Although generalized to triple integrals by Lagrange in 1773, and used by Legendre, Laplace, Gauss, and first generalized to n variables by Mikhail Ostrogradski in 1836, it resisted a fully rigorous formal proof for a surprisingly long time, and was first satisfactorily resolved 125 years later, by Élie Cartan in a series of papers beginning in the mid-1890s (; ).

* Although Gauss proved that the regular 17-gon is constructible, he did not actually show how to do it.

Although few of the results in these first sections are original, Gauss was the first mathematician to bring this material together and treat it in a systematic way.

Although it is not clear if Gauss really put Eisenstein in the same league as Newton, his writing show that Gauss thought very highly of Eisenstein.

Although the answer to this particular question was known in dimension 2 to Gauss and in higher dimensions to Christoffel and perhaps Riemann as well, Élie Cartan and his intellectual heirs developed a technique for answering similar questions for radically different geometric structures.

Although the Caiman has not been studied in-depth, scientists have learned that their mating cycles ( previously thought to be spontaneous or year-round ) are linked to the rainfall cycles and the river levels, which increases chances of survival for their offspring.

Although they were previously considered the sister group to the remaining crustaceans, it is now widely accepted that crustaceans form a paraphyletic group, and Branchiopoda are thought to be sister to a clade comprising Xenocarida ( Remipedia and Cephalocarida ) and Hexapoda ( insects and their relatives ).

Although not normally thought of as biotechnology, agriculture clearly fits the broad definition of " using a biotechnological system to make products " such that the cultivation of plants may be viewed as the earliest biotechnological enterprise.

Although the history of the Big Apple was once thought a mystery, research over the past two decades, primarily by amateur etymologist Barry Popik and Gerald Cohen of Missouri University of Science and Technology, has provided a reasonably clear picture of the term's history.

Although the game had " incredible role-playing potential ", the concept of role-playing rabbits can be viewed as bizarre, and as such at least one commentator believes that " most people thought it was stupid " when it was first released.

Although it is not known what functioned as a currency to facilitate these exchanges, it is thought that ox-hide shaped ingots of copper, produced in Cyprus may have functioned as a currency.

Although large cities are also municipalities, they are often thought of as a collection of communities, due to their diversity.

Although once thought to be a simple solution of molecules, multiple levels of organization exist in the cytosol.

Although the comet had approached Jupiter closely before, the July 7 encounter seemed to be by far the closest, and the fragmentation of the comet is thought to have occurred at this time.

Although " Oedipus's enquiry is based on supernatural, pre-rational methods that are evident in most narratives of crime until the development of Enlightenment thought in the seventeenth and eighteenth centuries " it has " all of the central characteristics and formal elements of the detective story, including a mystery sur-rounding a murder, a closed circle of suspects, and the gradual uncovering of a hidden past.

Although it is dated " 1631 ", this is thought to be the date of a subsequent refurbishment coincidental with major renovations of the church in the 17th century.

Although a fashioner, the demiurge is not necessarily thought of as being the same as the creator figure in the familiar monotheistic sense, because both the demiurge itself plus the material from which the demiurge fashions the universe are considered either uncreated and eternal, or the product of some other being, depending on the system.

Although a majority of distributism's later supporters were not Catholics and many were in fact former radical socialists who had become disillusioned with socialism ; distributist thought was adopted by the Catholic Worker Movement, conjoining it with the thought of Dorothy Day and Peter Maurin concerning localized and independent communities.

Although it was Sartre who explicitly coined the phrase, similar notions can be found in the thought of existentialist philosophers such as Kierkegaard and Heidegger.

Although Rutimeyer did not denounce Haeckel ’ s embryo drawings as fraud, he argued that such drawings are manipulations of public and scientific thought.

Although the theory of special relativity forbids objects to have a relative velocity greater than light speed, and general relativity reduces to special relativity in a local sense ( in small regions of spacetime where curvature is negligible ), general relativity does allow the space between distant objects to expand in such a way that they have a " recession velocity " which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light-years from us today have a recession velocity which is faster than light.

Although Hayek only met Wittgenstein on a few occasions, Hayek said that Wittgenstein's philosophy and methods of analysis had a profound influence on his own life and thought.

Although usually thought of as a spiritual, the earliest recorded use of the song was as a rallying anthem for the Contrabands at Fort Monroe sometime before July 1862.

Although traditionally labelled as " Yellow Fever " now it is thought to have been typhus.

Although his surviving works amount to some 3 million words, this is thought to represent less than a third of his complete writings.

Although they are thought to have been used in Europe much earlier, gambesons underwent a revolution from their first proven use in the late 11th and early 12th centuries as an item of armour that simply facilitated the wearing of mail to an item of independent armour popular amongst infantry.

