As to the first method of measuring the earth, besides being very difficult, it becomes also arbitrary unless measurements were always made by line. Much uncertainty is occasioned by this method, because, as we hear and say continually such and such leagues are very long, while others speak of them as small, each one judging according to his own opinion, and taking into consideration the time and rapidity it took him to walk them. On this account a much greater difference will result when the said leagues are measured by sea, for there are many more obstacles that alter or impede the correct calculation of them, such as, for instance, currents, tides, the ship's loss of speed, because of its meeting with strong head winds, or because of heavy seas coming athwart the bows, or from other directions. In addition to all these one may be deceived by the ship's burden and bulk; or by reason of the ship's bottom being cleaner or dirtier at one time than another; or whether it is towed or sailing alone; or whether it carries new or old sails and whether they are of good or ill pattern, and wet or dry; whether the day's run is estimated from the poop, prow, or amidships; and other special considerations that I pass by, such as the heaviness or lightness of the winds, the differences in compasses, etc. From the above then, I infer that it is difficult and unsatisfactory to determine the size of the earth by means of measuring it by traveling or sailing, and the same was maintained by Ptolemæus and other erudite men by actual test. 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.