650
Molesworth’s pocket-book
Cycloidal Curve—continued.
The area of AF P K B A is equal to that of the generating
circle. The tangent FG is parallel to the chord DE. The
urc 1) F is double the chord D E. The circular arc D E = F E
parallel to the base A B.
If the cycloid be turned upside down a body falls through
any are L K in the same time independently of the length of
the arc ; this time is to that of a body falling perpendicularly
from N to K as 3-14159 to 2 ; and, if a pendulum be made to
oscillate in the arc of a cycloid its vibrations will be isochro-
nous. The evolute of a cycloid is another equal cycloid. The
cycloid is the curve of quickest descent between any two
^°The cycloid is formed by a tracing point attached to a
generating circle which rolls on u straight line. It the tfftciug
point be beyond the circumference of the generating circle, a
curtate cycloid will be produced terminating in nodes; if the
tracing point be on the circumference a common cycloid will
be formed terminating in cusps, if within the circumference a
prolate cycloid will be formed.
CUKTATB CYCLOID.