Problema Austriacum. Plus ultra Quadratura Circuli. Auctore P. Gregorio
a Sancto Vincentio Soc. Jesu., Antwerp, 1647, folio.--Opus Geometricum
posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668,
folio.[227]

The first book has more than 1200 pages, on all kinds of geometry. Gregory
St. Vincent is the greatest of circle-squarers, and his investigations led
him into many truths: he found the property of the area of the
hyperbola[228] which led to Napier's logarithms being called _hyperbolic_.
Montucla says of him, with sly truth, that no one has ever squared the
circle with so much genius, or, excepting his principal object, with so
much success.[229] His reputation, and the many merits of his work, led to
a sharp controversy on his quadrature, which ended in its complete exposure
by Huyghens and others. He had a small school of followers, who defended
him in print.

{118}

RENE DE SLUSE.

Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liege], 1668,
4to.[230]

The Mesolabum is the solution of the problem of finding two mean
proportionals, which Euclid's geometry does not attain. Slusius is a true
geometer, and uses the ellipse, etc.: but he is sometimes ranked with the
trisecters, for which reason I place him here, with this explanation.

The finding of two mean proportionals is the preliminary to the famous old
problem of the duplication of the cube, proposed by Apollo (not Apollonius)
himself. D'Israeli speaks of the "six follies of science,"--the quadrature,
the duplication, the perpetual motion, the philosopher's stone, magic, and
astrology. He might as well have added the trisection, to make the mystic
number seven: but had he done so, he would still have been very lenient;
only seven follies in all science, from mathematics to chemistry! Science
might have said to such a judge--as convicts used to say who got seven
years, expecting it for life, "Thank you, my Lord, and may you sit there
till they are over,"--may the Curiosities of Literature outlive the Follies
of Science!

JAMES GREGORY.

1668. In this year James Gregory, in his _Vera Circuli et Hyperbolae
Quadratura_,[231] held himself to have proved that {119} the _geometrical_
quadrature of the circle is impossible. Few mathematicians read this very
abstruse speculation, and opinion is somewhat divided. The regular
circle-squarers attempt the _arithmetical_ quadrature, which has long been
proved to be im