A Budget of Paradoxes, Volume IDe Morgan, Augustus
Philosophy
A Budget of Paradoxes, Volume I
De Morgan, Augustus
Circle-squaring; Perpetual motion; Science -- Miscellanea; Trisection of angle
[562] For there is a well-known series
1 + 1/2^2 + 1/3^2 + ... = [pi]^2/6.
If, therefore, the given series equals 1, we have
2 = 1/6 [pi]^2
or [pi]^2 = 12,
whence [pi] = 2 [root]3.
But c = [pi]d, and twice the diagonal of a cube on the diameter is 2d
[root]3.
[563] There was a second edition in 1821.
[564] London, 1830.
[565] He was a resident of Chatham, and seems to have published no other
works.
[566] Richard Whately (1787-1863) was, as a child, a calculating prodigy
(see note 132, page 86), but lost the power as is usually the case with
well-balanced minds. He was a fellow of Oriel College, Oxford, and in 1825
became principal of St. Alban Hall. He was a friend of Newman, Keble, and
others who were interested in the religious questions of the day. He became
archbishop of Dublin in 1831. He was for a long time known to students
through his _Logic_ (1826) and _Rhetoric_ (1828).
[567] William King, D.C.L. (1663-1712), student at Christ Church, Oxford,
and celebrated as a wit and scholar. His _Dialogues of the Dead_ (1699) is
a satirical attack on Bentley.
[568] Thomas Ebrington (1760-1835) was a fellow of Trinity College, Dublin,
and taught divinity, mathematics, and natural philosophy there. He became
provost of the college in 1811, bishop of Limerick in 1820, and bishop of
Leighlin and Ferns in 1822. His edition of Euclid was reprinted a dozen
times. The _Reply to John Search's Considerations on the Law of Libel_
appeared at Dublin in 1834.
[569] Joseph Blanco White (1775-1841) was the son of an Irishman living in
Spain. He was born at Seville and studied for orders there, being ordained
priest in 1800. He lost his faith in the Roman Catholic Church, and gave up
the ministry, escaping to England at the time of the French invasion. At
London he edited _Espanol_, a patriotic journal extensively circulated in
Spain, and for this service he was pensioned after the expulsion of the
French. He then studied at Oriel College, Oxford, and became intimate with
men like Whately, Newman, and Keble. In 1835 he became a Unitarian. Among
his theological writings is his _Evidences against Catholicism_ (1825). The
"rejoinder" to which De Morgan refers consisted of two letters: _The law of
anti-religious Libel reconsidered_ (Dublin, 1834) and _An Answer to some
Friendly Remarks on "The Law of Anti-Religious Libel Reconsidered"_
(Dublin, 1834).
[570] The work was translated from the French.
[571] J. Hoene Wronski (1778-1853) served, while yet a mere boy, as an
artillery officer in Kosciusko's army (1791-1794). He was imprisoned after
the battle of Maciejowice. He afterwards lived in Germany, and (after 1810)
in Paris. For the bibliography of his works see S. Dickstein's article in
the _Bibliotheca Mathematica_, vol. VI (2), page 48.
[572] Perhaps referring to his _Introduction a la philosophie des
mathematiques_ (1811).
[573] Read "equation of the."
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