Although Dürer made no innovations in these areas, he is notable as the first Northern European to treat matters of visual representation in a scientific way, and with understanding of Euclidean principles.

Although conservatives opposed attempts to allow greater representation of the middle class in parliament, in 1834 they conceded that electoral reform could not be reversed and promised to support further reforms so long as they did not erode the institutions of church and state.

Although this movie is not the most accurate representation of a true amnesic patient, it is useful for informing viewers of the detrimental effects of amnesia.

Although it's probably not possible to have weak bosons acting on chiral fermions in this representation.

Although not reaching its 1970s peak in Westminster elections, the SNP had more success in the Scottish Parliamentary elections with their system of mixed member proportional representation.

Although the political discourse had been dominated at this time by Gopal Krishna Gokhale, a moderate who said that it was " madness to think of independence ", Nehru had spoken " openly of the politics of non-cooperation, of the need of resigning from honorary positions under the government and of not continuing the futile politics of representation.

Although populations shifted, representation in the Commons remained the same.

Although symmetric groups can be defined on infinite sets as well, this article discusses only the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory.

Although it is normal to regard the quantity demanded and the quantity supplied as functions of the price of the good, the standard graphical representation, usually attributed to Alfred Marshall, has price on the vertical axis and quantity on the horizontal axis, the opposite of the standard convention for the representation of a mathematical function.

Although this is in fact a shortening of the name Odile, it could also stand for " object " or " orifice ", an O being a symbolic representation of any " hole ".

Although Montevideo was the smallest department in terms of area ( divided into twenty-three geographic zones that generally coincided with the electoral zones ), its departmental board had sixty-five members in 1990 ; all other departments had thirty-one-member boards and a five-member executive council appointed by the departmental board, with proportional representation from the principal political parties.

Although the South African government wanted to incorporate " South-West Africa " into its territory, it never officially did so, although it was administered as the de facto ' fifth province ', with the white minority having representation in the whites-only Parliament of South Africa.

Although this strategy has been criticized for encouraging overwhelming force over strategy and tactics, defenders of the strategy argue that they're simply taking advantage of the strategies utilized, and some argue that it is a realistic representation of warfare.

Although much of the 1965 design has been retained, the arms have been altered by the addition of a representation of the Thames.

Although the n phonogram is a representation of waves on the surface of water, it was never used as an ideogram or determinative for the word water ( mw ), or for anything associated with water.

Although Ripon also sent representatives in 1307 and 1337, it did not have permanent representation.

Although they continued to lavishly spend money on representation, they favoured public appearances, like games and festivals, over the production of portraits.

Although in prose, they were regarded as poems ; in any case they were not intended for stage representation.

Although shapes themselves ( particularly paths ) can be decomposed further into nodes such as spline nodes, it is practical to think of the scene graph as composed of shapes rather than going to a lower level of representation.

Although such a city is a self-governing first-level entity, in many cases it is often presented as part of the province in which it is geographically located, or in the case of Zamboanga City, the province it last formed part the congressional representation of.

Although this theory of political representation has yet to be popularized, rigorously examined or critiqued, there are three broad areas of concern.

Although the ideas on which bicameralism are based can be traced back to the theories developed in Ancient Sumer and later ancient Greece, ancient India, and Rome, recognizable bicameral institutions first arose in medieval Europe where they were associated with separate representation of different estates of the realm.

Although the events of 1836 led to independence for the people of Texas, the Hispanic population of the state was very quickly disenfranchised to the extent that their political representation in the Texas State Legislature disappeared entirely for several decades.

Although the representation must be clear and unambiguous, a representation can be inferred from silence where there is a duty to speak or from negligence where a duty of care has arisen.

Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.

Although a look of alarm passed over his face, he did not arrest his movements but disappeared into the shower room just as the chambermaid emerged from number nine.

Although there were no startling developments in shotgun design this year, a number of new models and variations of existing models did hit the market.

Although there is no question but that the process of washing fabrics involves a number of phenomena which are related together in an extremely complicated way and that these phenomena and their interrelations are not well understood at the present, this section attempts to present briefly an up-to-date picture of the physical chemistry of washing either fabrics or hard surfaces.

Although a large number of coatings systems, particularly at low thicknesses fail cohesively by the cutting mechanism, frequently a second type of cohesive failure may also take place.

Although Brooklyn College does not yet have a junior-year-abroad program, a good number of students spend summers in Europe.

Although the primary mathematical properties of the middle number at the center of the Lo Shu, and the interrelation of all the other numbers to it, might seem enough to account for the deep fascination which the Lo Shu held for the Old Chinese philosophers, this was actually only a beginning of wonders.

Although England decisively won the Ashes 4 – 1, Bodyline caused such a furore in Australia that diplomats had to intervene to prevent serious harm to Anglo-Australian relations, and the MCC eventually changed the Laws of cricket to curtail the number of leg side fielders.

Although the vocalists varied, a small number of musicians worked with the Alan Parsons Project regularly.

Although a number of different broadcast television systems were in use worldwide, the same principles of operation apply.

Although gold has an atomic number of 79, immediately after Rutherford's paper appeared in 1911 Antonius Van den Broek made the intuitive suggestion that atomic number is nuclear charge.

Although it is commonly believed that assassins were under the influence of hashish during their killings or during their indoctrination, there is debate as to whether these claims have merit, with many Eastern writers and an increasing number of western academics coming to believe that drug-taking was not the key feature behind the name.

Although initial studies suggested that antioxidant supplements might promote health, later large clinical trials with a limited number of antioxidants detected no benefit and even suggested that excess supplementation with certain putative antioxidants may be harmful.

Although 64 is the highest number depicted on the doubling cube, the stakes may rise to 128, 256, and so on.

Although passengers rarely have cause to refer to either document, all travel is subject to the National Rail Conditions of Carriage and all tickets are valid subject to the rules set out in a number of so-called technical manuals, which are centrally produced for the network.

Although BJU never reapplied for federal tax-exempt status, and it continues to pay federal taxes, a number of its ancillaries, including Bob Jones Academy and the BJU Museum & Gallery, are tax-exempt entities.

Although counting the number of elements in a set is a rather broad mathematical problem, many of the problems that arise in applications have a relatively simple combinatorial description.

Although all the nuclei of all atoms belonging to one element will have the same number of protons, they may not necessarily have the same number of neutrons ; such atoms are termed isotopes.

Although not known with certainty the total number of species in the family, conservative estimates indicate approximately 2. 600 species worldwide, distributed in 109 genera.

Although Attlee's second government was less radical than the first, it oversaw the passage of a number of reforms relating to issues such as industry in development areas, the restoration of land which had been devastated by ironstone pollution, and river pollution.

Although Confucius claimed that he never invented anything but was only transmitting ancient knowledge ( see Analects VII, 1 ), he did produce a number of new ideas.

Although a " bijection " seems a more advanced concept than a number, the usual development of mathematics in terms of set theory defines functions before numbers, as they are based on much simpler sets.

Although Wegener's theory was formed independently and was more complete than those of his predecessors, Wegener later credited a number of past authors with similar ideas: