mselves.

How much was accomplished in applied science during the Middle Ages,
that is, in those departments of science {330} which are usually
supposed to have been least cultivated, since educators are prone to
ridicule the over-emphasis of speculation in education and the
constant preoccupation of mind of the scholars of these generations
with merely theoretic questions, may be appreciated from any history
of the arts and architecture during the thirteenth, fourteenth, and
fifteenth centuries. Some of the most difficult problems in mechanics
as applied to the structural work of cathedrals, palaces, castles,
fortresses, and bridges, were solved with a success that was only
equaled by the audacity with which they were attempted. Men hesitated
at nothing. There is no problem of mechanical engineering as applied
to structural work which these men did not find an answer for in their
wonderful buildings. This has been very well brought out by Prince
Kropotkin in certain chapters of his book, Mutual Aid a Factor of
Evolution, [Footnote 41] in which he treats of mutual aid in the
medieval cities. He says:

[Footnote 41: New York, McClure, Philips & Co., 1902.]

"At the beginning of the eleventh century the towns of Europe were
small clusters of miserable huts, adorned with but low clumsy
churches, the builders of which hardly knew how to make an arch; the
arts, mostly consisting of some weaving and forging, were in their
infancy; learning was found in but a few monasteries. Three hundred
and fifty years later, the very face of Europe had been changed. The
land was dotted with rich cities, surrounded by immense thick walls
which were embellished by towers and gates, each of them a work of
art itself. The cathedrals, conceived in a grand style and profusely
decorated, lifted their bell-towers to the skies, displaying a
purity of form and a boldness of imagination which we now vainly
strive to attain. The {331} crafts and arts had risen to a degree of
perfection which we can hardly boast of having superseded in many
directions, if the inventive skill of the worker and the superior
finish of his work be appreciated higher than rapidity of
fabrication. The navies of the free cities furrowed in all
directions the Northern Seas and the Southern Mediterranean; one
effort more and they would cross the oceans. Over large tracts of
land, well-being had taken the place of misery; learning had gro