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.