We can so determine these n covariants that every other covariant is expressed in terms of them by a fraction whose denominator is a power of the binary form.

The Babylonians expressed numbers less than r by the numerator of a fraction with denominator 60; the numerator only being written.

The ideas of expiation and atonement so prevalent in Ezekiel's scheme, which there find expression in the half-yearly sacrificial celebrations, are expressed in Lev.

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The points of the compass might similarly be expressed by numbers in a binary scale; but the numbers would be ordinal, and the expressions would be analogous to those of decimals rather than to those of whole numbers.

And III., the potential has been expressed as percentages of its mean value for the year or the day.

His Majesty expressed his displeasure, and summoned them before him in the councilchamber, where he insisted on his supreme prerogative, which, he said, ought not to be discussed in ordinary argument.

Rose also carried out experiments on the decomposition of cryolite, and expressed an opinion that it was the best of all compounds for reduction; but, finding the yield of metal to be low, receiving a report of the difficulties experienced in mining the ore, and fearing to cripple his new industry by basing it upon the employment of a mineral of such uncertain supply, Deville decided to keep to his chlorides.

ABHORRERS, the name given in 1679 to the persons who expressed their abhorrence at the action of those who had signed petitions urging King Charles II.

The resentment of the Copts finally expressed itself in a revolt, which broke out in the year 725, and was suppressed with difficulty.

The magisterial views seem to have prevailed in the professoriate, which formally in March 1642 expressed its disapprobation of the new philosophy as well as of its expositors.