A history of Pascal's Arithmetical Triangle, tracing its roots in Pythagorean arithmetic, Hindu combinatorics and Arabic algebra, and giving an account of the progressive solution of combinatorial problems from the earliest recorded examples through the Renaissance and later mathematicians. The author shows how Pascal's work in establishing the peroperties of the numbers and their application in various fields let to Newton's discovery of the binomial theorem for fractional and negative indices and to Leibniz's discovery of calculus.