time, as for long afterwards, was dependent wholly on
Euclid, of whose work a Latin translation was first published at
Venice. [Sidenote: 1505] Copernicus with his pupil George Joachim,
called Rheticus, and Francis Vieta, made some progress in trigonometry.
Copernicus gave the first simple demonstration of the fundamental
formula of spherical trigonometry; Rheticus made tables of sines,
tangents and secants {611} of arcs. Vieta discovered the formula for
deriving the sine of a multiple angle.

[Sidenote: Cardan, 1501-76]

As one turns the pages of the numerous works of Jerome Cardan one is
astonished to find the number of subjects on which he wrote, including,
in mathematics, choice and chance, arithmetic, algebra, the calendar,
negative quantities, and the theory of numbers. In the last named
branch it was another Italian, Maurolycus, who recognized the general
character of mathematics as "symbolic logic." He is indeed credited
with understanding the most general principle on which depends all
mathematical deduction.[1] Some of the most remarkable anticipations
of modern science were made by Cardan. He believed that inorganic
matter was animated, and that all nature was a progressive evolution.
Thus his statement that all animals were originally worms implies the
indefinite variability of species, just as his remark that inferior
metals were unsuccessful attempts of nature to produce gold, might seem
to foreshadow the idea of the transmutation of metals under the
influence of radioactivity. It must be remembered that such guesses
had no claim to be scientific demonstrations.

The encyclopaedic character of knowledge was then, perhaps, one of its
most striking characteristics. Bacon was not the first man of his
century to take all knowledge for his province. In learning and
breadth of view few men have ever exceeded Conrad Gesner, [Sidenote:
Gesner] called by Cuvier "the German Pliny." His _History of Animals_
(published in many volumes 1551-87) was the basis of zooelogy until the
time of Darwin. [Sidenote: Zooelogy] He {612} drew largely on previous
writers, Aristotle and Albertus Magnus, but he also took pains to see
for himself as much as possible. The excellent illustrations for his
book, partly drawn from previous works but mostly new, added greatly to
its value. His classification, though superior to any that had
preceded it, was in some respects astonishing, as when he put the
hippopotamus among