Re: [HM] POSTINGS OF MATH-HIST INTEREST IN GEOMETRY-* ML/NG
Ken Pledger (Ken.Pledger@vuw.ac.nz)
Wed, 17 Nov 1999 11:23:21 +1200
At 8.00 am +1200 17-11-99, Antreas P. Hatzipolakis wrote:
>
> Subject: What is the name of this gadget?
> From: Alexander Bogomolny <alexb@cut-the-knot.com>
> To: geometry-puzzles@forum.swarthmore.edu
> Date: 16 Nov 1999 11:14:47 -0500
>
> Can anybody please help me answer the question below:
>
>> The "analog gadget" you describe for drawing circles or ellipses is
>> often made as a folk toy with the axis points on wood blocks sliding
>> in a pair of grooves at right angles in a larger block. I have two of
>> these, one in painted wood with the grooves formed by gluing blocks
>> together and the other in walnut with the grooves cut in a solid block.
>>
>> The painted one has the words "NING Y NING" painted on it. What I am
>> curious about is - what is the name of this device as a folk/craft toy?
>>
>> I have one of David Wells' books that refers to it as a "trammel" and
>> says such devices were made commercially for drawing ellipses, but gives
>> no sources. The diagram in the book shows that it is in fact the same
>> device. But trammel is a vague general word that applies to several
>> gizmos - what was the toy called by its makers? Wells also refers to an
>> "ellipsograph", but doesn't say if it's the same thing.
Robert C. Yates, "Curves and their Properties," 1947, refers to it
several times as the "Trammel of Archimedes," but gives no reference to
Archimedes' works.
The underlying theorem is mentioned in Proclus's commentary on
Euclid I, Morrow's translation p.86 (Friedlein p.106):
"Nor is it true that a circular line comes about by mixture if one imagines
a straight line moving in a right angle and describing a circle with its
middle point; for when a straight line is moving thus, its extremities,
moving nonuniformly, describe straight lines, whereas the middle point,
moving nonuniformly, describes a circle, and the other points ellipses."
Here, Morrow has a footnote:
"Presumably this illustration is taken from Geminus, who may have provided
the demonstration for the interesting theorem employed. For this
demonstration see ver Eecke, 96, note 43."
Can anyone shed light on all this?
Ken Pledger.