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Brachistochrone Part III
Brachistochrone Part IV

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18th Century Model of the Brachistochrone

Brachistochrone Part V
 A working model demonstrating the difference in times.

Bernoulli's illustration

  Bernoulli's Illustration

Museum model of brach

The Spighi Model
All readers of this material will join the National Curve 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 Bernoulli.

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 "brachistochronus"
model 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 attractive force varies inversely with the square of the distance.

The Istituto e Museo di Storia della Scienza is one of the world's greatest collections related to science.   For more information please see  Institute and Museum of the History of Science - 18th Century Experimental Physics Model built by Francesco Spighi

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Brachistochrone Part  II
Brachistochrone Part  III
Brachistochrone Part IV