Mathematical Instruments and Models
1½" cube, inscribed with the letters a and b in various powers.
This is a cube illustrating the application of geometry to algebra. If it were required to cube the binomial a plus b, a cube may be found whose side is equal to a3 plus b3 plus 3a2b plus 3ab2. Rectangles and cubes illustrating the derivation of algebraic equations from geometric construction were in common use in the nineteenth century.
The source of this specimen is unknown.
The instrument consists of a plate supported by an L-shaped arm and foot. A thumbscrew on the plate causes a pencil below to describe the figure, through a train of four gears, the last of which carries the pencil at the end of an arm. Closed up its dimensions are 4" X 2 ¾"' X 2 ½". Unmarked. Brass construction. Received in 1819.
This was submitted by an anonymous contender for the Magellanic Premium, whose letter is dated November 25, 1819. This letter mentions two instruments, both of which are sketched and described. One uses four gears (the present specimen), the other (apparently lost) two gears and a pair of cranks. The writer speaks of the employment of a constructor, and indicates that the workmanship is defective (as indeed it appears to be). He acknowledges that the elliptograph is common, but says that this is the first of the type, to his knowledge, "except one described in the New Edinburgh Encyclopedia." He continues with a mechanical and mathematical analysis of the instruments.
The elliptograph was a common instrument at this time. In a communication to the Royal Society in 1780 a Mr. Ludlam stated that "the instrument for drawing ovals upon paper or board is so common that a particular description of it is need-