Concept

Summa de arithmetica

Summa de arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) is a book on mathematics written by Luca Pacioli and first published in 1494. It contains a comprehensive summary of Renaissance mathematics, including practical arithmetic, basic algebra, basic geometry and accounting, written for use as a textbook and reference work. Written in vernacular Italian, the Summa is the first printed work on algebra, and it contains the first published description of the double-entry bookkeeping system. It set a new standard for writing and argumentation about algebra, and its impact upon the subsequent development and standardization of professional accounting methods was so great that Pacioli is sometimes referred to as the "father of accounting". The Summa de arithmetica as originally printed consists of ten chapters on a series of mathematical topics, collectively covering essentially all of Renaissance mathematics. The first seven chapters form a summary of arithmetic in 222 pages. The eighth chapter explains contemporary algebra in 78 pages. The ninth chapter discusses various topics relevant to business and trade, including barter, bills of exchange, weights and measures and bookkeeping, in 150 pages. The tenth and final chapter describes practical geometry (including basic trigonometry) in 151 pages. The book's mathematical content draws heavily on the traditions of the abacus schools of contemporary northern Italy, where the children of merchants and the middle class studied arithmetic on the model established by Fibonacci's Liber Abaci. The emphasis of this tradition was on facility with computation, using the Hindu–Arabic numeral system, developed through exposure to numerous example problems and case studies drawn principally from business and trade. Pacioli's work likewise teaches through examples, but it also develops arguments for the validity of its solutions through reference to general principles, axioms and logical proof.

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Related concepts (5)
Trial balance
A trial balance is a list of all the general ledger accounts (both revenue and capital) contained in the ledger of a business. This list will contain the name of each nominal ledger account and the value of that nominal ledger balance. Each nominal ledger account will hold either a debit balance or a credit balance. The debit balance values will be listed in the debit column of the trial balance and the credit value balance will be listed in the credit column.
Double-entry bookkeeping
Double-entry bookkeeping, also known as double-entry accounting, is a method of bookkeeping that relies on a two-sided accounting entry to maintain financial information. Every entry to an account requires a corresponding and opposite entry to a different account. The double-entry system has two equal and corresponding sides known as debit and credit. A transaction in double-entry bookkeeping always affects at least two accounts, always includes at least one debit and one credit, and always has total debits and total credits that are equal.
Bookkeeping
Bookkeeping is the recording of financial transactions, and is part of the process of accounting in business and other organizations. It involves preparing source documents for all transactions, operations, and other events of a business. Transactions include purchases, sales, receipts and payments by an individual person or an organization/corporation. There are several standard methods of bookkeeping, including the single-entry and double-entry bookkeeping systems.
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