Every now and then comes a book that squeezes a lot of informative material into a
highly readable and fun package. Jim Tolpin and George Walker's latest effort, From Truth to Tools, is just such a book.
Sure, it's loaded with the geometric principles that underlie many of the tools we use in
carpentry and cabinetmaking. It offers up a bit of history on the ancient uses of these
truths, the basic geometric principles, to accomplish great works without modern
equipment. And it schools us gently in the roots of our terminology that lie in their
Greek and Latin origins. Sound boring? Not at all. This is a fun read that's easy on the
mind and informative at the same time.
Everything geometric begins with a single point, without which nothing else is possible.
The awl is the mechanical manifestation of the point. Attach two awls and you end up
with dividers and can now mark off distances. From these, standard units of measure
were developed—cubits in ancient Egypt defined by the length of the forearm of
whomever happened to be Pharaoh at the time, the foot in European application and
now the meter. Story sticks, folding rules and tape measures are the linear
measurement tools deriving from this truth.
Add a pencil to dividers and create a compass. Now you can draw circles. On a longer
stick, the compass becomes a trammel beam. As Tolpin and Walker explain, circles are
the foundation for much valuable geometry and many of the remaining principles are
based on work with circles. Draw two circles having their center points on the rims of
each other and you've created a condition of symmetry. The line connecting the
centers of these circles equals their radii and leads to the concept of the line segment.
In practical terms, this shows up as a string line and, better, a chalk line. Draw a line
through the center of symmetrical circles and you've created a condition of bilateral
symmetry, the truth underlying a perfect straightedge.
Then there are marking tools: the marking awl, birdcage or brad awl, and long-shafted
scribing awl. Other line-creating tools are markers and knives, and Tolpin and Walker
discuss when and how best to use them in woodworking.
When you connect the center points of symmetrical circles with their intersection you
form a triangle. This is the foundation of surfaces called planes and to the handplane,
which is essentially a rectangle with a bit of iron set in a triangular position. Chisels and
saw teeth employ the same triangular shape.
Draw lines through the origins of the symmetrical circles that connect with the
intersections of their rims and you've created a set of parallel lines. These are the truth
that underlies yet more tools. Winding sticks are one example, as are marking gauges
and table saw rip fences. A taper gauge lays out lines parallel to the edge of a tapered
board. Boat builders use another variant called a diminishing stick. Deriving from the
truth of parallelism are yet other tools: the miter block, bevel gauge and the transfer
gauge used to determine where to cut baseboard for a perfect fit, among others.
Returning to the circle, Tolpin and Walker show how a square is defined by constructing
triangles inside a circle encompassing a pair of symmetrical circles. This defines right
angles that lead to the square and try square, framing square, pinch sticks and the
resultant angle square developed by Peter Galbert to lay out the rake and splay of chair
Add a bit of lead to a string and you have a plumb line, the basis for yet other tools such
as the mason's level and center finder.
Tolpin and Walker return to the sector, discussed in their earlier books, a proportional
calculator and forerunner to the slide rule used until the end of the 18th century to
measure whole number relationships. Proportional dividers, used to scale up or down
drawings, derive from the same principle as sectors.
Angles can be set using a scale of chords or a protractor, and they describe how to
Not all tools are for small-scale use. In laying out large structures, such as bridges and,
yes, pyramids, various tools have been used in the field. The triplet uses a 3-4-5
relationship in the legs of a triangle as the foundation for other tools—the carpenter's
ten-foot pole and the thirteen-knot cord that are used to set right angles on large scale
projects. The groma and merchet used plumb lines and line-of-sight to establish right
angles over a distance, such as across a river.
The chorobate was a table used by the Romans that incorporated sight lines and a
water trough for measuring levels. This ancient tool is succeeded by today's spirit level.
They explain how geometry is also used by loggers, using a felling gauge that is
essentially a quadrant, to judge where a tree's top will land when the tree is felled.
The final section explains how Eratosthanes calculated the earth's circumference, or
geometron, 2300 years ago by employing several of the truths laid out in the book.
An appendix includes references to downloadable templates for a scale of chords,
sector, and Peter Galbert's resultant angle square, and to a resource for further
exploration of intuitive math.
This book is charmingly illustrated throughout and comes in a hardbound edition with
full color cover. You don't have to be a mathematician or a history scholar to fully
appreciate the book. It's accessibly written and laid out in logical, easy-to- digest bites.
Any woodworker with an interest in understanding the geometric underpinnings of
carpentry and cabinetmaking will both appreciate and enjoy it.
Find out more and purchase From Truth to Tools
J. Norman Reid is a woodworker, writer, and woodworking instructor living in the Blue Ridge Mountains with his wife, a woodshop full of power and hand tools and four cats who think they are cabinetmaker's assistants. He is the author of Choosing and Using Handplanes.
He can be reached by email at email@example.com.
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