There were various interpretations of the Treaty line, for instance in 1537 Pedro Nunes' maps claimed everything East of Paraguay River, and as late as 1688, maps were issued with a very liberal interpretation of the line. In 1535 when it was rumoured that King João III to the Rio de la Plata, the Spanish Ambassador, Luis Sarmiento de Mendoza informed King Carlos V that the Portuguese were claiming the region and that was the reason for the establishment of Buenos Aires. The Portuguese king protested this, claiming that the region belonged to Portugal.
Once the silver mines were discovered in Upper Peru in 1546, the temptation for settlers from Southern Brazil to engage in illegal trade in the Rio de la Plata became great. Portugal began to claim the rights to lands based on Uti possidetis, by settlement and conquest. This was finally agreed to in the Treaty of Madrid in 1750.
The map below is from 1574.
Once the silver mines were discovered in Upper Peru in 1546, the temptation for settlers from Southern Brazil to engage in illegal trade in the Rio de la Plata became great. Portugal began to claim the rights to lands based on Uti possidetis, by settlement and conquest. This was finally agreed to in the Treaty of Madrid in 1750.
The map below is from 1574.