Calculus of finite differences

-nature of the calculus of finite differences; direct theorems of finite differences; on integration and mechanical quadrature; finite integration and the summation of series; the approximate summation of series; bernoulli's numbers and factorial coefficients; convergency and divergency of series; exact theorems; difference: equations of the first order; general theory of the solutions difference and differential equations of the first order; linear difference: equations with constant coefficients; miscellaneous propositions and equations; simultaneous equations; linear equations with variable coefficients; symbolical and general methods; mixed and partial difference: equations of the calculus of functions; geometrical applications answers to exercises-