Napier's bones

Napiersche computing sticks (after John Napier, of these appeared in his 1617 work Rabdologiae seu numeratio by virgulas libri duo describes ) are computational chopsticks with which multiplication and division can be performed. They are also called Nepersche sticks or Neperianische Rechenstäblein.

The rods have a square cross-section. On the chopsticks is listed line by line on each side a series of multiplication tables. For example, standing on the right in photo ( Fig. 1) chopsticks one side, the 7-series of the multiplication of 1 × 7-9 × 7 The top of each side of the second factor of the 1 × x is, in the example to the right so the 7th

In each line of the rod a number of 1 × x is. The line is divided diagonally from bottom left to top right. In the lower right triangle is the units digit in the upper left triangle and the tens digit of the number. Example of line 7 of 1 × 7, top left is 4 and the bottom right is 9, what the result of the multiplication 7 × 7 = 49 corresponds.

The strips are placed in a manner to multiply tray at its left edge, the numbers 1 to 9 are shown below each other. The rods fit perfectly into this tray.

Multiplication

The multiplication with the chopsticks will be explained with an example.

46785399 To multiply the number with the 7, puts you in the rods of the type on the tablet that the far left one stick of series 4, so is the number 4 at the top, right next to a rod with the number 6, so from the 6 Series, and so on to the last, rightmost rod with the number 9 at the top ( see figure 2).

Now, to get the results you read in line 7 from left to right, the digits from. ( The line is highlighted in white in Figure 2. ) From right to left to read next, the numbers within the same diagonals, add them together and writes the respective ( single digit ) Earnings on. If the result of the addition is a number greater than 9, the tens digit ( 1) is taken over into the next left to be added diagonal. In this way arises from right to left, the result of production, where the units digit is right, left next to the tens digit and so on.

The result in this example would therefore 46785399 × 7 = 327,497,793th

But multiplication with larger numbers are possible. Intended to stay with the above example the number 46785399 will be multiplied by the 96431.

To this end, the rods are placed as shown in Figure 2. Now is sequentially read from the lying on the tray sticks each individual result and wrote to each other as shown in Figure 3.

By adding the products obtained, the result of the desired multiplication × 46785399 96431 results = 4,511,562,810,969th

Abacus

After a reconstruction Wilhelm Schickard has the rods used for its, the first calculating machine.