Arithmetica

Arithmetica (Greek: Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations.

Equations in the book are called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. It was these equations which inspired Pierre de Fermat to propose Fermat's Last Theorem, scrawled in the margins of Fermat's copy of Arithmetica, which states that the equation , where , , and are non-zero integers, has no solution with greater than 2.

In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of the form cannot be the sum of two squares. Diophantus also appears to know that every number can be written as the sum of four squares. If he did know this result (in the sense of having proved it as opposed to merely conjectured it), his doing so would be truly remarkable: even Fermat, who stated the result, failed to provide a proof of it and it was not settled until Joseph Louis Lagrange proved it using results due to Leonhard Euler.

Luca Pacioli

Fra Luca Bartolomeo de Pacioli (sometimes Paccioli or Paciolo; c. 1447–1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and a seminal contributor to the field now known as accounting. He is referred to as "The Father of Accounting and Bookkeeping" and he was the first person to publish a work on the double-entry system of book-keeping. He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany.

Life

Luca Pacioli was born between 1446 and 1448 in Sansepolcro (Tuscany) where he received an abbaco education. This was education in the vernacular (i.e. the local tongue) rather than Latin and focused on the knowledge required of merchants. He moved to Venice around 1464, where he continued his own education while working as a tutor to the three sons of a merchant. It was during this period that he wrote his first book, a treatise on arithmetic for the boys he was tutoring. Between 1472 and 1475, he became a Franciscan friar.