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By the above paragraph, one can show that any constructible point can be obtained by such a sequence of extensions.
Some Related Sentences
By and above
By now Harmony could see that most of the adults in the train were winded and resting, or else siphoned off from the games by the challenging lure of the great cliff towering above them.
By ancient common law it might be required of all persons above the age of 12, and it was repeatedly used as a test for the disaffected.
By application of a voltage during the presence of this gas, gas ions in the vicinity of the tip undergo ionisation, with greater numbers of ions generated immediately above atoms occupying edge or planar sites.
By his advice Benedict became a hermit and for three years, unknown to men, lived in this cave above the lake.
By the 16th century, Cairo also had high-rise apartment buildings where the two lower floors were for commercial and storage purposes and the multiple stories above them were rented out to tenants.
By contrast to the above philosophers, Immanuel Kant held that the account of the concept as an abstraction of experience is only partly correct.
By twice applying the transformation above from the stationary to the rotating frame, the absolute acceleration of the particle can be written as:
By moving the unit vectors so their tails coincide, as seen in the circle at the left of the image above, it is seen that u < sub > ρ </ sub > and u < sub > θ </ sub > form a right-angled pair with tips on the unit circle that trace back and forth on the perimeter of this circle with the same angle θ ( t ) as r ( t ).
By contrast, for higher frequency radiations at ultraviolet frequencies and above ( i. e., X-rays and gamma rays ) the damage to chemical materials and living cells by EMR is far larger than that done by simple heating, due to the ability of single photons in such high frequency EMR to damage individual molecules chemically.
By May 1949, the initial orders provided a primitive relocating assembler taking advantage of the mnemonic design described above, all in 31 words.
By means of psychological suggestion, it created a new type of religious man, a type that placed emotion above reason and rites, and religious exaltation above knowledge.
By the 1970s, because of the advent of psychedelic art, artists became used to brighter pigments, and pigments called " bright indigo " or " brite blue-violet " that are the pigment equivalent of the electric indigo reproduced in the section above became available in artists ' pigments and colored pencils.
As for the contradiction between German rearmament and his message of peace, Ribbentrop argued to whoever would listen that the German people had been “ humiliated ” by the Versailles treaty, that Germany wanted peace above all, and German violations of Versailles were part of an effort to restore Germany's " self-respect " By the 1930s, much of British opinion had been convinced that the treaty was monstrously unfair and unjust to Germany, so as a result, many in Britain like Thomas Jones were very open to Ribbentrop ’ s message that if only Versailles could be done away with, then European peace would be secured.
By contrast, the yarn in knitted fabrics follows a meandering path ( a course ), forming symmetric loops ( also called bights ) symmetrically above and below the mean path of the yarn.
By contrast, the median income is the level at which half the population is below and half is above.
By performing the calculation above in the familiar decimal system we see why 112 in octal is equal to 64 + 8 + 2
By this definition, in a normal population, half of students are expected to perform above grade level and half the students below grade level, no matter how much or how little the students have learned.
By contrast, the central and southern parts of Guangdong province experience an average January temperature of above, while the July mean is generally above.
( By comparison, the Standard Model is expected to start to break down above its cutoff at the much smaller scale of around 1000 GeV.
By and paragraph
Every simple R-module is isomorphic to a quotient R / m where m is a maximal right ideal of R. By the above paragraph, any quotient R / m is a simple module.
By the result of the previous paragraph, the limit function is also Lipschitz, with the same bound for the Lipschitz constant.
By 1908, this was described by the New York Times as a " long-established … preference " ( see article ) In modern usage in Scotland, " Scotch " is never used, other than as described in the following paragraph for certain articles ; it has gathered patronising and faintly offensive connotations (" frugal with one's money "), and a non-Scot who uses the word in conversation with Scots as a description of them may find this a good test of their courtesy.
By 20 May the Commons had agreed to one more minor alteration, but had not decided whether to accept the new paragraph.
By this time, to be precise, on July 15, 1937, because of Natascha ’ s status as “ Mischling ersten Grades ,” Emil had lost his post at the University — technically, compelled into early retirement — on the grounds of paragraph 6 of the Act to Restore the Professional Civil Service ( Gesetz zur Wiederherstellung des Berufsbeamtentums ) of April 7, 1933.
By the property noted in the above paragraph, if f is an irreducible ( non-zero ) polynomial with coefficients in the field F of prime characteristic p, and does not have distinct roots, it is possible to write f ( X )= g ( X < sup > p </ sup >).
With respect to ' the final paragraph, in which Jensen has Hanold asking Zoë to walk ahead of him and she complies with a smile, Freud put, " Erotic ... foot interest "'... By walking ahead of him in imitation of " Gradiva " on the plaque, she finds the key to his therapy '.
By taking Fourier transforms this follows from the fact that every polynomial has a distributional inverse, which is proved in the paragraph above.
By paragraph 2, foundlings recovered in Italy are citizens by birth if it cannot be proven that these persons are in possession of another citizenship.
By and one
By counting the number of stalls and urinals I attempted to form a loose estimate of how many men the hall would hold at one time.
By what one reader called a `` series of dissolving views '', he merges one period into another and gives a sense of continuous growth.
By sharing the load of important speeches with his colleagues, the president can develop a cadre of able spokesmen who will help to create a public perception of the university as an institution, something more than the lengthened shadow of one man.
By this scheme, pulling one signal to clear locks all the other switch and signal levers in safe positions until the first signal is again restored to normal.
By using the appropriate version any one of these factors can be determined for any combination of the other three.
By automobile from New York, for example, you can take a one or two-day tour to Annapolis, Maryland to see the colonial homes and the U.S. Naval Academy ( where you can shoot the dress parade on Wednesdays ) ; ;
`` By one fell swoop the Court now finds that Congress indulged in needless legislation in the acts of 1910, 1913, 1925, 1934 and 1937.
By saying `` another emotional death '', she reveals that there has been a previous one, although she has not described it in words.
By this same combination of the will and the imagination, each one of us can learn to portray permanently the kind of character we would like to be.
By 1926, when the mighty Yanks were at their mightiest, only a few of these were left but they still shone brightest, even beside able and agile rookies like Tony Lazzeri ( who managed never to have one of his epileptic fits on the field ), Mark Koenig, Lou Gehrig, George Pipgras, and gray-thatched Earl Combs.
By the time Felix turned up it was early afternoon, which, one would think, would be late enough so that by then, except for small children and a few hardy souls who had not yet sobered up, it could have been expected that people would no longer be having any sort of active interest in the previous night's noisemakers and paper hats.
By then, the stranger was thanking Haney profusely and had one arm around his shoulders as if he were an old friend.
By and large, Robert McEnroe's adaptation of Maurice Walsh's film, `` The Quiet Man '', provides the entertainment it set out to, and we have a lively musical show if not a superlative one.
By the end of his life Huxley was widely acknowledged as one of the pre-eminent intellectuals of his time and respected as an important researcher into visual communication and sight-related theories as well.
By 1850, Luanda was one of the greatest and most developed Portuguese cities in the vast Portuguese Empire outside Mainland Portugal, full of trading companies, exporting ( together with Benguela ) palm and peanut oil, wax, copal, timber, ivory, cotton, coffee, and cocoa, among many other products.
By preserving the value, only one division operation is needed and the higher-order statistics can thus be calculated for little incremental cost.
By the Rule of St Benedict, which, until the Cluniac reforms, was the norm in the West, the abbot has jurisdiction over only one community.
By having three stations, a total of three different cars can be operated on at the same time, each one at a different stage of its assembly.