A ready reckoner is a printed book or table containing pre-calculated values, often multiples of given amounts. They were widely used in shops and by tradesmen before the advent of cheap electronic calculators, metric weights and measures and decimal currencies in the 1970s.
Before the 1960s and the widespread introduction of calculators, multiplication was a laborious chore, often prone to error. This was especially so when calculations involved non-decimal currencies. [1] Various devices were invented to aid this process, such as the abacus, log tables, slide rule, stepped reckoner, or the comptometer, but the most commonly used device for everyday commerce was the ready reckoner. These could be either general-purpose – aimed to meet the needs of a variety of trades – or designed specifically for one trade or group of trades.
The earliest surviving ready reckoner in English dates from the 1570s; [2] other sources attribute the invention to the Dutch mathematician Simon Stevin, who calculated and published decimal tables in the 1580s. [3] William Webster published A plaine and most necessarie booke of tables, for simple and compound interest, in 1625. [4] There are several other seventeenth-century publications giving 'reckonings ready done' or 'accounts ready cast up' or tables of simple and compound interest. The most popular of these was William Leybourn's, Panarithmologia, being a mirror breviate treasure mate for merchants, bankers, tradesmen, mechanicks, and a sure guide for purchasers, sellers, or mortgagers of land, leases, annuities, rents, pensions, &c. in present possession or reversion. (1693). [5] Other works were published in France such as François Barrême's Le Livre des Comptes Faits. Paris: Thierry, which appeared in 1673, and was still being published in 1862. [1]
The term 'ready reckoner' was coined by the schoolmaster Daniel Fenning with the publication of The ready reckoner; or trader's most useful assistant in 1757. [6] This was a modernised and extended version of Leybourn's work, which was reprinted in Boston, Massachusetts, about 1770, and translated into German in Germantown, Philadelphia, 1774. [7] Fenning's work continued to be reprinted in England until the early 1820s when several of the tables were superseded by the advent Imperial Weights and Measures under the Weights and Measures Act 1824.
By the end of the eighteenth century, ready reckoners designed for the needs of particular trades or types of business began to appear. Thus The gentleman and farmers' assistant, by John Cullyer (1795) or The farmer's, grazier's, and butcher's ready reckoner (1796).
Hundreds of ready reckoners appeared, principally in the UK and US throughout the nineteenth century and the first half of the twentieth century, as they proved to be cheaper to produce and easier to use than alternative means of calculation. According to Williams and Johnson, 'Ready Reckoners were the dominant aid used for multiplication in trade from 1800 to 1950. Throughout this period their sales far exceeded any other calculating aid used in trade to assist in making routine calculations.' [8] It was only with the gradual introduction of mechanical and later electronic calculators that they began to be superseded.
An abacus, also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu-Arabic numeral system. An abacus consists of a two-dimensional array of slidable beads. In their earliest designs, the beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation.
An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.
A slide rule is a hand-operated mechanical calculator consisting of slidable rulers for evaluating mathematical operations such as multiplication, division, exponents, roots, logarithms, and trigonometry. It is one of the simplest analog computers.
An adding machine is a class of mechanical calculator, usually specialized for bookkeeping calculations. In the United States, the earliest adding machines were usually built to read in dollars and cents. Adding machines were ubiquitous office equipment until they were phased out in favor of calculators in the 1970s and by personal computers beginning in about 1985. The older adding machines were rarely seen in American office settings by the year 2000.
A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol also affects the choice of symbol for the thousands separator used in digit grouping.
In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as standard logarithm. Historically, it was known as logarithmus decimalis or logarithmus decadis. It is indicated by log(x), log10(x), or sometimes Log(x) with a capital L; on calculators, it is printed as "log", but mathematicians usually mean natural logarithm (logarithm with base e ≈ 2.71828) rather than common logarithm when writing "log". To mitigate this ambiguity, the ISO 80000 specification recommends that log10(x) should be written lg(x), and loge(x) should be ln(x).
Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely used until electronic calculators became cheap and plentiful in the 1970s, in order to simplify and drastically speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks, and specialized tables were published for numerous applications.
Napier's bones is a manually-operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called rabdology, a word invented by Napier. Napier published his version in 1617. It was printed in Edinburgh and dedicated to his patron Alexander Seton.
Significant figures, also referred to as significant digits or sig figs, are specific digits within a number written in positional notation that carry both reliability and necessity in conveying a particular quantity. When presenting the outcome of a measurement, if the number of digits exceeds what the measurement instrument can resolve, only the number of digits within the resolution's capability are dependable and therefore considered significant.
A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a slide rule. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator and the digital computer.
£sd, spoken as "pounds, shillings and pence", is the popular name for the pre-decimal currencies once common throughout Europe. The abbreviation originates from the Latin currency denominations librae, solidi, and denarii. In the United Kingdom, these were referred to as pounds, shillings, and pence.
The soroban is an abacus developed in Japan. It is derived from the ancient Chinese suanpan, imported to Japan in the 14th century. Like the suanpan, the soroban is still used today, despite the proliferation of practical and affordable pocket electronic calculators.
The suanpan, also spelled suan pan or souanpan) is an abacus of Chinese origin first described in a 190 CE book of the Eastern Han Dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue. However, the exact design of this suanpan is not known. Usually, a suanpan is about 20 cm (8 in) tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads on each rod in the bottom deck. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. The suanpan can be reset to the starting position instantly by a quick jerk around the horizontal axis to spin all the beads away from the horizontal beam at the center.
The arithmometer was the first digital mechanical calculator strong enough and reliable enough to be used daily in an office environment. This calculator could add and subtract two numbers directly and could perform long multiplications and divisions effectively by using a movable accumulator for the result.
Pascal's calculator is a mechanical calculator invented by Blaise Pascal in 1642. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the supervisor of taxes in Rouen. He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction.
Thomas Fowler was an English inventor whose most notable invention was the thermosiphon which formed the basis of early hot water central heating systems. He also designed and built an early mechanical calculator.
The stepped reckoner or Leibniz calculator was a mechanical calculator invented by the German mathematician Gottfried Wilhelm Leibniz around 1672 and completed in 1694. The name comes from the translation of the German term for its operating mechanism, Staffelwalze, meaning "stepped drum". It was the first calculator that could perform all four basic arithmetic operations.
The history of logarithms is the story of a correspondence between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer. The Napierian logarithms were published first in 1614. E. W. Hobson called it "one of the very greatest scientific discoveries that the world has seen." Henry Briggs introduced common logarithms, which were easier to use. Tables of logarithms were published in many forms over four centuries. The idea of logarithms was also used to construct the slide rule, which became ubiquitous in science and engineering until the 1970s. A breakthrough generating the natural logarithm was the result of a search for an expression of area against a rectangular hyperbola, and required the assimilation of a new function into standard mathematics.
A mechanical computer is a computer built from mechanical components such as levers and gears rather than electronic components. The most common examples are adding machines and mechanical counters, which use the turning of gears to increment output displays. More complex examples could carry out multiplication and division—Friden used a moving head which paused at each column—and even differential analysis. One model, the Ascota 170 accounting machine sold in the 1960s, calculated square roots.
A timeline of numerals and arithmetic.