Although several reviews were critical of the film – Pauline Kael said it " staggers along " and Stanley Kauffmann thought Cukor's direction was like " a rich gravy poured over everything, not remotely as delicately rich as in the Asquith-Howard 1937 Pygmalion " — the film was a box office hit which won him the Academy Award for Best Director, the Golden Globe Award for Best Director, and the Directors Guild of America Award after having been nominated for each several times.

* Although the perfective is often thought of as representing a " momentary action ", this is not strictly correct.

" Although Gregory does not fully develop the concept, the idea of procession would shape most later thought about the Holy Spirit.

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 his respect for Aristotle was diminished as his travels made it clear that much of Aristotle's geography was clearly wrong, when the old philosopher released his works to the public, Alexander complained " Thou hast not done well to publish thy acroamatic doctrines ; for in what shall I surpass other men if those doctrines wherein I have been trained are to be all men's common property?

Although amaranth was cultivated on a large scale in ancient Mexico, Guatemala, and Peru, nowadays it is only cultivated on a small scale there, along with India, China, Nepal, and other tropical countries ; thus, there is potential for further cultivation in those countries, as well as in the U. S. In a 1977 article in Science, amaranth was described as " the crop of the future.

Although Ajax speaks earnestly and is well received, he does not succeed in convincing Achilles.

Although metics had no direct political influence many were wealthy business owners who could, and sometimes did, influence policy by not allowing their citizen employees time off to attend the assembly, as well as having the simple expedient of wealth.

Although not as well supported by the biggest software publishers as rivals like the Commodore 64 and Sinclair ZX Spectrum, a good range of games were available for the Electron.

Although this is a relatively small value, it was well within the observational capability of the instruments available in the early eighteenth century.

Although oxidation reactions are crucial for life, they can also be damaging ; plants and animals maintain complex systems of multiple types of antioxidants, such as glutathione, vitamin C, and vitamin E as well as enzymes such as catalase, superoxide dismutase and various peroxidases.

Although well known in America as a pianist, ethnomusicologist and teacher, he was not well known as a composer.

Although the form declined in popularity towards the end of the 18th century its influence can be seen in light operas like that of Gilbert and Sullivan's early works like The Sorcerer as well as in the modern musical.

Although the collections centre on Mesopotamia most of the surrounding areas are well represented.

Although for instance the EU ( as well as many other developed countries ) has a balanced monetary balance of trade, its physical trade balance ( especially with developing countries ) is negative, meaning that a lot less material is exported than imported.

Although his popularity continued mostly due to the TV show, his musical works in 1990s were not well received.

Although its Academy Award was presented to Taiwan, Crouching Tiger, Hidden Dragon was in fact an international co-production between companies in four regions: the Chinese company China Film Co-Production Corporation ; the American companies Columbia Pictures Film Production Asia, Sony Pictures Classics and Good Machine ; the Hong Kong company EDKO Film ; and the Taiwanese Zoom Hunt International Productions Company, Ltd ; as well as the unspecified United China Vision, and Asia Union Film & Entertainment Ltd., created solely for this film.

Although all administrative links with Jamaica were broken in 1962, the Cayman Islands and Jamaica continue to share many links and experiences, including membership in the Commonwealth of Nations ( and Commonwealth citizenship ) and a common united church ( the United Church in Jamaica and the Cayman Islands ) and Anglican diocese ( although there is debate about this ) as well as a common currency ( until 1972 ).

Although Francois Bozizé has a background in FACA himself ( being its chief-of-staff from 1997 to 2001 ), he has been cautious by retaining the defence portfolio, as well as by appointing his son Jean-Francis Bozizé cabinet director in charge of running the Ministry of Defence.

Although the Fore's mortuary cannibalism was well documented, the practice had ceased before the cause of the disease was recognized.

Although this selected translation is not generally quoted by members of the Church, the English Bible issued by the Church and commonly used by Latter-day Saints contains cross references to the Joseph Smith Translation ( JST ), as well as an appendix containing major excerpts from it.

Although they are the most well known for their small, piston-powered aircraft, they also produce business jets.

Although water forms the large majority of the cytosol, its structure and properties within cells is not well understood.

Although water is vital for life, the structure of this water in the cytosol is not well understood, mostly because methods such as nuclear magnetic resonance only give information on the average structure of water, and cannot measure local variations at the microscopic scale.

Although the WHIP ratio was not calculated until well after Young's death, Young was the retroactive league leader in this category seven times and was second or third another seven times.

Although a longbow achieves comparable accuracy and faster shooting rate than an average crossbow, crossbows release more kinetic energy and can be used effectively after a week of training, while a comparable single-shot skill with a longbow takes years of strength training to overcome the draw strength of the longbow, as well as years of practice needed to use it with skill.

Although Xenakis could well have composed this music by hand, the intensity of the calculations needed to transform probabilistic mathematics into musical notation was best left to the number-crunching power of the computer.