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In the early sixteenth century, Portuguese navigators on voyages outside the tropics ran into an unexpected problem in navigating with the plane chart since the latter took no account of the convergence of the meridians. Voyages between Brazil and the Cape of Good Hope were accomplished much faster than the chart led them to forsee. To overcome this problem, were Portuguese pilots of the first half of the sixteenth century using globes to set their courses with on great circle courses? The general opinion is that they were not. Yet the mathematician Pedro Nunes (1502–78) describes in a short treatise entitled Tratado que ho Doutor Pedro Nunez fez sobre certas duvidas na navigação (published in 1537, but probably written in 1534) how the navigator Martim Afonso de Sousa, on his return from the east coast of Brazil in 1530–2, had asked him to solve several problems of navigation encountered on the voyage.

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Pedro Nunes' Discovery of the Loxodromic Curve (1537). How Portuguese Sailors in the Early Sixteenth Century, Navigating with Globes, had Failed to Solve the Difficulties Encountered with the Plane Chart

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Pedro Nunes' Discovery of the Loxodromic Curve (1537). How Portuguese Sailors in the Early Sixteenth Century, Navigating with Globes, had Failed to Solve the Difficulties Encountered with the Plane Chart