«i 
-- 
ee 
EPICYCLOID. 
- EPICYCLOID, in Geometry, is pects ireeat 
pe. foe int in the plane of a moveable ci 
1er on the inside, or the outside of the circum- 
ference of a fixed circle. If the circles be both in the 
same plane, the curve generated will be the plane epi- 
If again the moveable and fixed circles be in different 
planes, and the former be the base of a right cone, that: 
rolls on the surface of another right cone, the base of 
which is the latter, so that the vertices of the cones are 
at the same point ; then, in this case, the curve 
179 
death of Galileo, which happened-inr 1642, his disciples Epicycloid.. 
Torricelli and Viviani, were more successful ; the for- 
mer found the area, and the latter the method of draw 
ing tangents to the curve. The claim of Torricelli to- 
= porte of his discovery Maric omy “sin te 3 
t the charge of plagiarism, whi ght against 
the Italian reaabotadticien, has not been believed by his 
countryman Montucla, who has discussed the contro- 
versy in the second volume of his History of Mathe- 
ties, second edition. . 
The cycloid, the source of so much contention, and 
on that account compared to the golden apple thrown 
by Discord among the gods, was again brought into. 
notice by Pascal. This philosopher, not: less celebra~ 
ted for his piety and zeal in defence of the Christian. 
eligion, than his mathematical invention, took the cy- 
cloid as the subject of his meditation in those sleepless 
nights which he passed, in’ consequence of bad health ; 
and he soon extended his discoveries beyond what was 
then known. He was not of a disposition to boast of 
his discoveries in ; but some of his pious 
friends su that it would be useful to have it 
known, the man who had defended religion and 
Christiani inst infidelity, was perhaps the most. 
profound thinker, and the greatest eter in Eu-. 
his problems, 
of the first 
the celebrated H s; and Sir Christoph 
who discovered che Seebcaton of the curve. Pascal, 
published his own solutions in the beginning of the. 
year 1659, in a work entitled Letters from A. Detton- 
ville to M. de Careavi: In the same- year, Dr Wallis 
published a work on the cycloid, and other curves, in 
which he resolved some of Pascal's problems by his 
Arithmetic of Refiee ; and, in the following, La- 
louére also published a treatise on the cycloid ; and an- 
other work about the same time from the pen 
of P. Fabri, the jesuit. 
The cycloid is remarkable, as well on account of its. 
mechanical. as its ical properties ; and Mr Huy- 
s discovered some of the most interesting of both. 
inds. To.the latter class bel the property, which. 
we shall demonstrate in this sri, by which he shew- 
ed how a pendulum inay. be made to. vibrate in an arc: 
of a oycloid ; and to the former, the very beautiful pro- 
perty, that all. vibrations of a pendulum in ares of a, 
cycloid, are performed in. equal times. See Mecua-~ 
NICS. 
The very curious problem, eee John Ber 
noulli, 2 Ap * to find the path hich’ body may; 
roll from one given point to er, in the shortest: 
time possible, the points being supposed neither in the- 
