Or, lastly, we may leave the exponents h, k, j,1, untouched and consider the product i i i 2 .
The king was compelled to dismiss Johannes Schlayer (1792-1860) and his other ministers, and to call to power men with more liberal ideas, the exponents of the idea of a united Germany.
When algebra had advanced to the point where exponents were introduced, nothing would be more natural than that their utility as a means of performing multiplications and divisions should be remarked; but it is one of the surprises in the history of science that logarithms were invented as an arithmetical improvement years before their connexion with exponents was known.
In estimating the influence of recent writers on geography it is usual tc assign to Oscar Peschel (1826-1875) the credit of having corrected the preponderance which Ritter gave to the historical element, and of restoring physical geography to its old pre-eminence.2 As a matter of fact, each of the leading modern exponents of theoretical geography - such as Ferdinand von Richthofen, Hermann Wagner, Friedrich Ratzel, William M.
BASILIDES, one of the most conspicuous exponents of Gnosticism, was living at Alexandria probably as early as the first decades of the 2nd century.
It took its name from Elea, a Greek city of lower Italy, the home of its chief exponents, Parmenides and Zeno.
Although some of its foremost exponents were famous Talmudists, it was a protest against excessive intellectualism and Aristotelian scholasticism.
Hence in the above general form of covariant we may suppose the exponents h 1, h2, h3,...ki, k2, k3,...
Or, if we please, we may leave the determinant factors untouched and consider the exponents ji, j2, j3,ï¿½ï¿½ï¿½11, 12, 1 3, ...
It was reserved for Charles Darwin, in the year 1859, to place the whole theory of organic evolution on a new footing, and by his discovery of a mechanical cause actually existing and demonstrable by which organic evolution doctrine must be brought about, entirely to change the attitude in regard to it of even the most rigid exponents of the scientific method.
Both of the South German journals were previously exponents of a very much more democratic trend of opinion than that which came to characterize them under the new proprietorship. Ancillary to these acquisitions large interests were secured by Stinnes in paper-works in order to make his newspapers independent of the paper market.
Among the clearest and most logical exponents of this theory was Hobbes, who in his Leviathan expounded his notion of an agreement by which absolute power was irrevocably transferred to the ruler.
The Girondists were, indeed, rather a group of individuals holding certain opinions and principles in common than an organized political party, and the name was at first somewhat loosely applied to them owing to the fact that the most brilliant exponents of their point of view were deputies from the Gironde.
But the false prophets were by no means mere common impostors; they were the accredited exponents of the common orthodoxy of their day, for the prophets who opposed Jeremiah took their stand on the ground of the prophetic traditions of Isaiah, whose doctrine of the inviolability of Yahweh's seat on Zion was the starting-point of their opposition to Jeremiah's predictions of captivity.
Though the idea of preserving peace by general international regulation has had several exponents in the course of ages, no deliberate plan has ever yet been carried into effect.
Among its exponents were Wegscheider, Bretschneider and H.
Stevinus printed little circles round the exponents of the different powers of one-tenth.
For instance, 237578 w was printed @ 5070 8 3D; and the fact that Stevinus meant those encircled numerals to denote mere exponents is evident from his employing the very same sign for powers of algebraic quantities, e.g.
Not even avoid fractional exponents ("Racine cubique de serait en circle"), and is ignorant only of negative exponents.
Many of its most distinguished exponents are Flemings by birth, and their writings reflect the characteristic Flemish scenery; they have the sensuousness, the colour and the realism of Flemish art; and on the other hand the tendency to mysticism, to abstraction, is far removed from the lucidity and definiteness associated with French literature properly so-called.
The New Hampshire Patriot, founded here in 1808 (and for twenty years edited) by Isaac Hill (1788-1851), who was a member of the United States Senate in 1831-1836, and governor of New Hampshire in 1836-1839, became one of the leading exponents of Jacksonian Democracy in New England.
In modern times the chief exponents of panpsychist views are Thomas Carlyle, Fechner and Paulsen: a similar idea lay at the root of the physical theories of the Stoics.
They thus seemed to come forward in the character of exponents rather than critics of the Western belief in God, freedom and immortality.
The exponents of psychological atomism, on the other hand, with the association of ideas for their one principle of agglutination had come to mean by experience the mental phantasmagoria of the individual.
To the development of the post-Kantian psychological logic. Another movement helped also; the exponents of naturalistic evolution were prepared with Spencer to explain the so-called a priori in knowledge as in truth a posteriori, if not to the individual at any rate to the race.
Finally, there is what may be termed psychological-voluntaryist logic. It is in the rapidity of development of logical investigations of the third and fourth types and the growing number of their exponents that the present shows most clearly the history of logic in the making.
Theosophic teachings on this subject are not, however, exclusively Oriental, for following their contention that they are the exponents of the universal and unchangeable "Wisdom Religion" of all the ages, theosophists have selected from various sources - Vedic, Buddhist, Greek and Cabalistic - certain passages for the purpose of exposition and illustration.
Furthermore, the bishops being in most cases the exponents of the imperial power, the struggle for freedom from the latter ended in a radical riddance from all temporal episcopal government as well.
Dante and Milton are still more faithful exponents of the religion and politics of their time.
It expressed itself at last in the monumental work of Don Quixote, which places Cervantes beside Rabelais, Ariosto and Shakespeare as one of the four supreme exponents of the Renaissance.
The consequence was that the two leading members of the cabinet, Alexander Hamilton and Thomas Jefferson, exponents for the most part of diametrically opposite political doctrines, soon occupied the position, to use the words of one of them, of "two game-cocks in a pit."
The most famous of the systematic exponents of evolutional utilitarianism is, of course, Herbert Spencer, in whose Data of Ethics (1819) the facts of morality are viewed in relation with his vast conception of the total process of cosmic evolution.
Incidentally, it will be noticed that this important Methodist revival had its origin and found its chief supporters and exponents in a restricted corner of South Wales, of which Carmarthen was the centre, in curious contrast with the literary movement in Elizabeth's reign, which was largely confined to the district round St Asaph.
- The I 9th century witnessed a general revival of letters, beginning with the Romantic movement, of which the chief exponents were Garrett (q.v.) and Herculano (q.v.), both of whom had to leave Portugal on account of their political liberalism, and it was inaugurated in the xxii.
They had, however, been the leading parliamentary exponents of Bond policy for a considerable time.
With Descartes the use of exponents as now employed for denoting the powers of a quantity becomes systematic; and without some such step by which the homogeneity of successive powers is at once recognized, the binomial theorem could scarcely have been detected.
APn 1 2 3 ' the summation being for all permutations of the indices which result in different terms. The function is written (plp2p3ï¿½4n) for brevity, and repetitions of numbers in the bracket are indicated by exponents, so that (p1p1p2) is written (p1p 2).
He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional.
The British moralists who wrote with political prepossessions are interesting, not merely as contributors to speculation, but as exponents of spiritual tendencies which were expressed practically in the political agitations of their times.
Carried away by the Russians in his early youth, he settled in Rumania, learned Church music, and became one of its best exponents, married four times, had an adventurous life, but lived among the people for whom he wrote and composed his tunes.