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A further step was the 1770 paper Réflexions sur la résolution algébrique des équations by the French-Italian mathematician Joseph Louis Lagrange, in his method of Lagrange resolvents, where he analyzed Cardano and Ferrarri's solution of cubics and quartics by considering them in terms of permutations of the roots, which yielded an auxiliary polynomial of lower degree, providing a unified understanding of the solutions and laying the groundwork for group theory and Galois theory.
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further and step
And she really tried to go a step further and say she hoped they'd be just as right as they now were for her and for Rod.
There was one further step in my religious progress.
It is relatively easy to go a step further and reason that an attacker, in possession of such absolute power, would simultaneously destroy his opponent's cities and people.
Go a step further and list all the wonderful barbecue basics -- cervelat, salami, Vienna sausages, mettwurst, bratwurst, bockwurst, knackwurst, Bologna, pepperoni, blutwurst -- and you have a long list of easy specialties.
We may carry this sequence one step further and say that at seventy he was a poet at the height of his powers, wanting only the impetus of two tragedies, one personal, the other national, to loose those powers in poetry.
But to operate in American politics one must go a step further -- one must build a bridge to such names, establish a warmth, a personal connection ''.
Steiner added to this the conception that a further step in the development of thinking is possible when the thinker observes his or her own thought processes.
Since the Church of England is a state church, a further step, sending the proposed revision to Parliament in the form of a " Deposited Book ", was required.
Other formula-based calendars can have lengths which are further out of step with the solar cycle, for example, the Julian calendar has an average length of 365. 25 days, and the Hebrew calendar has an average length of 365. 2425
Caligula took things a step further and had those in Rome, including Senators, worship him as a physical living god.
Raymond Lindeman took these ideas one step further to suggest that the flow of energy through a lake was the primary driver of the ecosystem.
However, Eusebius takes it a step further saying that Simon had demonic qualities and performed black magic in order to convince others he was divine.
The technique got to Europe almost immediately, and Segundo de Chomon and others at Pathé took it further, adding clay animation, in which sculptures were deformed from one thing into another thing frame by frame in Sculpture moderne ( 1908 ), and then Pathé made the next step to the animation of silhouette shapes.
Other artists go a step further, by using an eight-string guitar with two extra low strings.
Brown goes one step further by suggesting that the Beloved Disciple had been a follower of John the Baptist before joining Jesus.
A further step was taken by the idea of the Shaktis.
Anxious to curb further disorders in the region, the United States began to urge Carías to step aside and allow free elections when his current term in office expired.
A further step would be to then weigh these cases, and sort by case weight.
The facsimile ( fax ) machine took this one step further: an entire letter could be completely transferred electrically from the sender's house to the receiver's house by means of the telephone network as an image.
The next step to commercialization of liquid crystal displays was the synthesis of further chemically stable substances ( cyanobiphenyls ) with low melting temperatures by George Gray.
Another Minor Threat song from the second EP, Out of Step, further demonstrates the belief: " Don't smoke / Don't drink / Don't fuck / At least I can fucking think / I can't keep up / I'm out of step with the world.
Taking this a step further are MUDs devoted solely to this sort of conflict, called pure PK MUDs, the first of which was Genocide in 1992.
After James took the step of forcing Anglican clergymen to read the Declaration of Indulgence — the proclamation granting religious liberty to Catholics and dissenters — from their churches in May 1688, his popularity plunged further.
While advancement of research proves that targeting and distribution can be augmented by nanoparticles, the dangers of nanotoxicity become an important next step in further understanding of their medical uses.
" About a year after the Court's jurisdictional decision, the United States took the further, radical step of withdrawing its consent to the Court's compulsory jurisdiction, ending its previous 40 year legal commitment to binding international adjudication.
further and was
The depersonalization continued as the dancer was further metamorphosed by the play of lights upon his figure.
But his own work was evolving further.
`` The case was that Bang-Jensen came up to Shann claiming he had found further errors in the report.
Without further inquiry, Pike jumped to the conclusion that Robinson was guilty, and, following the honorable route that would eventually lead to the dueling ground, sent a message to Robinson through his friends, demanding that he either confirm or deny his complicity.
In the eyes of those who still cared for such things, it was a reflection on his honor, and it gave further grounds for complaint to his overtaxed subjects, who were already grumbling -- although probably not in Latin -- `` Non est lex sana Quod regi sit mea lana ''.
In 1954 I was drafted and after serving two years honorably on Active Duty I was not required to participate in any further Army Reserve activities.
In order to further refine the management of passenger vehicles, on July 1, 1958, the actual title to every vehicle was transferred, by Executive Order, to the Division of Methods, Research and Office Services.
Counsel for the Government invited Du Pont's views on this proposal before recommending a specific program, but stated that if the court desired, or if counsel for Du Pont thought further discussion would not be profitable, the Government was prepared to submit a plan within thirty days.
He says that he was not permitted to rebut before the hearing officer statements attributed to him by the local board, and, further, that he was denied at trial the right to have the Department of Justice hearing officer's report and the original report of the Federal Bureau of Investigation as to his claim -- all in violation of the Fifth Amendment.
Considering the high cost of the F-108 system -- over $4 billion for the force that had been planned -- and the time period in which it would become operational, it was decided to stop further work on the project.
Referring further to the Foundation's officers, Dr. James F. Mathias, for eleven years our discerning colleague as Associate Secretary, was promoted to be Secretary.
The new work was a boon to the partnership, not only for its own value but particularly for the stimulation it provided to the imagination of J. R. Brown toward yet further developments for production equipment.
Not until the group was satisfied in this area were they willing to venture further to ( 2 ), Specific adjustment areas, such as sex, in-laws, religion, finance, and so on.
Then the fact that the lower channel line was pierced had further forecasting significance.
There was further elimination of all companies that were not accompanied by the name of a responsible company executive.
The prevalent opinion which we encountered in a variety of expressions in your country denied not only the existence of this conflict but it was elaborated even further with an incredible semantic dexterity.
A further example of the incompatible difference in personalities was when two policemen held up a Torrio beer convoy on a West Side street and demanded $300 to let it through.
There was no cleaning or further care, but the wound healed in less than two weeks and showed no scar.
There was another on this side, a little further down.
The jury further said in term-end presentments that the City Executive Committee, which had over-all charge of the election, `` deserves the praise and thanks of the City of Atlanta '' for the manner in which the election was conducted.
But he further said that it was better politics to let others question the wisdom of administration policies first.
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