Elements of Quaternions

William Rowan Hamilton

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treating p as constant, represents the real plane (comp. 282, (12. )) of the (real or imaginary} circle, which is the ultimate intersection of the near sphere with the given one ; the radius of this circle, which we shall call r, being found by the follow- ing formula, CXXXI. . . RV2 = & (R' z -f (/), or CXXXl'. . . R 2 TV 2 = & (TV2 - fl'*), and being therefore real when CXXXII. . . R' 2 +

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