By secretly giving inside information to the Komnenoi, Maria was an invaluable ally.

By one estimate, it has the fourth highest gross national income at purchasing power parity in Africa, giving it a standard of living around that of Mexico and Turkey.

By giving it the title ' knowledge ', conspiracy theory is considered alongside more ' legitimate ' modes of knowing.

By the end of the " Kino-Pravda " series, Vertov made liberal use of stop motion, freeze frames, and other cinematic " artificialities ," giving rise to criticisms not just of his trenchant dogmatism, but also of his cinematic technique.

By defeating Russia in 1917 Germany was able to bring hundreds of thousands of combat troops from the east to the Western Front, giving it a numerical advantage over the Allies.

By 1343, last of these dynasties had ceased to exist, giving rise to the Vijayanagar empire.

By 500 BC, Melanesian seafarers had reached Fiji and intermarried with the Polynesian inhabitants, giving rise to the modern Fijian people.

By giving away their ICQ product for free and preventing interoperability between their client software and other products, they were able to temporarily dominate the market for instant messaging.

By analogy with the phoneme, linguists have proposed other sorts of underlying objects, giving them names with the suffix-eme, such as morpheme and grapheme.

By September, Porsche owned a 35. 14 % plurality stake in Volkswagen AG, effectively giving it control over the company.

By paying attention to the army, giving much freedom to Finland, and freeing the serfs in 1861, he gained much popular support ( Finns still dearly remember him ).

By the late 1810s, under siege from the Quadrille, dancing masters began to invent " new " forms of country dance, often with figures borrowed from the Quadrille, and giving them exotic names such as the Danse Ecossoise and Danse Espagnuole which suggested entire new dances but actually covered very minor variations in the classic form.

By the mid-16th century, the " v " form was used to represent the consonant and " u " the vowel sound, giving us the modern letter " u ".

By demanding that high-frequency light must be emitted by an oscillator of equal frequency, and further requiring that this oscillator occupy higher energy than one of a lesser frequency, Planck avoided any catastrophe ; giving an equal partition to high-frequency oscillators produced successively fewer oscillators and less emitted light.

By 1997, 81 % of the developing world's wheat area was planted to semi-dwarf wheats, giving both increased yields and better response to nitrogenous fertilizer.

By the end of the king's long reign, rich Baroque designs were giving way to lighter elements with more curves and natural patterns.

By a misadventure, all of the Republican electors cast their votes for both Jefferson and Burr, giving them each 73 votes.

By taking the derivative of the optical path length, the stationary point is found giving the path taken by the light ( though it should be noted that the result does not show light taking the least time path, but rather one that is stationary with respect to small variations as there are cases where light actually takes the greatest time path, as in a spherical mirror ).

By giving the lender the cloak as well the debtor was reduced to nakedness.

By testing the samples from the spring water, the team was at least able to identify the substance's current presence at the site, giving them insight that a presumably larger quantity existed in the waters thousands of years earlier.

By giving the President the authority to negotiate these deals, the Congress effectively ceded a part of their power ( authorized under US Constitution, Article I, Section VIII ) to the executive branch.

By giving common people the power not only to elect officials but also to call them to account, Solon appears to have established the foundations of a true democracy.

By World War II, every twelfth resident of the city was a student, giving rise to the city's informal name-Siberian Athens.

By virtue of finishing last the year before, the Isles were also able to claim goaltender Chris Osgood with the first pick in the waiver draft, adding a former championship goaltender without giving up any players in exchange.

By clarifying fundamental premises in the social sciences, and defining the logical problems emergent at the borderlands of each new scientific discipline, philosophy can offer the sort of distinction that can accelerate growth in human understanding.

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 using instruments of gradually increasing size, the vagina is gently, and with minimum pain at each stage, taught to yield to an object of the appropriate shape.

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.

By treating each candidate as a separate question, " Do you approve of this person for the job?

By the 1920s, each state in the United States had passed public laws that stipulated a certain day to be Arbor Day or Arbor and Bird Day observance.

By patiently transcribing each word of the text, the writer was made to contemplate the meaning of it.

* By whether the same key is used for both encryption and decryption ( symmetric key algorithms ), or if a different key is used for each ( asymmetric key algorithms ).

By this method each bull can serve very many cows, so only a very few of the purebred dairy male calves are needed to provide bulls for breeding.

By exposing an azeotrope to a vacuum or positive pressure, it's possible to bias the boiling point of one component away from the other by exploiting the differing vapour pressure curves of each ; the curves may overlap at the azeotropic point, but are unlikely to be remain identical further along the pressure axis either side of the azeotropic point.

* By adding bits to each encoded unit, the redundancy allows both to detect errors in coded data and to correct them based on mathematical algorithms.

* By adding bits to each encoded unit, the redundancy allows both to detect errors in coded data and to correct them based on mathematical algorithms.

By externalizing such functionality to the DBMS, applications effectively share code with each other and are relieved of much internal complexity.

By contrast, a dynamic web page is a broader concept, covering any web page generated differently for each user, load occurrence, or specific variable values.

By construction, each point on the curve shows productive efficiency in maximizing output for given total inputs.

By the mid — 18th century the French chemist Charles François de Cisternay du Fay had discovered two types of static electricity, and that like charges repel each other whilst unlike charges attract.

By reversing the steps in the Euclidean algorithm, the GCD can be expressed as a sum of the two original numbers each multiplied by a positive or negative integer, e. g., 21 = × 105 + × 252.

By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.

By 1927 readers, often young adults, would write to each other, bypassing the magazine.

By inspection, each of the small natural numbers 1, 2, 3, 4, ... is the product of primes.

By the 1st century BCE, noxii were being condemned to the beasts ( damnati ad bestias ) in the arena, with almost no chance of survival, or were made to kill each other.

By 2006, such was the confusion from these multiple Acts, each amending the others ( and not all of which were ever actually commenced and thus were in the public record but not enforced as actual legislation ); and the amendments of Irish firearms legislation by other Acts ranging from the Wildlife Acts ( mostly relating to hunting law ) to the Road Traffic Acts ( relating to how and where firearms could be transported ) and others ; the large amount of secondary legislation ( Statutory Instruments, which set out regulations, the design of application forms for licences and so forth, as well as the details of when various parts of the Acts came into force ); as well as the introduction of EU firearms law into the canon of Irish legislation ; led the Irish Law Reform Commission to recommend that all the extant legislation be restated a legal process by which all the existing primary and secondary legislation would be read as one and a single document produced as the new Firearms Act ( and all prior Acts would be repealed ).

By sorting formulas according to the number of atoms of each element present in the formula according to these rules, with differences in earlier elements or numbers being treated as more significant than differences in any later element or number — like sorting text strings into lexicographical order — it is possible to collate chemical formulas into what is known as Hill system order.

By typing " HINT " twice the player would open up a screen of possible topics where they could then reveal one hint at a time for each puzzle, just like the books.