Here the symmetry points at once to the selection of the three principal axes as the directions for i, j, k; and it would appear at first sight as if quaternions could not simplify, though they might improve in elegance, the solution of questions of this kind.
To simplify this, we take a new unit Y, which is 2 of X.
These equations simplify very much in their application to plane waves.
These points, together with a truly turned and polished cylinder, with carefully planned means of adjustment, much simplify the preparation of making-ready of any kind of type-forme or blocks for printing, which is carried out much in the same way as on the ordinary single cylinder, but in a more convenient manner.
There is not a single branch of the law which he did not simplify and amend, and the iron firmness with which he caused justice to be administered, irrespective of persons, if it exposed him to the charge of tyranny from the nobles, also won for him from the common people the epithet of " the Just."