`` we the People of the United States, in order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common Defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America ''.

He was referring not only to the general college situation but more especially to the preparatory schools.

And it is clearly argued by Lord Percy of Newcastle, in his remarkable long essay, The Heresy Of Democracy, and in a more general way by Voegelin, in his New Science Of Politics, that this same Rousseauan idea, descending through European democracy, is the source of Marx's theory of the dictatorship of the proletariat.

In this essay, we are, along with most historians, interested in the more general or more inclusive ideas, that are so to speak `` writ large '' in history of literature where they recur continually.

An idea, of the sort that we have in mind, although of necessity readily available to imagination, is more general in connotation than most poetic or literary images, especially those appearing in lyric poems that seek to capture a moment of personal experience.

The publication of Father Connolly's The Man Has Wings has made more of the group available in print so that a general picture of what it contained can now be had without difficulty.

But Morgan evidently reported matters of intelligence much more important to his commanding general.

Those who do have occasion to deal with the invasions in a more general way, like T.W. Shore and Arthur Wade-Evans, are on the side of a gradual and often peaceful Germanic penetration into Britain.

One is impressed with the dignity, clarity and beauty of this new translation into contemporary English, and there is no doubt that the meaning of the Bible is more easily understandable to the general reader in contemporary language in the frequently archaic words and phrases of the King James.

On this point there was fairly general agreement that assessors would like to do more than they are doing now.

and ( C ) to finance, for not more than three years beyond the end of said period, such activities as are required to correlate, coordinate, and round out the results of studies and research undertaken pursuant to this Act: Provided, That funds available in any one year for research and development may, subject to the approval of the Secretary of State to assure that such activities are consistent with the foreign policy objectives of the United States, be expended in cooperation with public or private agencies in foreign countries in the development of processes useful to the program in the United States: And provided further, That every such contract or agreement made with any public or private agency in a foreign country shall contain provisions effective to insure that the results or information developed in connection therewith shall be available without cost to the United States for the use of the United States throughout the world and for the use of the general public within the United States.

In general, such apartments afford more protection than smaller buildings because their walls are thick and there is more space.

As I have repeatedly stated, this provision is much more restrictive than the general law, popularly known as the Buy American Act.

For the near term, however, it must be realized that the industrial and commercial market is somewhat more sensitive to general business conditions than is the military market, and for this reason I would expect that any gain in 1961 may be somewhat smaller than those of recent years ; ;

In type 3, this general relationship is maintained peripherally but not centrally where the pulmonary vein follows a more independent path to the hilum as is the case throughout the lung in type 2.

This will be more or less our general method for the second problem.

The theorem which we prove is more general than what we have described, since it works with the primary decomposition of the minimal polynomial, whether or not the primes which enter are all of first degree.

In general, the approach is more active than passive, more out-reaching than reflective.

A more realistic analysis must take into account the fact that Brandywine people in the urban-fringe area are, in general, less segregated locally than group members in rural areas.

All of them felt a compelling need for more coverage on areas that could be only lightly touched upon in a general survey functional course.

Thus, this readiness to relax controls, evidenced in the Kohnstamm situation, appears to be a more general personality factor.

The tendency for general business activity to soften somewhat is becoming more evident.

A mathematical formula is nothing more than a pattern for solving a specific problem.

A more radical defense is to deny the separation of physical world and the platonic world, i. e. the mathematical universe hypothesis.

In computer science, an abstract data type ( ADT ) is a mathematical model for a certain class of data structures that have similar behavior ; or for certain data types of one or more programming languages that have similar semantics.

For those of the Cardinal, Melanchthon, and Dürer's final major work, a drawn portrait of the Nuremberg patrician Ulrich Starck, Dürer depicted the sitters in profile, perhaps reflecting a more mathematical approach.

The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and require a degree of mathematical maturity and experience before they can be assimilated.

It was intended specifically for the new class of users that time-sharing systems allowed — that is, a less technical user who did not have the mathematical background of the more traditional users and was not interested in acquiring it.

A more general binomial theorem and the so-called " Pascal's triangle " were known in the 10th-century A. D. to Indian mathematician Halayudha and Persian mathematician Al-Karaji, in the 11th century to Persian poet and mathematician Omar Khayyam, and in the 13th century to Chinese mathematician Yang Hui, who all derived similar results .< ref > Al-Karaji also provided a mathematical proof of both the binomial theorem and Pascal's triangle, using mathematical induction.

A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.

The actual degree of security achieved over time varies, as more computational power and more powerful mathematical analytic methods become available.

The term ' Copenhagen interpretation ' suggests something more than just a spirit, such as some definite set of rules for interpreting the mathematical formalism of quantum mechanics, presumably dating back to the 1920s.

Another application of category theory, more specifically: topos theory, has been made in mathematical music theory, see for example the book The Topos of Music, Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola.

This work showed that the quantum approach to chemical bonds could be fundamentally and quantitatively correct, but the mathematical methods used could not be extended to molecules containing more than one electron.

Compactness in this more general situation plays an extremely important role in mathematical analysis, because many classical and important theorems of 19th century analysis, such as the extreme value theorem, are easily generalized to this situation.

New mathematical techniques made it possible to control, more accurately, significantly more complex dynamical systems than the original flyball governor.

The " space " in cyberspace has more in common with the abstract, mathematical meanings of the term ( see space ) than physical space.

It is a constitutive equation which provides a mathematical relationship between two or more state functions associated with the matter, such as its temperature, pressure, volume, or internal energy.

It has often been categorized as science fiction although it could more precisely be called " mathematical fiction ".

He disliked complicated theories, and while he had great mathematical ability, he would never use it when the job could be done much more simply.

The greatest common divisor is often written as GCD ( a, b ) or, more simply, as ( a, b ), although the latter notation is also used for other mathematical concepts, such as two-dimensional vectors.

The word " fractal " often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception.

The term representation of a group is also used in a more general sense to mean any " description " of a group as a group of transformations of some mathematical object.