This paper examines the mathematical stimuli that induced George Boole to conceive of a general calculus of symbols, and eventually of his first algebra of logic, as in his Mathematical Analysis of Logic (1847). We focus our attention particularly on Boole's first mathematical masterpiece "On a General Method in Analysis' (1844), a work grounded on the laws of combination of non-commutative symbols, which apparently convinced Boole of the immense power afforded by symbolical methods, a power largely due to their main property of not depending upon conditions of their interpretation. Our aim is twofold. Firstly we argue that Boole's discovery of a general method was motivated by R.L. Ellis's study of the differential equation involved in the theory of the earth's shape. Secondly, we pick up indicative instances from his first work on logic which manifest the implicit or explicit import that his general method had upon the genesis of his general method in logic.