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 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, however, a layer of paper remains stuck to the surface, the adhesive has not failed.

If the depletion layer is large enough to catch the whole shower or to stop a heavy particle, a fairly accurate measurement of the particle ’ s energy can be made, simply by measuring the charge conducted and without the complexity of a magnetic spectrometer, etc.

If only layer C changes, we should find a way to avoid re-blending all of the layers when computing F. Without any special considerations, four full-image blends would need to occur.

If all layers of an image change regularly but a large number of layer still need to be composited ( such as in distributed rendering ), the commutativity of a compositing operator can still be exploited to speed up computation through parallelism even when there is no gain from pre-computation.

If both copies are damaged, the Purkinje layer ( a part of the cerebellum that contains better-connected neurons than any other ) develops abnormally, runting is more common, and pups die within weeks due to inadequate lung development.

If pathogens successfully evade the innate response, vertebrates possess a second layer of protection, the adaptive immune system, which is activated by the innate response.

If the applied voltage is large enough, the liquid crystal molecules in the center of the layer are almost completely untwisted and the polarization of the incident light is not rotated as it passes through the liquid crystal layer.

If each additional layer contains less oil, the final painting will crack and peel.

If the word is entirely on the first board layer, they instead score two points per letter.

If enough stabilization occurs, an inversion layer is formed.

If a mapping is available, presentation service data units are encapsulated into session protocol data units, and passed down the stack. This layer provides independence from data representation ( e. g., encryption ) by translating between application and network formats.

If present, a layer of liquid water would suggest the possibility, however unlikely, of life.

If each scanline has its own layer, the Pole Position effect is produced, which creates a pseudo-3D road ( or a pseudo-3D ball court as in NBA Jam ) on a 2D system.

If the distinction between confined and unconfined is not clear geologically ( i. e., if it is not known if a clear confining layer exists, or if the geology is more complex, e. g., a fractured bedrock aquifer ), the value of storativity returned from an aquifer test can be used to determine it ( although aquifer tests in unconfined aquifers should be interpreted differently than confined ones ).

If these confining layers are composed of compressible silt or clay, the loss of water to the aquifer reduces the water pressure in the confining layer, causing it to compress from the weight of overlying geologic materials.

If a problem can be adequately parallelized, a “ thin ” layer of “ grid ” infrastructure can allow conventional, standalone programs, given a different part of the same problem, to run on multiple machines.

If a surface heating the liquid is significantly hotter than the liquid then film boiling will occur, where a thin layer of vapor, which has low thermal conductivity, insulates the surface.

If the vapor is re-condensed, the layers will reform in the condensate, and will do so in a fixed ratio, which in this case is 4. 4 % of the volume in the top layer and 95. 6 % in the bottom layer.

If the scarring is deeper but not excessive, it can be repaired by machining off a layer of the disc's surface.

If the ice contains enough ammonia or other antifreeze, Oberon may possess a liquid ocean layer at the core – mantle boundary.

If the middle layer is made thin enough, it acts as a quantum well.