I love to read but never would have dreamed that I’d spend so much time devouring obscure historical design texts from the 17th through early 19th centuries. From a writing standpoint the language is obtuse, wordy, confusing, haughty, and just plain difficult to stomach. Even after years of reading and re-reading Batty Langley’s *The City and Country Workman’s Treasury of Designs…* it still feels like reading a bad translation of a bad translation. Yet, nuggets of gold keep dropping off the pages and I find myself pouring over an engraving late into the night.

Those nuggets are like pieces of a mosaic, a way of approaching design that’s both liberating and quite powerful. One concept that’s slowly emerging is a different way to view objects in space and with it the ability to visualize a design in the minds eye. To explain I have to back up a bit. Period artisans and designers used geometry to visualize and express ideas. Now before I lose you, I’m not talking about the geometry you were bombarded with in grade school. A very different geometry, not a bunch of theorems to memorize but a simple pure form of geometry made up of shapes and lines that helped the mind comprehend reality. Case in point, recently I was reading an English math primer Cocker’s Arithmetick, sort of the McGuffey reader of math for the 18th century. The author kept turning to geometry to explain math concepts. Trying to explain the concept of zero, he stated it’s like a point in geometry, has no size, cannot add or subtract from another value etc.

Why this is important? From a designer’s standpoint it equips the mind with a vocabularyof simple shapes. We might not be able to easily visualize a rectangle that’s 27” wide X 54” high but we can visualize two squares stacked on top of each other. All those old engravings brimming with a confusion of circles, chords, arcs, and angles are using geometry to communicate how the design is tied together proportionally. Sometimes I find myself driving down the street and imagine buildings with circles and arcs drawn across the façade defining the underlying form. When I get that look in my eye, my wife Barb gets nervous and wants to take the wheel (but that’s another post).

So that’s part of what I’m trying to convey through this apprentice sketchbook series. Give you a visual geometry library in your mind to construct and deconstruct images in space. When you begin to see the simple underlying shapes that make up a form you will begin to realize how powerful this is. Guess I got a little ahead of myself when I began this in February. Should have begun down at bedrock just the way most of the historical texts do. Most begin with a series of simple intuitive methods to find a perpendicular from a line. If you follow Chris Schwarz you know doubt have learned how to make your own square. What if you don’t have a square? Actually all you need is two nails and a stick (to fashion a crude set of dividers). Anyway, here’s three methods of finding a right angle from a plane or line.

This first should be self explanatory. From a given point, scribe identical marks on either side. Open up the divers wider and from those two intersections create two more above and below your starting point. Connect all three to find a perpendicular.

Here’s another way(drawing at top of post)Scribe an arc that crosses the line and extends almost to the other side. Leave the dividers on the same setting and starting at point A step off two identical chords. Set your divider point in B & C to locate an intersection above your original centerpoint of your arc. Connect the center of your arc with that intersection. Voila, a perpendicular!

Finally, what if you need to find a perpendicular near the end of a board (or deck, or cliff)? From point A step off five equal spaces. Set your dividers in point A and adjust them to span three spaces out. Use that distance to strike an arc straight up from point A. Reset your dividers to span all five divisions. Keeping that setting, anchor one leg in point four and scribe an intersection with your previous arc. You have just created a 3,4,5 triangle and a perpendicular with your original starting point.

Try “poring”, not “pouring” – the book will last longer.

Hi George,

This is great stuff that we should have learned when we were, supposedly, taught geometry. Why couldn’t they have made it fun by showing practical applications? Right now I’m going to use this last trick when I go to set some posts for a dock on the land alongside our pond.

I had bought your DVDs some time ago but they never played in my machine. I thought about returning them to L-N but gave one more try the other night. After eight minutes the machine began playing the “Secrets of Traditional Design”. It’s fantastic. Toward the end there is a quick overlay of a cabriole leg onto the molding above the doorway- a very powerful way of demonstrating how the design language weaves all through the architectural landscape.

Perhaps I mentioned to you a great film called “Die Stille Vor Bach” by Pere Portabella. It’s an abstract view of how the architecture of Bach’s music informs so many levels of European society, from the running of transportation systems, layout of architecture, to, of course its musical development.

I liked your demonstration of the intervals in music, tying that in with the orders.

Tico,

Glad you were finally able to see the DVD’s. I’ll have to look up the film you mention. More recently, I’ve been thinking alot about another connection between music and design. For some reason we can visualize music in our minds so clearly. Just about everyone can clearly imagine the birthday song or the national anthem. Yet, visualizing a design is quite a leap for many. Why is that? Don’t know if I have all the answers but this traditional simple geometry made up of simple shapes offers a glimpse into something very powerful.

Hi George,

Isn’t that triangle a 3,5,6 ?

Rob,

The short leg nearest the end of the board is 3 parts, the leg extending along the baseline goes from point ’4′ up to that original arc. Hypotenuse is five parts – 3:4:5.

These basic constructions were taught when I went to school, back in the dark ages of the Fifties. I’ve also just come across a small volume of these constructions, and many more complicated, called “Ruler and Compass” by Andrew Sutton. No archaic language, no translations directly from the Greek into seventeenth century English. Apply these to the illustrations in Palladio’s or Chamber’s books and many productive afternoons can be the result.

Thanks much for the lead on Sutton’s book, I’ll definitely try to snag a copy!

Seems that this approach to design was pervasive in the pre-industrial era. I just had a conversation with a violin maker who told me that the traditional makers never used measurements to lay out the form of their instruments. The overall volume of the sound box was 5:8 and it went on from there right down to the position, size and shape of the sound holes. Not to mention the layout of the frets–which really ties in the proportional systems of both the form and the sound of the instrument! I think we are just seeing the tip of the iceberg here George!

Oops! This dunce had anchored the leg in point 5 instead of 4. Thanks George – more of this sort of thing please!

Greg, I’m writing a quick article for the Toolmera blog about an error in the Practical Geometry section of Nicholson’s “Mechanics Companion”. It is a quick correction to another method of using a 30 – 60 – 90 triangle to erect a perpendicular. May I reference this as example of another way to use the same geometry?

Michael,

Be my guest. Actually there are many sets of numbers that will yeild a perpendicular, the 3,4,5 being the most easy and simple to recall.

George

3-4-5, 5-12-13, 1.414, Pythagorus, multiple methods using 30 – 60 – 90, I’ve used them all . . . the method in Nicholson is the most elegant, has the fewest steps, which is why I want people to know the corrected way to use it.