An Elementary Treatise on Quaternions

angle application axes axis becomes centre Chapter circle condition cone conjugate constant contains course curvature curve cylinder determine differential direction distance drawn easily effect element Eliminating ellipsoid envelop equal equation equivalent evidently example expression extremity fact factors fixed forces formula function given given lines gives Hamilton Hence integral intersection involves length linear and vector locus means multiplied normal obtain obviously once operating origin parallel pass perpendicular position properties prove quaternion radius rectangular referred represents respectively result right angles rotation Saß satisfied scalar second order seen shew sides similar Similarly simple solution sphere spherical student suppose surface tangent plane tensor theorem tion transformation triangle unit-vector vector vector function write written