[53] The title is correct except for a colon after Astronomicum. Nicolaus Raimarus Ursus was born in Henstede or Hattstede, in Dithmarschen, and died at Prague in 1599 or 1600. He was a pupil of Tycho Brahe. He also wrote De astronomis hypothesibus (1597) and Arithmetica analytica vulgo Cosa oder Algebra (1601).
[54] Born at Dôle, Franche-Comté, about 1550, died in Holland about 1600. The work to which reference is made is the Quadrature du cercle, ou manière de trouver un quarré égal au cercle donné, which appeared at Delft in 1584. Duchesne had the courage of his convictions, not only on circle-squaring but on religion as well, for he was obliged to leave France because of his conversion to Calvinism. De Morgan's statement that his real name is Van der Eycke is curious, since he was French born. The Dutch may have translated his name when he became professor at Delft, but we might equally well say, that his real name was Quercetanus or à Quercu.
[55] This was the father of Adriaan Metius (1571-1635). He was a mathematician and military engineer, and suggested the ratio 355/113 for π, a ratio afterwards published by his son. The ratio, then new to Europe, had long been known and used in China, having been found by Tsu Ch'ung-chih (428-499 A.D.).
[56] This was Jost Bürgi, or Justus Byrgius, the Swiss mathematician of whom Kepler wrote in 1627: "Apices logistici Justo Byrgio multis annis ante editionem Neperianam viam præiverunt ad hos ipsissimos logarithmos." He constructed a table of antilogarithms (Arithmetische und geometrische Progress-Tabulen), but it was not published until after Napier's work appeared.
[57] Ludolphus Van Ceulen, born at Hildesheim, and died at Leyden in 1610. It was he who first carried the computation of π to 35 decimal places.
[58] Jens Jenssen Dodt, van Flensburg, a Dutch historian, who died in 1847.
[59] I do not know this edition. There was one "Antverpiae apud Petrum Bellerum sub scuto Burgundiae," 4to, in 1591.
[60] Archytas of Tarentum (430-365 B.C.) who wrote on proportions, irrationals, and the duplication of the cube.
The Circle Speaks.