 Geometrically Imaginary quantities are additional roots of the above equation of a purely symbolic nature.In article 214 of "Elements" Hamilton proves that if there is an i, j and k there also has to be another quantity h which is an imaginary scalar, which he observes should have already occurred to anyone who had read the preceding articles with attention.Article 149 of "Elements" is about Geometrically Imaginary numbers and includes a footnote introducing the term "biquaternion".