Editing Promptuary (section)

==Design of the Promptuary==

The promptuary consists of four parts:

* a set of number strips, engraved with a large digit at one end and with many small digits along the strip
* a set of mask strips, which Napier called excised or perforated strips. Each has a single digit engraved at one end and various triangular holes cut in it
* a board on which to place the strips when performing a calculation
* a box to store the strips. In Napier's design, the top of the box was the board on which the calculations were performed.

The dimensions of the strips depends on the maximum number of digits in the numbers to be multiplied. For a device capable of multiplying two N-digit numbers together, the strips should be (N+1) times as long as they are wide, and there should be 10N number strips and 10N mask strips. So for example, for a promptuary capable of multiplying two five-digit numbers together, the strips should 6 times as long as they are wide, with 50 number strips and 50 mask strips. Napier's example specified strips 1 finger (19mm) wide and 11 fingers (209mm) long, enabling the device to multiply two 10-digits numbers to produce a 20-digit result.

Napier specified that the number strips should be a different thickness from the mask strips - one quarter of a finger (5mm) versus one eight of a finger (2.5mm). This is not necessary for the operation of the device.

The promptuary contains a lot more pieces than a set of Napier's Bones. A set of Napier's Bones with 20 rods is capable of multiplying numbers of up to 8 digits. An equivalent promptuary needs 160 strips.

In the examples and illustrations below, N is set to 5 - that is, the illustrated promptuary can multiply numbers of up to 5 digits.

===Number Strips===

The number strips are divided into five squares, with about half a square free at each end. A large digit, known as the ''simple'', is marked in the space at the top of the strip. A multiplication table is placed in each of the five squares. Each of these multiplication tables is identical—it lists the multiples of the simple and is laid out in a particular way:

The square is divided into nine smaller squares in a three-by-three arrangement. Each of these is divided into two triangles by a diagonal line running from lower left to upper right. The multiples of the digit at the top of the strip, the simple, are marked in the table as in the diagram.

[[File:Promptuary diagram 1.png|center|Napier's Promptuary: Placing multiples on promptuary grid]]

* The simple itself is marked in the triangle labelled × 1.
* The number that is two times the simple is marked in the two triangles marked × 2. If the number is two digits, the first digit is placed to the left of the main diagonal (marked in red) and the second digit to the right of the diagonal. If the number is a single digit, it is marked to the right of the diagonal
* The number that is 3 times the simple is written in the triangles marked × 3 in the same way as the multiple of 2
* The other multiplies of the simple are marked in the other triangles in the same way.
* Zeroes may be written in or left blank. This does not affect the operation of the device.
* The triangle in the bottom left of the table is always blank.

The following diagram shows the multiplication table for the simple 7:

[[File:Promptuary diagram 2.png|center|Napier's Promptuary: multiple diagram for digit 7]]

Complete number strips for the simple 7 and the simple 2 are shown in the following diagram. The lines delineating the triangles have been omitted.

[[File:Promptuary diagram 3.png|center|300px|Napier's Promptuary: two number strips from the promptuary, for digits 7 and 2]]

===The Mask Strips===

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.

[[File:Promptuary diagram 4.png|center|300px|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:

[[File:Promptuary diagram 5.png|center|600px|Napier's Promptuary: Three mask strips, for digits 3, 6 and 9]]

The guide lines in the patterns are for positioning the holes. They do not need to appear on the strips. The main diagonal line of each mask pattern, however, shown here in red, is marked on the mask strip. It is an important part of the device. The pattern given here for the simple 0 is from later editions of Napier's book. The version of the 0 strip in the first edition had no holes in it.