As to the second method, namely, by determining what portion of the earth corresponds to another known part of the heavens, it is more probabile etiam per demonstrationem. But the difficulty of this method lies in the fact that this proof or demonstration has been made by many learned and experienced men, and we discover a great diversity in their results, as I pointed out in my opinion when it was agreed that every one should commit in scriptis the number of leagues corresponding to each degree, of which the following is a copy.
[Here follow the different calculations of the length of a degree and the circumference of the earth, beginning with Aristotle. Briefly these are as follows: Aristotle, 800 stadia to a degree, making the terrestial circumference, 12,500 leagues; Strabo, Ambrosius, Theodosius, Macrobius, [189] and Eratosthenes, each 700 stadia to the degree, and a circumference of 7,875 leagues; Marinus and Ptolemæus, 500 stadia to the degree, and a circumference of 5,625 leagues; Tebit, Almeon, Alfragano, Pedro de Aliaco [190] "in the tenth chapter of De imagine mundi and the author of the sphere in the division of the zones," Fray Juan de Pecan "in the fourth chapter of the treatise of the sphere," and the "first Admiral of the Indies, [191] as is evident from many papers made by him," each "fifty-six and two-thirds miles" or "fourteen leagues and two-thirds of a mile" to a degree, and a circumference of 5,100 leagues. "If no opposition is given to this latter ex adverso mere voluntarie," continues Colon, "then necessarily we must have recourse to verify it by experience, which is hindered by many obstacles." In further reasoning he says:]
It is clear from the above, that, supposing the measurement of the degrees to be conclusive, it is not reduced to such practical form that the place where such and such a number of leagues correspond to a degree can be told, nor is it easy to determine this; so that it will be necessary, both sides concurring, to select persons and instruments and the place for making the test. After these men had been ordered to proceed, instruction and advice must be given them, which being a huge matter and outside of the present discussion, I shall not dwell upon. If such practical experience is not acquired, then rightly and quite reasonably the measurement or size of degrees used by the authors of tables, or of almanacs and daily calculations of the stars, should be accepted; and such a view seems quite conclusive to whomever is not obstinate, since it is proved that the diversity of the relative positions of the superior bodies proceeds from the difference between the places of observation.
Supposing that the number of miles or leagues corresponding to each degree were to be verified by the care and skill of the men abovesaid, then another very long and difficult calculation would be necessary, namely, the appointment of experienced men to measure and determine the number of measures or degrees from one continent or province to another. And when they shall reach the half [one hundred and eighty degrees] counting from the line passing at the end of the three hundred and seventy leagues, at that place they shall establish a point or mark to show what pertains to each side. But as this manner of measuring degrees may be difficult from east to west, although easy from north to south, recourse must be had to certain fine and subtile methods, of which, although everybody is well informed concerning them, I shall not hesitate to state a few facts I have been able to acquire, in order to give these other deputies an opportunity to explain those facts of which I am ignorant.
[Various methods for estimating the length of a degree follow. Colon concludes thus:]
But inasmuch as the determination of the above methods seems to be and is difficult, each one of them must be employed, and each one put into execution, so long as one does not conflict with the other. Furthermore the day's run must conform to these methods, and pilots of great experience and judgment chosen. In this way it might be hoped to determine a division in which neither part would suffer and great loss or inconvenience. Inasmuch as, in another form, rebus stantibus ut nunc, I consider it impossible that one side can succeed in convincing the other by demonstrating that the Malucos fall within his territory, although one might show that it is more in accordance with equity and reason, and thus obtain his object, if the judges imagine that they could determine it according to rigorous and absolute judgment; therefore in order to accomplish my utmost as well as to do everything that I think can be of use in this question, upon the day determined by the assembly I shall present in writing all the evidences, documents, and drawings bearing upon this case that, to my mind, might prove useful.
Now to sum up in conclusion of the above, neither side can convince the other that he is trying to shift his ground; and therefore, I say, no sentence can at the present time be passed upon this case, except that it will be necessary to agree upon an expedition to compute the size of the degrees; and this done, ships and men must be chosen, for the purpose of measuring the longitude by one or the other of the various methods found to be best, and for definitely determining and marking the beginning and end of the said demarcation, and the lands falling in each part or hemisphere. [His signature and the notarial countersignature follow. The date of this document is April 13, 1524.]
Opinions of Fray Tomas Duran, Sebastian Caboto, and Juan Vespucci
Rendered at the Junta of Badajoz Regarding the Ownership of Maluco
Inasmuch as you wish, it appearing to have some value, that each one should set down in writing his opinion regarding the demarcation that his Majesty commended to us, we, Fray Tomás Duran, Sebastian Caboto, captain and pilot, and Juan Vespuchi, pilot, concert together in setting down and explaining our opinion regarding this demarcation.
First we must calculate the leagues, giving as few at possible to the celestial degree, because giving fewer leagues [to the celestial degree] there will be fewer throughout the earth, which suffices quite well for their Majesties' service. However, as we pointed out formerly, it seems to us that we must employ the number used commonly by sailors both in Portugal and Castilla. These men assign to each heavenly degree seventeen and one-half leagues, to the first following point of the compass from the north [north by east] eighteen and one-half, to the northeast by north twenty, etc. The second fundamental is that we must conform ourselves to that most grave and practical astrologer Ptolemaeus, who, writing later than Pomponius, Marinus, Plinius, and Strabo, calculated sixty-two and one-half miles to each degree.