From A Merely Formal Point Of View, We Have In The **Barycentric** Calculus A Set Of " Special Symbols Of Quantity " Or " Extraordinaries " A, B, C, &C., Which Combine With Each Other By Means Of Operations And Which Obey The Ordinary Rules, And With Ordinary Algebraic Quantities By Operations X And =, Also According To The Ordinary Rules, Except That Division By An Extraordinary Is Not Used.

All this is analogous to the corresponding formulae in the **barycentric** calculus and in quaternions; it remains to consider the multiplication of two or more extensive quantities The binary products of the units i are taken to satisfy the equalities e, 2 =o, i ej = - eeei; this reduces them to.

Also, by giving suitable values (positive or negative) to the ratios a :7 we can make G assume any assigned position in the plane ABC. We have here the origin of the **barycentric** co-ordinates of MObius, now usually known as areal co-ordinates.