a_, and it is not remarkable that his brilliancy brought
him a wide circle of friends on the continent and the offer of a pension
from Louis XIV. He became professor of mathematics at St Andrews and later
at Edinburgh, and invented the first successful reflecting telescope. The
distinctive feature of his _Vera quadratura_ is his use of an infinite
converging series, a plan that Archimedes used with the parabola.

[232] Jean de Beaulieu wrote several works on mathematics, including _La
lumiere de l'arithmetique_ (n.d.), _La lumiere des mathematiques_ (1673),
_Nouvelle invention d'arithmetique_ (1677), and some mathematical tables.

[233] A just estimate. There were several works published by Gerard
Desargues (1593-1661), of which the greatest was the _Brouillon Proiect_
(Paris, 1639). There is an excellent edition of the _Oeuvres de Desargues_
by M. Poudra, Paris, 1864.

[234] "A certain M. de Beaugrand, a mathematician, very badly treated by
Descartes, and, as it appears, rightly so."

[235] This is a very old approximation for [pi]. One of the latest
pretended geometric proofs resulting in this value appeared in New York in
1910, entitled _Quadrimetry_ (privately printed).

[236] "Copernicus, a German, made himself no less illustrious by his
learned writings; and we might say of him that he stood alone and unique in
the strength of his problems, if his excessive presumption had not led him
to set forth in this science a proposition so absurd that it is contrary to
faith and reason, namely that the circumference of a circle is fixed and
immovable while the center is movable: on which geometrical principle he
has declared in his astrological treatise that the sun is fixed and the
earth is in motion."

[237] So in the original.

[238] Franciscus Maurolycus (1494-1575) was really the best mathematician
produced by Sicily for a long period. He made Latin translations of
Theodosius, Menelaus, Euclid, Apollonius, and Archimedes, and wrote on
cosmography and other mathematical subjects.

[239] "Nicolaus Copernicus is also tolerated who asserted that the sun is
fixed and that the earth whirls about it; and he rather deserves a whip or
a lash than a reproof."

[240] "Algebra is the curious science of scholars, and particularly for a
general of an army, or a captain, in order quickly to draw up an army in
battle array and to number the musketeers and pikemen who compose it,
without the figures of arithmetic. This science