The City of Mantua, located in the northern Italian plain (see map), had for centuries been a center of cloth manufacture. The wealth of the city made possible a brilliant court culture under the Gonzaga. This family had ruled the city since 1329, initially as "Captains General of the People," and since 1530 as Dukes. Because of the city's wealth and the Gonzaga support of arts and letters, the Mantua court became one of the most brilliant in Italy.

At the turn of the seventeenth century, Mantua was in economic decline. Although Vincenzo Gonzaga was still one of the great patrons in Italy, his spendthrift habits were accelerating the decline of the city, and after his death in 1612 Mantua ceased being an important cultural center.

Vincenzo Gonzaga had been tutored in the mathematical subjects by Giuseppe Moletti, Galileo's predecessor in the chair of mathematics at the University of Padua. During the winter of 1603-1604, Galileo visited the Mantuan court in an effort to obtain a position there. He was offered a salary of 300 ducats per year plus living expenses for himself and a servant. At this time Galileo's salary at the University of Padua was 320 ducats, and he had further income from his boarding students. He therefore requested instead a salary of 500 ducats with an expense account for himself and two servants. No terms could be worked out, and Galileo retained his post in Padua. But for one of his proportional compasses (no doubt an especially ornate one) and his instruction manual, the Duke did give Galileo a gold chain with a medal, and two silver dishes. It was the custom that the medal could not be sold but that the chain and the cups could. In his account books for 1604 Galileo put down the chain for 900 lire and the cups for 440 lire.