Why did Brazilian colonists expand beyond the boundary set by the Treaty of Tordesillas?

Brazilian colonists expanded beyond the boundary set by the Treaty of Tordesillas primarily through the activities of three groups: missionaries, cattlemen, and bandeirantes.1

• Bandeirantes: These explorers and slave hunters from São Paulo organized major expeditions into the interior to capture and enslave Indigenous people and to search for gold and precious stones. Their efforts were often violent and cruel, but they were instrumental in establishing Brazil's claims to the South American interior.12
• Cattlemen: In the Northeast, cattlemen seeking new pastures pushed inland from sugar-producing zones, expanding into regions such as Piauí, Maranhão, and Goiás.1
• Missionaries: Jesuit missionaries extended their reach along the Amazon River and into the South and Southeast, establishing missions that often became targets for bandeirante raids.21

These westward movements laid the foundation for Brazil's claims to vast areas of the interior, which were later recognized by treaties with Spain in the 18th century.34