"The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared, for its importance, with the invention of triple coordinates by Descartes. The ideas of this calculus, as distinguished from its operations and symbols, are fitted to be of the greatest use in all parts of science." 
Welcome to a brief introduction to the quaternions! The quaternions are a number system that utilize the complex numbers and can be applied to mechanics in three-dimensional space. Similar to the real numbers they can be added, subtracted, multiplied, and divided. So why have we never heard them? Well, today most people use vector notation to describe geometric and abstract spaces, which is a much simpler system to comprehend! Don't think that the quaternions are an antiquated method though, they still have their uses!