I know the radius of the earth was measured in Egypt during the Ancient Greece period, but how well known was this fact during medieval times? Was this a well known fact, or was it an ancient discovery that had been mostly forgotten?
Edit: to further explain, I started thinking of this because the treaty of Tordesillas does not take into account the fact that the earth is spherical. As far as I know, the treaty of Zaragoza, signed in 1529, was the first official document to state that the earth is spherical. This treaty was signed a few years after Magellan's circumnavigation expedition.
Short Answer: Yep.
Long Answer: Right Here!
Here's some documentary proof too:
Thomas Aquinas' Summa Theologica written ~1265:
"Further, different sciences are different habits. But the same scientific truth belongs to different sciences: thus both the physicist and the astronomer prove the earth to be round, as stated in Phys. ii, text. 17. Therefore habits are not distinguished by their objects."
http://www.newadvent.org/summa/2054.htm#2
Aquinas, Thomas. "Article 2 Objection 2." Summa Theologica. Vol. 54. 1915. Print.
Since the questions on Columbus are coming up often, I cite a previous post:
Even before Columbus had set off on his expedition, it was already generally accepted by scholars in Spain and Portugal that his estimate of the diameter of the earth was off, meaning that the earth was much larger than he claimed it to be.
Columbus was not a scholar, and he selectively read books that were either wrong or misinterpreted. The most important one was the work of Pierre d'Ailly, a French scholar and cartographer, whom Columbus misunderstood to have given an estimate of circumference of the earth to be around 30,000 km whereas in reality it is around 40,000 km. Further, he believed the land mass of Eurasia to be shorter than one accepted by most scholar, namely the old estimate of Ptolemy. Combining the two, he though that China were much closer westward than it really was (and still is!).
This was one reason that John II of Portugal rejected Columbus' proposal in 1485. However, Columbus came to the court of Isabella and Ferdinand in 1489 at the best possible time: they were just finishing off the Reconquesta and they were feeling threatened by progress made by Portuguese navigators. It wasn't long ago that they were in conflict with the Portuguese over the Castilian succession crises. So they decided to retain Columbus on their payroll, even if it took until 1492 for the famous expedition to launch.
When Columbus made landfall in Hispaniola, he claimed that it was not only on the way to China, but that it could be reached by ocean from there and that there was land mass nearby that was attached to China. If you look at a map such as one made in 1492 by Martin Behaim, you see that he expected to be able to sail westwards from Spain and reach China, and later on Columbus claimed that Hispaniola was merely a land mass "slightly" east of China.
This is why Columbus' further expeditions went farther southwards. The third voyage was to look for such an ocean route, instead they reached Trinidad, concluded that it was near a large land mass and then returned to Hispaniola. The fourth voyage searched for a passage through today's central America, similarly failed.
So while Columbus could continue in his navigational delusion until the last voyage, the Spaniards were more cognizant that they may in fact have discovered a new land mass not attached to China.
The first passage to the Pacific Ocean, by land was by de Balboa in 1513. They crossed Panama successfully and reported their findings back in Spain. This was the point at which arguments that the Americas were attached to China became moot and lose all credibility.
Source: Columbus by Fernandez-Armesto.
And on the Treaty of Tordesillas:
The Treaty of Tordesillas was viewed as a very bad deal for the Portuguese. Up to that point, Portugal was by far the bigger investor in navigation and exploration.
During the Castilian War of Succession, Alfonso V of Portugal invaded Castile in support of his wife Juana Trastamara's claim. The rival claimant was Isabella, newly married to Ferdinand of Aragon. The Treaty of Alcacovas, which settled the dispute, recognized Isabella as Queen of Castile but all territories and shores under dispute were given to Portugal except for the Canary Islands. Further, Portugal was given exclusive rights to navigate and conquer all territories south of those islands. This included Guinea, Cape Verde, etc. In short, Castile won in the Iberian continent, but Portugal won elsewhere.
Portugal was confident in their art of navigation, such that they rejected Columbus' claim which was based on egregiously wrong estimates of the size of the earth and the shapes of the continents. Spain hired Columbus partly in order to keep for themselves the option of exploring westwards even if it was wrong.
Thus, when Columbus made a stop in Lisbon on the return leg of his first trip, Alfonso threatened the Spanish with war, and that he would send a fleet to claim all those lands in accordance to the treaty. Unfortunately for them, Spain had placed their champion on the papal throne, namely Rodrigo Borgia or Pope Alexander VI. That Pope decreed that all lands SW of the Azores were to be given to Castile. In addition, all lands belonging to India would also be given to Castile regardless of where it is exactly. This is what really angered Alfonso, and this is what led to the negotiations that gave the Treaty of Tordesillas, which was endorsed by Pope Julius II. The Tordesillas is thus viewed as a strictly worse deal than what Portugal had had before.
