Leonardo's contract for the work with the ruler of Florence, the Gonfaloniere Signoria, is co-signed by Machiavelli in his capacity as a government official. It was the Gonfaloniere Signoria who asked Leonardo to conduct a feasibility study of the river project. Leonardo was well qualified for the job, having earlier drawn elaborate plans to divert the Arno in another direction for peaceful purposes. Those plans, however, were never carried out.

The records of Florence show that in order to make his later assessment, Leonardo traveled to the outskirts of Pisa in ''six horse coaches.'' There, after ''many discussions and doubts,'' he concluded that the project was ''very appropriate.''

Machiavelli was second chancellor and secretary of the Committee of Ten, the top-ranking Florentine military council. Leonardo, according to Florentine records, reported his conclusion ''in person,'' and Machiavelli, as secretary of the military council, would have had to be present to hear it, Professor Masters writes.

It is well known that Machiavelli then became deeply involved in the Arno diversion, writing 93 letters and directives on such matters as the excavation of the new river bed, the construction of weirs and the repair of a captured fort in the area.

It would not be until after Florence had fallen to the Medicis and Machiavelli was tortured as a conspirator that he would write his major works, which included ''The Prince,'' ''Discourses on Titus Livy'' and his play ''Mandragola.''

On Aug. 29, 1503, a force of 2,000 Florentine laborers started digging a new course for the Arno. One thousand soldiers were assigned to protect them from attack by the Pisans. But after months of excavation, it turned out that the new channel was too shallow. In a test, the river gushed into the new bed but then backed up, demolished a dam and caused flooding that disrupted farming on which the Florentines depended. Disgusted with the project, the Gonfaloniere Signoria canceled it.

Nevertheless, lessons were learned, Professor Masters says.

In his view, the Arno project -- elliptically referred to in ''The Prince'' as the ''dikes and dams'' that control ''the river of fortune'' -- inspired Machiavelli's intellectual synthesis, which today defines modern society.