in 1685 wallis published "algebra", preceded by a historical account of the development of the subject, which contains a great deal of valuable information. the second edition, issued in 1693 and forming the second volume of his "opera", was considerably enlarged. this algebra is noteworthy as containing the first systematic use of formulae. a given magnitude is here represented by the numerical ratio which it bears to the unit of the same kind of magnitude: thus, when wallis wants to compare two lengths he regards each as containing so many units of length. this perhaps will be made clearer by noting that the relation between the space described in any time by a particle moving with a uniform velocity is denoted by wallis by the formula