The Treatise on the Arithmetical Triangle

The Treatise on the Arithmetical Triangle explores Pascal's Triangle, a triangular array of numbers with patterns that reveal binomial coefficients. Each number is the sum of the two numbers directly above it, illustrating combinations and probabilities. This triangle helps in calculating likelihoods, algebraic expansions, and understanding patterns in mathematics. Pascal's work made these concepts accessible, showing that complex problems could be broken down into simple, elegant structures. It’s a foundational tool that connects algebra, probability, and combinatorics, providing insight into how numbers relate and grow systematically.