His treatises and contributions to scientific journals (to the number of 789) contain investigations on the theory of series (where he developed with perspicuous skill the notion of convergency), on the theory of numbers and complex quantities, the theory of groups and substitutions, the theory of functions, differential equations and determinants.
- The cyclical meaning of the succession of zodiacal signs, though now obscured by interpolations and substitutions, was probably once clear and entire.
The motive of some of the substitutions was to avoid the confusion which must have ensued from the duplication of previously existing native asterisms; thus, the Egyptian and Greek Lions were composed of totally different stars.: Abstractions in other cases replaced concrete objects, with the general result of effacing the distinctive character of the Greek zodiac as a " circle of living things."
Restricted Substitutions We may regard the factors of a binary n ip equated to zero as denoting n straight lines through the origin, the co-ordinates being Cartesian and the axes inclined at any angle.
In addition, and transform each pair to a new pair by substitutions, having the same coefficients a ll, a12, a 21, a 22 and arrive at functions of the original coefficients and variables (of one or more quantics) which possess the abovedefinied invariant property.