"Nesselmann observes that we can, as regards the form of exposition of algebraic operations and equations, distinguish three historical stages of development... 1. ...Rhetoric Algebra, or "reckoning by complete words." ...the absolute want of all symbols, the whole of the calculation being carried on by means of complete words, and forming... continuous prose. As representatives... Nesselmann mentions Iamblichos "and all Arabian and Persian algebraists who are at present known." In their works we find no vestige of algebraic symbols; the same may be said of the oldest Italian algebraists and their followers, and among them Regiomontanus. 2. ...Syncopated Algebra... is essentially rhetorical and therein like the first in its treatment of questions, but we now find for often-recurring operations and quantities certain abbreviational symbols. To this stage belongs Diophantos and after him all the later Europeans until about the middle of the seventeenth century (with the exception of... Vieta... we must make an exception too... in favour of certain symbols used by Xylander and Bachet... 3. ...Symbolic Algebra ...uses a complete system of notation by signs having no visible connection with the words or things which they represent, a complete language of symbols, which supplants entirely the rhetorical system, it being possible to work out a solution without using a single word of the ordinary written language, with the exception (for clearness' sake) of a conjunction here and there, and so on. Neither is it the Europeans posterior to the middle of the seventeenth century who were the first to use Symbolic forms of Algebra. In this they were anticipated many centuries by the Indians."