tices of Monge and Hachette appear in
_Encyclopaedia Britannica_, ed. 11. See also _L'Ecole Polytechnique,
Livre du Centenaire_, Paris, 1895, vol. 1, p. 11ff.]

Gaspard Monge (1746-1818), who while a draftsman at Mezieres originated
the methods of descriptive geometry, came to the Ecole Polytechnique as
professor of mathematics upon its founding in 1794, the second year of
the French Republic. According to Jean Nicolas Pierre Hachette
(1769-1834), who was junior to Monge in the department of descriptive
geometry, Monge planned to give a two-months' course devoted to the
elements of machines. Having barely gotten his department under way,
however, Monge became involved in Napoleon's ambitious scientific
mission to Egypt and, taking leave of his family and his students,
embarked for the distant shores.

"Being left in charge," wrote Hachette, "I prepared the course of which
Monge had given only the first idea, and I pursued the study of machines
in order to analyze and classify them, and to relate geometrical and
mechanical principles to their construction." Changes of curriculum
delayed introduction of the course until 1806, and not until 1811 was
his textbook ready, but the outline of his ideas was presented to his
classes in chart form (fig. 28). This chart was the first of the widely
popular synoptical tables of mechanical movements.[62]

[Footnote 62: Jean N. P. Hachette, _Traite elementaire des machines_,
Paris, 1811, p. v.]

[Illustration: Figure 28.--Hachette's synoptic chart of elementary
mechanisms, 1808. This was the first of many charts of mechanical
movements that enjoyed wide popularity for over 100 years.

From Jean N. P. Hachette, _Traite Elementaire des Machines_ (Paris,
1811, pl. 1).]

Hachette classified all mechanisms by considering the conversion of one
motion into another. His elementary motions were continuous circular,
alternating circular, continuous rectilinear, and alternating
rectilinear. Combining one motion with another--for example, a treadle
and crank converted alternating circular to continuous circular
motion--he devised a system that supplied a frame of reference for the
study of mechanisms. In the U.S. Military Academy at West Point,
Hachette's treatise, in the original French, was used as a textbook in
1824, and perhaps earlier.[63]

[Footnote 63: This work was among the books sent back by Sylvanus Thayer
when he visited France in 1816 to observe the education of the French
ar