• 2025-05-31
• 6 min read

Euclid's Toolworks—Connecting Ancient Geometry to Hand tool Woodworking

Publisher's Note

I apologize for this post being over two weeks late. This was a hard post to write without slipping into my grad school teaching mode—i.e., dry and boring. I’ve also learned to keep AI at a distance in the writing process, or it will just take over and you’ll lose your own voice. AI has its uses, but caveat emptor, as the saying goes. I did find image generation helpful, since there aren’t many historical images that relate well to this post, but even those took far too long to get anatomically correct.

Introduction

Picture a 17th-century cabinetmaker, marking a bookshelf with a simple stick, no ruler in sight. Now imagine a modern woodworker, tape measure and dimensioned drawing in hand, checking precise dimensions. Both rely on principles from a Greek mathematician named Euclid, who lived over 2,000 years ago. In this post, we'll explore how Euclid’s geometry shaped woodworking tools, from ancient compasses to today’s protractors, and why his ideas inspired my hand tool wood shop, Euclid’s Toolworks.

18th Century Cabinetmaker using a story stick—AI Generated by Microsoft Copilot. (2025)

Who Was Euclid?

Euclid was a Greek mathematician who lived and worked around 300 BC during the reign of Ptolemy, in the city of Alexandria, Egypt, an important intellectual hub with its famous Library. Likely influenced by Plato's Academy in Athens, Euclid became known as the "Father of Geometry" for his most significant and influential work, Elements.¹ Euclid organized Greek mathematical knowledge into clear rules about points, lines, angles and shapes that we've all studied in our high school geometry classes. Euclid's ideas are so much more than theory: they make possible the very tools we've used for centuries to craft everything from furniture to ships.

Geometry in Traditional Woodworking

Why do we as artisans, craftsmen, woodworkers, metalworkers, care about a 2000-year-old mathematician? The answer is simple. Euclid's geometry shapes how we build things. Until the late 18th century we built everything using Geometry. Compass, dividers, straightedge, squares, the sector, string, pinch rods and story sticks. These tools were usually built by the craftsmen who used them using Euclid's principles of geometry to make them. We didn't have standardized rulers and protractors, although Joseph Moxon was making sophisticated scientific instruments, astrolabes and sundials, and writing about it as early as 1683 AD,² again using Euclid's geometry. We didn't measure in the normal sense that we know today. We transferred measurements from physical examples to the work; proportion was used to scale and design.

The Shift to Modern Measurement

It wasn't until the late 1700s that we started using standardized rulers and building to dimensioned drawings. Imagine: your wife asks you to build her a bookshelf so she can store her cookbooks in the corner of the kitchen. What's your first thought? You probably google some free plans on the internet that include measured drawings, and go to town. Maybe you look up some standardized dimensions from a reference on furniture. Maybe you take your tape measure and a notebook and create a dimensioned drawing based on the size of the corner. An early cabinetmaker would have gone to the corner, marked or scribed the necessary dimensions directly on the story stick. He might have even measured his wife's height and reach in a similar fashion, to make sure she could comfortably use the shelves. Once he had some basic dimensions, he could fill in other necessary dimensions on the story stick using Euclid's principles of proportion. Finally, he might have presented that story stick to the stock that he was working and transferred the dimensions, laid out the cuts, and gone to work. Careful work would have been precise and accurate and wouldn't have involved a lot of mental gymnastics. I'm not saying that the modern ways are bad, or even not as good as the old ways. I just don't want to see the traditional ways disappear, since they are useful, probably less prone to error, and they allow us to do excellent, precise, and accurate work with tools we can build ourselves.

Why Euclid's Toolworks?

Why open a toolworks and name it after Euclid. It's personal. After decades at a desk as a software architect and engineer. health challenges have pushed me toward early retirement. It's time for a change. Working in the shop seems to help a lot, but there's no way I can have a full woodworking shop like the one I had access to in highschool. All those excellent free-standing machines are too expensive and take up too much space. Hand tools don't need much space and they are considerably less expensive. I've got a little experience with hand tools; with practice, I can make that work. Voila, become a hand tool woodworker.

Inspiration from Walker and Tolpin

But what should I build? Something small, no space, remember. I came across George Walker and Jim Tolpin's books.³ I'm a closet mathematician, an engineer, and a computer scientist. When I read their books, I saw the way that Euclid's principles bridge the gap between the theoretical and the practical. I was thrilled. I'm also the grandson and grandnephew of machinists, tool and die makers, and I really appreciate precision. I have a thing for layout and measurement tools. Here were books about making and using the layout and measurement tools of artisan geometry! I owe a large debt to George, Jim, and Lost Art Press for giving me something to get excited about and do my best to crush it, in my retirement!

Looking Ahead

So there you have it Euclid's Toolworks will make, very accurate and precise tools of artisan geometry, out of wood, using traditional hand tool methods. I'll also make workbenches—nothing too large—shop furniture, tool chests, and jigs. Oh, and probably chairs. A few anyway. Chris may not know it, but he's corrupted me. I'm planning to replace 6 dining room chairs with stick chairs. Maybe I'll make a few more, if I get good at it.

What's Next

I've got several projects in the works for the short term so I'll be writing about those in the coming weeks. My planned last day in corporate America is either August 29th or September 5th. Here's the list of projects in priority order. The last two projects are "smalls". They may get done first because I can probably do them with my current set up.

1. Roman Workbench
2. Shop Setup—A lot of the tools need to be tuned and sharpened
3. A couple of practice/warmup projects
   1. A Gottshall Block⁴
   2. A Joinery Window
4. A tool chest for my woodworking tools
5. The first complete set from Euclid's Door⁵—I have ambitions of gifting a few of the first sets to folks who have helped me get started.
6. I've been riffing on a design of John Steinbeck's infamous pencil cup. If you don't know the story, stay tuned.
7. Refurbishing an old child's bookcase that I've had since I was a wee laddie, Circa 1960. This will become the new home for the shop library

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1. Euclid, Elements, trans. Thomas L. Heath (Green Lion Press, 2002) ↩

2. Mechanick Exercises or The Doctrine of Handy-Works—I originally purchased this directly from LAP, but it's currently not on their site so Lee Valley will have to do. ↩

3. Books on artisan geometry by George Walker and Jim Tolpin ↩

4. Reproducing Antique Furniture: Instructions and Measured Drawings for 40 Classic Projects By Franklin H. Gottshall ↩

5. Euclid's Door: Building the Tools of ‘By Hand & Eye’ ↩