Sentence Examples with the word Necessary condition

The qualification that the circular function must apply to all time is important, and unless it is recognized as a necessary condition of homogeneity, confusion in the more intricate problems or radiation becomes inevitable.

On the other hand the democratic tone which distinguishes Micah from Isaiah, and his announcement of the impending fall of the capital (the deliverance of which from the Assyrian appears to Isaiah as the necessary condition for the preservation of the seed of a new and better kingdom), are explained by the fact that, while Isaiah lived in the centre of affairs, Micah, a provincial prophet, sees the capital and the aristocracy entirely from the side of a man of the oppressed people, and foretells the utter ruin of both.

It is also a necessary condition for the application of the preceding laws that no form of energy except heat and the intrinsic energy of the substances should be ultimately involved.

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These were: (1) that the divine decree of predestination is conditional, not absolute; (2) that the Atonement is in intention 'universal; (3) that man cannot of himself exercise a saving faith; (4) that though the grace of God is a necessary condition of human effort it does not act irresistibly in man; (5) that believers are able to resist sin but are not beyond the possibility of falling from grace.

Now among the Jews, as we have seen, the hierarchy proper has for its necessary condition the destruction of the state and the bondage of Israel to a foreign prince, so that spiritual power is the only basis left for a national aristocracy.

Now, this oppositing of the Anstoss is the necessary condition of the practical ego, of the will.