fulfilled.  Another copy of the book Kepler sent to Reymers the Imperial astronomer with a most fulsome letter, which Tycho, who asserted that Reymers had simply plagiarised his work, very strongly resented, thus drawing from Kepler a long letter of apology.  About the same time Kepler had married a lady already twice widowed, and become involved in difficulties with her relatives on financial grounds, and with the Styrian authorities in connection with the religious disputes then coming to a head.  On account of these latter he thought it expedient, the year after his marriage, to withdraw to Hungary, from whence he sent short treatises to Tuebingen, “On the magnet” (following the ideas of Gilbert of Colchester), “On the cause of the obliquity of the ecliptic” and “On the Divine wisdom as shown in the Creation”.  His next important step makes it desirable to devote a chapter to a short notice of Tycho Brahe.

[Footnote 2:  Since the sum of the plane angles at a corner of a regular solid must be less than four right angles, it is easily seen that few regular solids are possible.  Hexagonal faces are clearly impossible, or any polygonal faces with more than five sides.  The possible forms are the dodecahedron with twelve pentagonal faces, three meeting at each corner; the cube, six square faces, three meeting at each corner; and three figures with triangular faces, the tetrahedron of four faces, three meeting at each corner; the octahedron of eight faces, four meeting at each corner; and the icosahedron of twenty faces, five meeting at each corner.]

CHAPTER III.

Tycho brahe.

The age following that of Copernicus produced three outstanding figures associated with the science of astronomy, then reaching the close of what Professor Forbes so aptly styles the geometrical period.  These three Sir David Brewster has termed “Martyrs of Science”; Galileo, the great Italian philosopher, has his own place among the “Pioneers of Science”; and invaluable though Tycho Brahe’s work was, the latter can hardly be claimed as a pioneer in the same sense as the other two.  Nevertheless, Kepler, the third member of the trio, could not have made his most valuable discoveries without Tycho’s observations.

Of noble family, born a twin on 14th December, 1546, at Knudstrup in Scania (the southernmost part of Sweden, then forming part of the kingdom of Denmark), Tycho was kidnapped a year later by a childless uncle.  This uncle brought him up as his own son, provided him at the age of seven with a tutor, and sent him in 1559 to the University of Copenhagen, to study for a political career by taking courses in rhetoric and philosophy.  On 21st August, 1560, however, a solar eclipse took place, total in Portugal, and therefore of small proportions in Denmark, and Tycho’s keen interest was awakened, not so much by the phenomenon, as by the fact that it had occurred according to prediction.