A Budget of Paradoxes, Volume IIDe Morgan, Augustus
Philosophy
A Budget of Paradoxes, Volume II
De Morgan, Augustus
Circle-squaring; Perpetual motion; Science -- Miscellanea; Trisection of angle
[27] The notes on this page were written on the day of the funeral of
Wilbur Wright, June 1, 1912, the man who realized all of these prophecies,
and then died a victim of municipal crime,--of typhoid fever.
[28] John Charles, third Earl Spencer (1782-1845), to whose efforts the
Reform Bill was greatly indebted for its final success.
[29] This was published in London in 1851 instead of 1848.
[30] This appeared in 1846.
[31] This was done in _The Circle Squared_, published at Brighton in 1865.
[32] It first appeared in 1847, under the title, _The Scriptural Calendar
and Chronological Reformer, 1848. Including a review of tracts by Dr.
Wardlaw and others on the Sabbath question. By W. H. Black._ The one above
mentioned, for 1849, was printed in 1848, and was also by Black
(1808-1872). He was pastor of the Seventh Day Baptists and was interested
in archeology and in books. He catalogued the manuscripts of the Ashmolean
Museum at Oxford.
[33] William Upton, a Trinity College man, Dublin. He also wrote _Upton's
Physioglyphics_, London, 1844; _Pars prima. Geometria vindicata;
antiquorumque Problematum, ad hoc tempus desperatorum, Trisectionis Anguli,
Circulique Quadraturae, Solutio, per Eucliden effecta, London_ (printed at
Southampton), 1847; _The Uptonian Trisection_, London, 1866; and _The
Circle Squared_, London, 1872.
[34] For example, if [theta] = 90 deg. we should have 3 cos 30 deg. = 1
+ [root](4 - sin^2 90 deg.), or 3. 1/2 [root]3 = 1 + [root]3, or
1/2 [root]3 = 1.
[35] Nathaniel Wallich (1786-1854) was surgeon at the Danish settlement at
Serampore when the East India Company took over the control in 1807. He
entered the British medical service and was invalided to England in 1828.
His _Plantae Asiaticae Rariores_ (3 vols., London, 1830-1832) was
recognized as a standard. He became vice-president of the Linnean Society,
F. R. S., and fellow of the Royal Asiatic Society.
[36] But if [theta] = 90 deg. this asserts that
cos 30 deg. = (sin 270 deg. . cos 225 deg. + sin^2 90 deg.
. sin 225 deg.) / [root](sin^2
270 deg. . cos^2 225 deg. + sin^{4} 90 deg. + sin 270 deg.
. sin 450 deg. . sin^2 90 deg.),
or that
1/2 [root]3 = (-1 . (-1 /[root]2) + 1 . (-1/[root]2) / [root]1
. 1/2 + 1 - 1 . 1 . 1) = 0 / [root](1/2),
so that De Morgan must have made some error in copying.
[37] John Bonnycastle (died in 1821) was professor of mathematics at
Woolwich. His edition of Bossut's _History of Mathematics_ (1803), and his
works on elementary mathematics were well known.
[38] The bibliographies give Husain Rifki as the translator, a practical
geometry as the work, and 1802 as the date.
[39] See Vol. I, page 309, note 2 {670}.
[40] Probably in _The Improvement of the Mind_ which Isaac Watts
(1674-1748) published in 1741. His _Horae Lyricae_ appeared in 1706, and
the _Hymns_, by which he is still well known, in 1707.
Public-domain text, read in full here on John Shaqi.
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