The latter was a result of the Pythagorean theorem and the former the assumption that a + b ≤ c. The contradiction means that it is impossible for both to be true and it is known that the Pythagorean theorem holds.

mtDNA cytochrome b sequence and allozyme studies confirm these findings except that the Synthliboramphus murrelets should be split into a distinct tribe, as they appear more closely related to the Alcini-in any case, assumption of a closer relationship between the former and the true guillemots was only weakly supported by earlier studies.

" The new title symbolized an assumption of powers equivalent and parallel to those held by former Byzantine Emperor and the Tatar Khan, both known in Russian sources as Tsar.

Despite the promise of safe passage, and Constantine's assumption of clerical offices, Constantius imprisoned the former soldier and had him beheaded on his way to Ravenna in either August or September 411.

The former assumption interprets individual, group and official action as part of a single system and reduces politics and governmental policies to a derivative of three basic analytical terms: society, culture and personality.

This was based on the assumption by former president, Andrew Jackson, that the government was selling land for state bank notes of questionable value.

Sonic Foundry () is the former developer of various media software suites, which were purchased by Sony in late 2003 for $ 18 million in cash and the assumption of certain liabilities and obligations.

Three reasons supported the judgment: first, the PET approved the recommendation of Hearing Commissioner and former Commission on Elections ( Comelec ) Chair retired SC Justice Bernardo P. Pardo that “ the pilot-tested revision of ballots or re-tabulation of the certificates of canvass would not affect the winning margin of the protestee in the final canvass of the returns, in addition to the ground of abandonment or withdrawal by reason of Protestant ’ s candidacy for, election and assumption of the office Senator of the Philippines ”; second, Legarda ’ s failure to pay the P 3. 9 million ($ 1 = P 40 ) revision of ballots ( in 124, 404 precincts ) fee despite court extension under Rule 33 of the PET ; and third, jurisprudence of Defensor Santiago v. Ramos, teaches that Legarda " effectively abandoned or withdrawn her protest when she ran in the Senate, which term coincides with the term of the Vice-Presidency 2004-2010 ".

Borehole temperatures in Greenland were responsible for an important revision to the isotopic temperature reconstruction, revealing that the former assumption that " spatial slope equals temporal slope " was incorrect.

This convinced many former party members of the desirability of an underground existence, including the assumption that a new period of violent repression was at hand.

In Korogocho human degradation was frightful and Zanotelli's assumption " Maybe God is sick " became the title of a book on Africa, written by Walter Veltroni, former secretary of the Italian DS party ( Democratici di Sinistra, left wing democratics ), presently major of Rome and the only political leader ( besides the American pastor and activist Jesse Jackson ) who ever visited the place.

For instance, Doug Gurian-Sherman ( former science director for CSPI's biotechnology project, now a member of the Union of Concerned Scientists ) responded to a 2005 position paper on the regulation of genetically engineered crops by saying, " CSPI ’ s assumption that these crops should take less time is inconsistent with its own positions and clearly misunderstands the science involved.

This idea was challenged by Wilson's former student Daniel Simberloff who pointed out that this idea relied on the assumption that smaller reserves had a nested species composition-it assumed that each larger reserve had all the species presented in any smaller reserve.

This period in the 1990s would be marked by his party's assumption of power in alliance with former army-backed opponents, a focus only on provincial politics, the increasing influence of his wife in party affairs, corruption scandals hitting the once clean image of his supporters and in particular the focus on renaming the NWFP Pakhtunkhwa (' The Pashtun side / territory ').

Indeed, in 1769 another former British officer, John Bradstreet, filed a claim to based on that very assumption.

The occasion of the both hymns was the Pythian Festival, held only once every ten years, and according to the former assumption of dating the earlier hymn was probably written for the boys ' choir at the Pythian Games in 138 BCE.

( Whether historical nationalism helped the peoples of the remainder of the world, and whether today's nationalism in the former colonial areas has equally beneficial aspects, are other questions.

Our understanding of the solar system has taught us to replace our former elaborate rituals with the appropriate action which, in this case, amounts to doing nothing.

Much of the former extreme uneasiness associated with visions and hallucinations and with death has disappeared.

No good can come of contemplating the sad, inevitable fact that once youth has passed `` a worse and worse time still succeeds the former ''.

It was a sort of poetic justice that at the time of his own demise a new plot to overthrow the Venezuelan government, reportedly involving the use of Dominican arms by former Venezuelan Dictator Marcos Perez Jimenez, has been uncovered and quashed.

The White House itself has taken steps to remove a former Batista official, Col. Mariano Faget, from his preposterous position as interrogator of Cuban refugees for the Immigration Service.

In his CDC work, Carvey has the close-in support and advice of one of California's shrewdest political strategists: former Democratic National Committeeman Paul Ziffren, who backed him over a Northland candidate espoused by Atty. Gen. Stanley Mosk.

It may be noted, parenthetically, that to evade `` desegregation '' an ex-Justice and former southern governor has urged Congress to abolish this reviewing authority.

the former contains no poem dated before 1909 - 10 -- that is, no poem from a period covered by a previous volume -- and the latter has only a few such.

Secretary of State Dean Rusk, a former Rhodes Scholar and Mills College dean, has headed the Rockefeller Foundation and in that role expended large sums for international cultural exchange.

