Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution ; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.

( Initially composed of an infantry division, eventually covering all Brazilian military forces who participated in the conflict.

Initially, Emperor Wilhelm II told the Archduke Franz Ferdinand that Germany was ready to support Austria in all circumstances — even at the risk of a world war, but the Austro-Hungarians hesitated.

Initially such topics cover most, if not all, of the sub-disciplines of electrical engineering.

Initially, the opening sequence included all five characters from the original film, but, in an effort to save time and money, all but Ash and Linda were cut from the final draft.

Initially, their proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand.

Initially the components required for kernel and development were written: editors, shell, compiler and all the others.

Initially, the Central Junta declared support for Ferdinand VII, and convened a " General and Extraordinary Cortes " for all the kingdoms of the Spanish Monarchy.

Initially confined to the immigrant communities during the mid-19th century, it was gradually assimilated into mainstream society and by the first decade of the 20th century it was being celebrated coast to coast by people of all social, racial and religious backgrounds.

Initially, the issue taken was limited to distilled liquors, but quickly evolved into teetotalism and Methodists were commonly known to abstain from all alcoholic beverages.

Initially, the consuls possessed all of the king ’ s powers in the form of two men, elected for a one-year term, who could veto each others actions.

Initially, Saladin attempted to organize his men into battle order, but as his bodyguards were being killed, he saw that defeat was inevitable and so with a small remnant of his troops mounted a swift camel, riding all the way to the territories of Egypt.

Initially all tape cells are marked with 0.

Initially developed with the theme of equal opportunity access and inclusion of students with learning or physical disabilities, the themes governing universal access to education have now expanded across all forms of ability and diversity.

Initially covering a wide variety of fantasy and science-fiction role-playing and board games, particularly the role playing games ( Advanced ) Dungeons & Dragons, RuneQuest and Traveller ( which were all published by other games companies ), the magazine underwent a major change in style and content in the late 1980s and is now dedicated exclusively to the miniature wargames produced by Games Workshop, mainly the core systems of Warhammer Fantasy Battle, Warhammer 40, 000 and The Lord of the Rings Strategy Battle Game.

Initially the groupe comprised a group of French fighter pilots sent to aid Soviet forces on the Eastern Front at the suggestion of Charles de Gaulle, leader of the Free French Forces, who felt it important that French servicemen serve on all fronts in the war.

Initially, only British riders were allowed to compete ( although women were allowed, despite being banned from riding in the Olympics ), but the competition is now an international open to all riders from around the world who have qualified for this level of competition.

Initially, this format was only to be used in endurance races, but was eventually applied to all races.

Initially, all of the functional structural elements of the building were colour-coded: green pipes are plumbing, blue ducts are for climate control, electrical wires are encased in yellow, and circulation elements and devices for safety ( e. g., fire extinguishers ) are red.

Initially, in the 14th and 15th centuries, the name was used for all kinds of foreign gold coins used in Poland, most notably Venetian and Hungarian ducats.

Initially, all modern linguistics was historical in orientation, even the study of modern dialects involved looking at their origins.

Initially all troubadour verses were called simply vers, yet this soon came to be reserved for only love songs and was later replaced by canso, though the term lived on as an antique expression for the troubadours ' early works and was even employed with a more technically meaning by the last generation of troubadours ( mid-14th century ), when it was thought to derive from the Latin word verus ( truth ) and was thus used to describe moralising or didactic pieces.

Initially all were top loading, usually with cassette on one side, and VU meters and recording level controls on the other side.

Initially, all ERPI-wired theaters were made Vitaphone-compatible ; most were equipped to project Movietone reels as well.

Initially states emerged over territories built by conquest in which one culture, one set of ideals and one set of laws have been imposed by force or threat over diverse nations by a civilian and military bureaucracy.

Initially, the start of the series focused on the human nations which make up the Eastern Kingdoms, and the Orcish Horde which arrived in Azeroth via a dark portal, beginning the great wars.

Initially it comprised only Tatars and Bashkirs in the former Kazan and Ufa governorates, although other, non-Muslim and non-Turkic, nations of the area joined in a few months later: the Komi peoples, Mari, and Udmurts, who speak Uralic languages and practice either Orthodox Christianity or shamanism.

Initially wary, Straczynski finally did and was hired on as story editor under Jeri Taylor and David Moessinger.

Initially directed toward the amateur market, Kodak hired Willard Beech Cook from his 28 mm Pathescope of America company to create the new 16 mm Kodascope Library.

Initially, Moore achieves his dream of avoiding factory life after being hired by a magazine in San Francisco, but this venture fails for him and he ultimately travels back to Flint.

Initially hired to play piano and organ ( and to sing occasional backing vocals ), Wallinger's multi-instrumental and production skills impressed Mike Scott and ensured that he played a far greater role on This Is The Sea than he had on the previous album.

Initially hired as a shipbuilder, he soon discovered other opportunities to use his talents as an engineer and inventor, constructing industrial machinery and experimenting with steel production.

Initially, it is said that he was hired by the Under Sheriff of Staffordshire to save the cost of bringing Calcraft up from London.

Initially using the Lisbon Militia units plus 5, 000 to 7, 000 hired peasants and later by conscription of all people within 40 miles, supervised by 18 engineering officers and around 150 NCOs and at a cost of just £ 100, 000 the work was completed, just in time.

Initially, Taylor was hired to fix bicycles, but increasingly took over running of the bicycle business as the Wright brothers spent more time on their aeronautical pursuits.

Initially writer Paul Dehn who had provided the script for every sequel was hired to provide a story treatment for the fifth film in the series.

" Initially hired for only one year, he remained on contract through 2009.

Initially he was hired as a session musician, helping to complete their eponymous album Whitesnake ( known as 1987 in Europe ) after a mass-firing of the original band members by Coverdale.

Initially he was requested to write an emergency chart for the following day, but he was hired as a score writer and continued writing and conducting on the show, before replacing Tommy Oliver as music director.

Initially a small, all-boys middle and high school, in 1991, the school admitted its first female students, and in 1998 the Board of Trustees hired Susan Haberlandt as Head of School.

Initially O ' Kelly got his wish and he was transported to the 1945 Irish presidential inauguration in the landau of the late Queen Alexandra the Queen Mother, which had been hired specially from a Dublin livery company.

Initially he took the photographs himself, but as success came, he hired people to help him and set about establishing his postcard company, a firm that became one of the largest photographic studios in the world.

Initially, horses were hired with civilian drivers.

Initially hired to solve a mystery involving missing stocks from a zero-g satellite production facility, he is then re-hired to find the source of attacks on a stored personality of Philip Evans after the industrialist's death.