Elements of Quaternions

algebra already angle anharmonic arbitrary axis becomes Calculus called centre CHAP circle coefficients common comp Compare complanar conceive condition cone conjugate connected considered constant construction corresponding cubic curvature curve definition denote derived determined differential direction equal equation example expression fact factors formula four function geometrical given given point gives Hence imaginary interpreted intersection known length limit locus manner mean multiplication namely negative normal Note obtained operation opposite origin osculating pass perpendicular plane positive present principles proportional proved quaternion quotient radius recent reciprocal regards relation represented respect result right line roots rotation satisfied scalar seen sides simply space sphere spherical square supposed surface symbol tangent tensor third tion transformations triangle variable vector versor VIII whence write