He is married to the former Audrey Knecht and has a daughter, Karol, 13.

He took a midnight train out of Cleveland Saturday, without an official word to anybody, and has stayed away from newsmen on his train trip across the nation to Reno, Nev., where his wife, former Olympic Diving Champion Zoe Ann Olsen, awaited.

Miss Shirley Joan Meredith, a former student of North Texas State University, was married Saturday to Larry W. Mills, who has attended Arlington State College.

In the former, the encounter with multiple, distinct cultures, often very different in organization and language from those of Europe, has led to a continuing emphasis on cross-cultural comparison and a receptiveness to certain kinds of cultural relativism.

In addition, mixed race ( European and African ) people amount to about 2 %, with a small ( 1 %) population of whites, mainly ethnically Portuguese ( as a former overseas territory of Portugal until 1975, the Portuguese make up currently the largest non-African population, with certainly more than 100, 000, a number that has been constantly increasing from the 2000s, because of Angola's growing demand for qualified human resources.

At the same time, Angola has promoted the revival of the Community of Portuguese-Speaking Countries ( CPLP ) as a forum for cultural exchange and expanding ties with Portugal ( its former ruler ) and Brazil ( which shares many cultural affinities with Angola ) in particular.

The latter has been shown to be extensively paraphyletic, and has now been divided into 11 subfamilies, but the former still stands.

A new party, the Republic Party, is headed by ex-Prime Minister Aram Sargsyan, brother of Vazgen Sargsyan, and has become the primary voice of the opposition, which also includes the Armenian Communist Party, the National Unity party of Artashes Geghamyan, and elements of the former Ter-Petrosyan government.

Several of Alexander's works were published in the Aldine edition of Aristotle, Venice, 1495 – 1498 ; his De Fato and De Anima were printed along with the works of Themistius at Venice ( 1534 ); the former work, which has been translated into Latin by Grotius and also by Schulthess, was edited by J. C. Orelli, Zürich, 1824 ; and his commentaries on the Metaphysica by H. Bonitz, Berlin, 1847.

Vinge's former wife, Joan D. Vinge, has also written stories in the Zones of Thought universe, based on his notes.

For example, armoured personnel carriers were generally replaced by infantry fighting vehicles in a very similar role, but the latter has some capabilities lacking in the former.

An alternate explanation of the red fox's gains involves the gray wolf: Historically, it has kept red fox numbers down, but as the wolf has been hunted to near extinction in much of its former range, the red fox population has grown larger, and it has taken over the niche of top predator.

Many Jews converted to Christianity, however, prejudice against Jewish converts persisted and led many of these former Jews to move to the New World ( see History of the Jews in Latin America ).

The revised constitution of May 11, 1957, omitted reference to the French Union, though close educational, health and technical ties with the former colonial power persisted.

This collective effort was at the origin of many of Britain's building societies, which however developed into " permanent " mutual savings and loan organisations, a term which persisted in some of their names ( such as the former Leeds Permanent ).

The livestock and local farmers ' market persisted into the 1970s, as did a nearby auction site ; the latter is now a new housing estate and the former is part-occupied by a branch of Budgens, with the other part remaining a market, although essentially for tourist purposes: no livestock is now bought or sold there.

The lands of the former Kingdom of Israel and Kingdom of Judah ( c. 930 BCE – 586 BCE ), had been occupied in turn by Assyria, Babylonia, the Achaemenid Empire, and Alexander the Great's Hellenic Macedonian empire ( c. 330 BCE ), although Jewish religious practice and culture had persisted and even flourished during certain periods.

This identification persisted into the 1990s, even as the company signed former WWF stars such as Hulk Hogan and Randy Savage.

Most of the former Maratha Empire was absorbed by British India, although some of the Maratha states persisted as quasi-independent princely states until India became independent in 1947.

This began a prolonged period of conflict between church and state that persisted until the 1940s when the Church enjoyed a restoration of its former status under the presidency of Colonel Juan Perón.

The lake persisted for several thousand years as melting ice and eroding moraine dams slowly drained the former lake basin.

When the end of slavery came, the distinction between former free coloreds and former slaves persisted in some societies.

line was that the organization's motivation for doing so is stopping the continual fragmentation of the Serbian political scene which " leads to voter confusion and enables the strengthening of the Serbian Radical Party ( SRS )", the accusations of embezzlement from certain former members persisted.

It is bordered on the east and southeast by Štokavian dialects roughly along a line that was the former division between Civil Croatia and the Habsburg Military Frontier ; in southwest along Kupa and Dobra rivers, it persisted in ancient ( medieval ) contact with Čakavian dialects.

" In the out-of-the-way villages on the borders of Romney marsh, the former home of shepherds and smugglers, the light of civilisation has not long shone, and many rites and superstitions connected with the worship of the oak are still persisted in by the inhabitants.

Rumours always persisted amongst the pupils of a thoroughly unpleasant ghost named The Green Lady, which haunted the former Wester Elchies House.

The Indian community of Nicoya persisted weakly as a shadow of its former self, maintained by a tradition of reciprocal ties of rights and obligations to patriarchal Crown authority.

As older former orphans were volunteers the old Creole dialect persisted around the orphanage with the encouragement of the elders of the denomination.