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 Ptolemaeus, 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.