It may be remarked that we cannot with a real point and line obtain the node with two imaginary tangents (conjugate or isolated point or acnode), nor again the real double tangent with two imaginary points of contact; but this is of little consequence, since in the general theory the distinction between real and imaginary is not attended to.

He showed that an imaginary spheroidal shell, concentric with the earth and cutting the slope between the elevated and depressed areas at the contour-line of 1700 fathoms, would not only leave above it a volume of the crust equal to the volume of the hollow left below it, but would also divide the surface of the earth so that the area of the elevated region was equal to that of the depressed region.6 A similar observation was made almost simultaneously by Romieux, 7 who further speculated on the equilibrium between the weight of the elevated land mass and that of the total Areas of waters of the ocean, and deduced some interesting relathe cru st tions between them.

Modern scholars have sometimes found in the name the expression of the aseity 14 of God; sometimes of his reality, in contrast to the imaginary gods of the heathen.

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There also he wrote the life of St Paul of Thebes, probably an imaginary tale embodying the facts of the monkish life around him.

For a crunodal cubic the six inflections which disappear are two of them real, the other four imaginary, and there remain two imaginary inflections and one real inflection.

The treatment of equations of the second and higher degrees introduces imaginary and complex numbers, the theory of which is a special subject.

Much of the argument is thrown into the form of a dialogue between (1) Nestorius and an imaginary opponent Superianus, (2) Nestorius and Cyril.

Trifler rather than as a monster of lust and cruelty, is the reproduction of a real or imaginary scene from the reign of Domitian, and is animated by the profoundest scorn and loathing both of the tyrant himself and of the worst instruments of his tyranny.

The radio was playing a waltz as she walked through the family room and she moved to the sway of it, dancing with an imaginary friend.

After he had gone Pierre continued pacing up and down the room for a long time, no longer piercing an imaginary foe with his imaginary sword, but smiling at the remembrance of that pleasant, intelligent, and resolute young man.