The Spighi Model of this material will join the National Bank -
A MATH Archive in thanking the Istituto e Museo di Storia della
Scienza, in Florence, Italy, for permitting us to enjoy this
model of the brachistochrone dating to the last half of the 18th
century. On November 29, 1602, Galileo, a resident of Florence,
demonstrated the observable effects that a body takes less time
to fall along an arc of a circumference, than to fall along the
"line" of the corresponding chord. The mathematical proof that
the faster path was the arc of a cycloid was provided later
(1697) by The model had to be larger than one might expect (~
2.6 yards wide) in order to vividly demonstrate the difference
in times of the two simultaneously falling balls. Interestingly,
this shares a room in the Museo with another model of Galileo's
investigations into timing a falling body rolling down an
inclined plane. Clearly, the experimental genius of Galileo was
invaluable to Newton's derivation of the inverse-squares law,
i.e., the attract