they breach the order, proceedings can be started and in theory the person involved can be sent to prison.

If the case is dismissed, creditors will look to non-bankruptcy law in order to satisfy their claims.

If the first letters are the same, then the second letters are compared, and so on, until the order is decided.

If each pixel on the display actually contains three rectangular subpixels of red, green, and blue, in that fixed order, then things on the screen that are smaller than one full pixel in size can be rendered by lighting only one or two of the subpixels.

If we insert vertices in random order, it turns out ( by a somewhat intricate proof ) that each insertion will flip, on average, only O ( 1 ) triangles – although sometimes it will flip many more.

" If we cannot move on to point B until we have proved point A, and if in order to prove point A we must establish it with absolute certainty, then it looks as though we will have a very hard time proving any point at all.

If several planets in the same system are discovered at the same time, the closest one to the star gets the next letter, followed by the other planets in order of orbital size.