t not be divisible by a prime number of the form 4n -
1," except for the omission of the words "when divided ... measures
it."

# AUTHORITIES.--The first to publish anything on Diophantus in Europe
was Rafael Bombelli, who embodied in his Algebra (1572) all the
problems of Books I.-IV. and some of Book V. interspersing them with
his own problems. Next Xylander (Wilhelm Holzmann) published a Latin
translation (Basel, 1575), an altogether meritorious work, especially
having regard to the difficulties he had with the text of his MS. The
Greek text was first edited by C. G. Bachet (_Diophanti Alexandrini
arithmeticorum libri sex, et de numeris multangulis liber unus, nunc
primum graece et latine editi atque absolutissimis commentariis
illustrati_ ... Lutetiae Parisiorum ... MDCXXI.). A reprint of 1670 is
only valuable because it contains P. de Fermat's notes; as far as the
Greek text is concerned it is much inferior to the other. There are
two German translations, one by Otto Schulz (1822) and the other by G.
Wertheim (Leipzig, 1890), and an English edition in modern notation
(T. L. Heath, _Diophantos of Alexandria: A Study in the History of
Greek Algebra_ (Cambridge, 1885)). The Greek text has now been
definitively edited (with Latin translation, Scholia, &c.) by P.
Tannery (Teubner, vol. i., 1893; vol. ii., 1895). General accounts of
Diophantus' work are to be found in H. Hankel and M. Cantor's
histories of mathematics, and more elaborate analyses are those of
Nesselmann (_Die Algebra der Griechen_, Berlin, 1842) and G. Loria
(_Le Scienze esatte nell' antica Grecia_, libro v., Modena, 1902, pp.
95-158). (T. L. H.)

DIOPSIDE, an important member of the pyroxene group of rock-forming
minerals. It is a calcium-magnesium metasilicate, CaMg(SiO3)2, and
crystallizes in the monoclinic system. Usually some iron is present
replacing magnesium, and when this predominates there is a passage to
hedenbergite, CaFe(SiO3)2, a closely allied variety of monoclinic
pyroxene. These are distinguished from augite by containing little or no
aluminium. Diopside is colourless, white, pale green to dark green or
nearly black in colour, the depth of the colour depending on the amount
of iron present. The specific gravity and optical constants also vary
with the chemical composition; the sp. gr. of diopside is 3.2,
increasing to 3.6 in hedenbergite, and the angle of optical extinction
in