Earth's circumference

"In making his own calculation, however, Christopher Columbus preferred the values given by the medieval Persian geographer, Alfraganus: one degree (at the equator) is equal to 56.67 miles. That was Columbus’s first error, which he compounded with a second: he assumed that the Persian was using the 4 856-foot Roman mile; in fact, Alfraganus meant the 7 091-foot Arabic mile.Taken together, the two miscalculations effectively reduced the planetary waistline to 16,305 nautical miles, down from the actual 21,600 or so, an error of 25 percent."

"You climb a mountain situated close to the sea or a level plain, and then observe the setting of the sun and find out the dip of the horizon... [Then] find the value of the perpendicular of the mountain. You multiply this height into the sine of the complementary angle of the dip, and divide the total by the versed sine of this dip itself. Then multiply (twice) the quotient into 22 and divide the result by 7. You will get the... earth's circumference (in the same units) in which the height of the mountain has been found."