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 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 ball originated with the shortstop and was then thrown to the second baseman, the play is referred to as a " 6-4-3 double play ", after the numbers assigned to the players in order of field position ; if it is hit to the second baseman and then thrown to the shortstop, it is known as a 4-6-3 double play ( 6-shortstop, 4-second base, 3-first base ; see baseball positions ).

If the bases are loaded, or if the runner on first base is not a base stealing threat, the first baseman will position himself behind the runner and appropriate for the current batter.

( If the catcher drops the third strike and has to throw the batter-runner out at first base, the first baseman receives the putout while the catcher receives an assist.

* If a batter hits a ball on the ground to the shortstop, who throws the ball to the first baseman to force the first out, it would be noted on the scoresheet as 6 – 3, with 6 for the shortstop and 3 for the first baseman.

* If the batter reaches base because the first baseman dropped the throw from the shortstop, the basepath is drawn and E3 ( an error committed by the first baseman ) is written below.

* If a batter gets a base hit then in the same play advances due to a fielding error by the second baseman, these are written as two events.

If one looks at the fields around the Deserted Village and right up the mountain, one can see the tracks in the fields of ' lazy beds ', which is the way crops like potatoes were grown.

If one quantizes a real scalar field, then one finds that there is only one kind of annihilation operator ; therefore, real scalar fields describe neutral bosons.

If an interlaced video has a frame rate of 15 frames per second the field rate is 30 fields per second.

If the fields have components in the same direction, they constructively interfere, while opposite directions cause destructive interference.

* If someone is careless when watering his fields, and he floods someone else's by accident, he will pay for the grain he has ruined.

If the term has nonetheless retained a certain consistency in its use across these fields and would-be movements, it perhaps reflects the word ’ s position in general English usage: though the standard dictionary definition of irreal gives it the same meaning as unreal, irreal is very rarely used in comparison with unreal.

# If G is any group acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.

If they did exist, both Gauss's law for magnetism and Faraday's law would need to be modified, and the resulting four equations would be fully symmetric under the interchange of electric and magnetic fields ; see magnetic monopoles for details.

If plasma is pushed hard enough, it generates electric fields which allow it to move in response to the push, often ( not always ) deforming the magnetic field in the process.

He asks why postmodernist intellectuals do not respond like people in other fields when asked, " what are the principles of their theories, on what evidence are they based, what do they explain that wasn't already obvious, etc ?... If requests can't be met, then I'd suggest recourse to Hume's advice in similar circumstances: to the flames.

If the strip was in the same place each year, the soil built up into a ridge, creating the ridge and furrow topography still seen in some ancient fields.

If the papilledema has been longstanding, visual fields may be constricted and visual acuity may be decreased.

** If there is an error it is because one of the fields in the Open message doesn ’ t match between the peers, e. g. BGP version mismatch, MD5 password mismatch, the peering router expects a different My AS.

If more than one charge is present, the total electric field at any point is equal to the vector sum of the separate electric fields that each point charge would create in the absence of the others.

If some of the stellar magnetic fields are really induced by dynamos, then field strength might be associated with rotation rate.

If it goes somewhere else, the Newtonians argue, one must question one's measurements of the original position of the object, the exact direction of the striking object, gravitational or other fields that were inadvertently ignored, etc.

If a pacemaker has been embedded in a patient's chest ( usually for the purpose of monitoring and regulating the heart for steady electrically induced beats ), care should be taken to keep it away from magnetic fields.

) If formulated in von Neumann – Bernays – Gödel set theory, the surreal numbers are the largest possible ordered field ; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals ; it has also been shown that the maximal class hyperreal field is isomorphic to the maximal class surreal field.

If the containment fields ever fail, the subsequent interaction of the antimatter fuel with the container walls would result in a catastrophic release of energy, with the resultant explosion capable of utterly destroying the ship.

If the manifold M is smooth ( respectively analytic )--- that is, the change of coordinates are smooth ( respectively analytic )--- then one can make sense of the notion of smooth ( respectively analytic ) vector fields.

#> If the chart uses more than one bar color, add a legend by selecting the appropriate fields from the following six options ( use only the colors that are used in the graphic.

If you scatter them through the wide fields, they will give you back fruitful harvests, and ripening crops.