RENE DE SLUSE.
Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liège], 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 Hyperbolæ Quadratura,[[231]] held himself to have proved that
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 impossible. Very few attempt the geometrical quadrature. One of the last is Malacarne, an Italian, who published his Solution Géométrique, at Paris, in 1825. His method would make the circumference less than three times the diameter.
BEAULIEU'S QUADRATURE.
La Géométrie Françoise, ou la Pratique aisée.... La quadracture du cercle. Par le Sieur de Beaulieu, Ingénieur, Géographe du Roi ... Paris, 1676, 8vo. [not Pontault de Beaulieu, the celebrated topographer; he died in 1674].[[232]]