A Budget of Paradoxes, Volume I

by Augustus De Morgan

[560] Mary Fairfax (1780-1872) married as her second husband Dr. William Somerville. In 1826 she presented to the Royal Society a paper on The Magnetic Properties of the Violet Rays of the Solar Spectrum, which attracted much attention. It was for her Mechanism of the Heavens (1831), a popular translation of Laplace's Mécanique Céleste, that she was pensioned.

[561] Dominique François Jean Arago (1786-1853) the celebrated French astronomer and physicist.

[562] For there is a well-known series

1 + 1/2² + 1/3² + ... = π²/6.

If, therefore, the given series equals 1, we have

2 = 1/6 π²

or π² = 12,

whence π = 2 √3.

But c = πd, and twice the diagonal of a cube on the diameter is 2d √3.

[563] There was a second edition in 1821.