The Promptuary and the Napier's Bones at the National Archaeological Museum of Spain in Madrid. An example of the Promptuary is in the National Archaeological Museum of Spain in Madrid. It also includes an example of Napier's bones. The apparatus is a box of wood with inlays of bone.
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Mask strips are placed horizontally across the calculating board, that is, from left to right rather than from top to bottom. They have a large digit written in the space at one end and the rest of the strip contains five squares. Each square has triangular holes cut in it according to the patterns given in the following diagram. Napier's Promptuary: the mask patterns for digits 0 to 9 So for example the mask strips for the simples 3, 6 and 9 will look as follows: Napier's Promptuary: Three mask strips, for digits 3, 6 and 9 The guide lines in the patterns are for positioning the holes.
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In the top section it contains the "bones" calculation device, and in the bottom section is the promptuary. This example consists of 300 stored cards in 30 drawers. One hundred of these cards are covered with numbers (referred to as the "number cards"). The remaining two hundred cards contain small triangular holes, which, when laid on top of the number cards, allow the user to see only certain numbers.
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Napier coined the word rabdology (from Greek ῾ραβδoς [rhabdos], rod and λoγoς [logos] calculation or reckoning) to describe this technique. The rods were used to multiply, divide and even find the square roots and cube roots of numbers. The second device was a promptuary (Latin promptuarium meaning storehouse) and consisted of a large set of strips that could multiply multidigit numbers more easily than the bones. In combination with a table of reciprocals, it could also divide numbers.
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The section titled "Yu xuyu" 禹須臾 "Promptuary/Instant of Yu" begins by listing the stem and branch sexagenary cycle in five groups of twelve signs each, and gives, for the days in each group, a certain lucky time of day to safely begin a journey. This section concludes with a ritual to be performed before going out of the city gate. > When traveling, on reaching the threshold-bar of the capital gate, perform > the Pace of Yu thrice. Advance one pace.
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Andersen (1989:17) notes that the term Sanbu jiuji was later used synonymously with Yubu. Yu is closely associated with travel in the Rishu (Harper 1999:872). The section titled "Yu xuyu" "Promptuary/Instant of Yu" begins by listing the stem and branch sexagenary cycle in five groups of twelve signs each, and gives, for the days in each group, a certain lucky time of day to safely begin a journey. This section concludes with a ritual to be performed before going out of the city gate.
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An ivory set of Napier's Bones from around 1650 A set of Napier's calculating tables from around 1680 His work, Mirifici Logarithmorum Canonis Descriptio (1614) contained fifty-seven pages of explanatory matter and ninety pages of tables of numbers related to natural logarithms (see Napierian logarithm). The book also has an excellent discussion of theorems in spherical trigonometry, usually known as Napier's Rules of Circular Parts. See also Pentagramma mirificum. Modern English translations of both Napier's books on logarithms and their description can be found on the web, as well as a discussion of Napier's bones and Promptuary (another early calculating device).
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The promptuary, also known as the 'card abacus' is a calculating machine invented by the 16th-century Scottish mathematician John Napier and described in his book Rabdologiae in which he also described Napier's bones. It is an extension of Napier's Bones, using two sets of rods to achieve multi-digit multiplication without the need to write down intermediate results, although some mental addition is still needed to calculate the result. The rods for the multiplicand are similar to Napier's Bones, with repetitions of the values. The set of rods for the multiplier are shutters or masks for each digit placed over the multiplicand rods.
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In fact, part of his motivation to publish the treatise was to establish credit for his invention of the technique. The bones were easy to manufacture and simple to use, and several variations on them were published and used for many years. The promptuary was never widely used, perhaps because it was more complex to manufacture, and it took nearly as much time to lay out the strips to find the product of numbers as to find the answer with pen and paper. Location arithmetic was an elegant insight into the simplicity of binary arithmetic, but remained a curiosity probably because it was never clear that the effort to convert numbers in and out of binary form was worth the trouble.
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