Intro to Napier's bones

Let's have fun learning how to multiple and divide numbers with the antique Napier's bones, an early calculating machine was invented by John Napier. It was a clever way to perform complex multiplication and division far before any automated calculating machine, in 1617!!

Mr. Owl teaches you on a simple example! Assuming you already assembled the machine (instructions below), let's calculate 268 x 7. For this, turn the knobs so 2-6-8 appears in the top (header row):

Now look at the 7th row:

You obtain the results by getting first the single number, then the tens, then the hundreds. The single number is given by the rightmost bottom number (circled in blue), i.e. 6. Then, we get the tens by summing the numbers circled in green, i.e. 5+2=7. The hundreds are then obtained similarly, by summing the numbers circled in red, i.e. 4+4=8. Finally, we observed that there is a thousand (circled in yellow). The results is therefore 1876!

You can of course do bigger multiplication, like 598 x 82, and even division! Here is a great video explaining how to do these operations.

How to print and assemble

Very easy! You need to print the following parts:

• 3 cylinders
• 3 knobs
• 1 frame
• optionally, 2 or more reading rulers

All these parts can be print in one go, no supports needed! Such an example is given in the napier_bones.3mf file. Now let's assemble.

1. Place the frame on a table, its face featuring the cylinder resting holes up.
2. Insert the knobs in the cylinders.
3. Put the cylinders on the frame.
4. Optionally, put one reading ruler on the top most row (the one featuring only one number).
5. Optionally, put other reading rulers one any row you want to use for multiplication.

If you want to remix it, feel free to use the provided step files containing all the parts, or to duplicate my public Onshape document.

Enjoy a piece of history printed with modern tools ;)