Mordell's theorem had an ad hoc proof ; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which was not to be clearly named as that for two more decades.

The supporters of these views feel that the Afrikaner designation ( or label ) was used from the 1930s onwards as a means of unifying ( politically at least ) the white Afrikaans speakers of the Western Cape with those of Trekboer and Voortrekker descent ( whose ancestors began migrating eastward during the late 17th century and throughout the 18th century and later northward during the Great Trek of the 1830s ) in the north of South Africa, where the Boer Republics were established.

" The Puritan minister began to embrace the sentiment that smallpox was an inevitability for anyone, both the good and the wicked, yet God had provided them with the means to save themselves.

James, who was supportive of Frederick, and had been seeking marriage between the new Prince of Wales and the Spanish Infanta, Maria Anna of Spain, since Prince Henry's death, began to see the Spanish Match as a possible means of achieving peace in Europe.

As response to this operation, the Awami League announced the declaration of independence of East Pakistan on March 26, 1971 and began an armed struggle against the Pakistan, with India staunchly supporting Awami League by the means of providing arm ammunition to its guerrilla forces.

Gairy won re-election in Grenada's first general election as an independent state in 1976 ; however, the opposition New Jewel Movement refused to recognize the result, claiming the poll was fraudulent, and so began working towards the overthrow of the Gairy regime by revolutionary means.

As Hitler began his aggressions, Mussolini decided to occupy Albania as a means to compete with Hitler's territorial gains.

He was no longer satisfied with his chair as the means of propagating his ideas, and soon after his return from Bruges he began to express them in tracts and longer works – his great work, the Summa Theologica, was written in support of them.

These estimates have been confirmed by the 2009 population census, and this means that the decline in population that began after 1989 has been arrested and reversed.

People began to study the Bible at home, which effectively decentralized the means of informing the public on religious matters and was akin to the individualistic trends present in Europe during the Protestant Reformation.

One such distributor, Public Software Library ( PSL ), began an order-taking service for programmers who otherwise had no means of accepting credit card orders.

In the late 18th century, the term " class " began to replace classifications such as estates, rank, and orders as the primary means of organizing society into hierarchical divisions.

Rewriting the state constitution became Marshall's central focus as governor, and after the General Assembly refused to call a constitutional convention he began to seek alternative means by which to have a new constitution adopted.

Writing most likely began as a consequence of political expansion in ancient cultures, which needed reliable means for transmitting information, maintaining financial accounts, keeping historical records, and similar activities.

Writing most likely began as a consequence of political expansion in ancient cultures, which needed reliable means for transmitting information, maintaining financial accounts, keeping historical records, and similar activities.

When wheat flour began to come into common use for making cakes and puddings, cooks in the north of England devised a means of making use of the fat that dropped into the dripping pan to cook a batter pudding while the meat roasted in the oven.

This had both short and long term outcomes: in the short term the guests began to scheme about and invent ' steering means ' for the sleds, which became the luge, bobsleighs ( bobsleds ), and head-first skeleton.

All of these groups were led to articulate notions of popular sovereignty by means of a social covenant or contract: all of these arguments began with proto -“ state of nature ” arguments, to the effect that the basis of politics is that everyone is by nature free of subjection to any government.

Instead of traditional means of bands reaching their audiences through large music labels, bands began recording, manufacturing albums and merchandise, booking their own tours, and creating opportunities for smaller bands to get wider recognition and gain cult status through repetitive low-cost DIY touring.

In Québec, Val-Jalbert is a well-known tourist ghost town ; founded in 1901 around a mechanical pulp mill which became obsolete when paper mills began to break down wood fibre by chemical means, it was abandoned when the mill closed in 1927 and re-opened as a park in 1960.

Work began in 486 BC, south of Yangzhou to north of Huai ' an in Jiangsu, and within three years the Han Gou had connected the Yangtze River to the Huai River by means of existing waterways, lakes, and marshes.

The bombardment, which had been carefully targeted by means of aerial photography, began on 22 September.

In the early 1870s, in a shift that historians attribute to the influence of the West, Japanese men began cutting their hair into styles known as jangiri or zangiri ( which roughly means " random cropping ").

The guerrillas began a frantic search for pails in which to bring water from the spring.

Then Little Billy began shouting orders to round up the ponies and fill the water buckets and for the cooks to hurry up with the meal.

School began in August, the hottest part of the year, and for the first few days Miss Langford was very lenient with the children, letting them play a lot and the new ones sort of get acquainted with one another.

These began to be apparent in a press conference held during the second illness in order that the consulting specialists might clarify the President's condition for the nation.

He was then asked for a solution of the difficulty, and began to talk trenchant sense, though private anguish showed through in the vehemence of his manner.

Just when it was needed for the campaign, Hearst Paper No. 8, the Boston American, began publication.

Orders of the day began to specify the standard map for the movement.

Aroused by what they considered an evil influence, some members of the clergy, joined by city authorities, merchants, and master craftsmen, began the attack on the plays and the actors for what they called `` the abuses of the art '', but by 1582 some of them began to denounce the whole idea of acting.

Under these conditions a new generation of Europeans began to discover the bonds of long association and shared values that for so long had been subordinated to nationalist xenophobia.

The immense amount of interest that the new jazz had for the younger generation must have impressed him, and he began working toward the merger of jazz and poetry, as he had previously attempted the union of graphic art and poetry.

He returned to New York to work for The New Yorker, to edit a Western pulp, to `` duck the war in the OWI '', to write publicity for Paramount Pictures and commentary for a newsreel, then he began his career as critic for various magazines.

For it was the millions of buffalo and prairie chicken and the endless seas of grass that symbolized for a whole generation of Americans the abundant supply that was to take many of them westward when the Ohio and Mississippi valleys began to fill.

Thus a new pattern of days began to develop, for Granny Albright did not die.

I doubt, for example, that, 3 months before the leadership began to talk about what came to be the Marshall plan, any public-opinion expert would have said that the country would have accepted such proposals.

The basic market for textiles is growing with the expansion of the population that began 20 years ago.

In the military field, incoming orders turned down early in the year, and remained rather slow until late fall when the upturn in procurement of equipment began to make itself felt in rising orders for components.

Thus it was that Barco, apprehended for mere larceny, now began to suspect that one or another of his murders had been uncovered.

The writer began this special class by explaining his background thinking for creating such a section in the first place.

Voting preparations began in the fall of 1959, although the actual demarcation and planning for the rural communes was completed in 1958.

It was there, in the course of trying to prepare new men for the `` culture shock '' they might encounter in remote overseas posts, that he first began to develop a system of charting the `` norms of human communication ''.

`` To give up these notions required a revolution in thought '', Mr. Clark said in reminiscing about the abrupt changes in ideas he experienced when he began reading `` Organic Gardening '' And `` Modern Nutrition '' in a search for help with his problems.