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The Madrid Promptuary

IP.com Disclosure Number: IPCOM000129543D
Original Publication Date: 1988-Dec-31
Included in the Prior Art Database: 2005-Oct-06
Document File: 9 page(s) / 35K

Publishing Venue

Software Patent Institute

Related People

ERWIN TOMASH: AUTHOR [+2]

Abstract

In a work entitled Rabdologiae, published in 1617, John Napier describes three inventions for facilitating calculation. They are: the ";virgules"; or rods, the ";multiplicationes promptuario"; or promptuary of multiplication and the ";scacchiae abaco"; or chessboard abacus. Examples of the rods are to be found in many collections but no examples of the other two devices were known to exist. On a recent visit to the Museo Arqueologico in Madrid, I identified an early promptuary in excellent condition. This paper discusses the principles of operation of the promptuary and describes the Madrid example.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

Copyright ©; 1988 by the American Federation of Information Processing Societies, Inc. Used with permission.

The Madrid Promptuary

ERWIN TOMASH

(Image Omitted: Author's Address: 110 South Rockingham Avenue, Los Angeles, California, 90049. (213)394-8468.)

In a work entitled Rabdologiae, published in 1617, John Napier describes three inventions for facilitating calculation. They are: the "virgules" or rods, the "multiplicationes promptuario" or promptuary of multiplication and the "scacchiae abaco" or chessboard abacus. Examples of the rods are to be found in many collections but no examples of the other two devices were known to exist. On a recent visit to the Museo Arqueologico in Madrid, I identified an early promptuary in excellent condition. This paper discusses the principles of operation of the promptuary and describes the Madrid example.

Categories and Subject Descriptors: K.2 [Computing Milieux]: History of Computing -- hardware, people. B.2 [Hardware]: Arithmetic and Logic Systems -- design styles, calculator. General Terms: Design Additional Terms: John Napier, Promptuary, Museo Arquelogico

Introduction

John Napier (1550-1617) is justly famous as the inventor of logarithms. His widely known invention has been used for centuries to reduce the burden, tedium, and error rate associated with large-scale arithmetical calculations. Not nearly so well known today are Napier's mechanical inventions, intended for the same purpose. With these devices, he sought the same end -- to facilitate the carrying out of arithmetic calculations by persons who possessed only minimal mathematical knowledge.

In Napier's day, the notation and processes for arithmetical manipulation that we now take for granted and think of as elementary were still in the development stage. He lived at a time when skill in arithmetic processes was rare and knowledge of ordinary arithmetic uncommon. The first arithmetic book published in England, Tonstall's De Arte Supputandi, was issued less than 30 years before his birth. As for texts in English, Robert Recorde's Ground of Artes, first published in 1642, only began to be used in English schools after Napier's lifetime [Smith 1908]. The situation, as Napier saw it, is clear from the preface to the work in which he announced his Canon of Logarithms (translated by Edward Wright):

(Image Omitted: Seeing there is nothing, (right well beloved students in the mathematics,) that is so troublesome to mathematical practice, nor that cloth more molest and hinder calculations, than the multiplications, divisions, square, and cubical extractions of great numbers, which beside the tedious expence of time, are for the most part subject to many slippery errors, I began, therefore, to consider in my mind, by what certain and ready art I might remove those hindrances.... [Wright 1616].)

In the last year of his life, Napier published the Rabdologiae [from the Greek rha...