Elements of Quaternions

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