# Origin of the latitude 36 of Eratosthenes

How did Eratosthenes come up with the latitude 36 line, also called 36th parallel north, in the Mediterranean world? Rhodes was one of the navel points in his calculations and even today N36.00 goes through the southern part of the Rhodes. So I'd like to know the history of the calculation of this latitude and the origin of the latitudes in general.

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• I think he got lucky. He was using locations that had similar lengths of day at the equinoxes/solstices. It just happened that one set ended up on what became the 36th parallel. – mkennedy Apr 19 '17 at 0:03
• A point may be that 36° is 1/10th of a full circle. Since Erastothenes famous derivation of the circumference of the earth also involved the elevation of the sun. I would use the conjecture the following procedure: At noon on an equinox, measure the angle between sun and zenith. If it is 1/10th of a circle, you are at the 36th parallel. – mlk Apr 20 '17 at 13:37

He laid down the parallel of latitude in the following manner. He knew that at all places on the equator the day was exactly the same length all the year round, and that the lengths of the days and nights varied more and more as you went northward; therefore he reasoned that, if he could draw a line east and west through a number of places whose longest day was exactly the same length, those places would be exactly the same distance from the equator. He began at the Straights of Gibraltar, when the longest day was exactly $14\frac{1}{2}$ hours, and then observing all those places whose longest day was also $14\frac{1}{2}$ hours, he drew a line through the south coast of Sicily, across the south of the Peloponnesus, the island of Rhodes, the bay of Issus, and across the Euphrates and Tigris, out to the mountains of India. If you follow this line on a map you will find it is the $36$th parallel of north latitude and that Eratosthenes observation was perfectly correct.

Of course, Eratosthenes would not have identified this parallel as $36$ degrees north. (According to Boyer's A History of Mathematics, the introduction of the $360$ degree circle came a little later.) However, he could calculate its distance from the equator using the same techniques he employed in calculating the circumference of the Earth.

According to Boyer,

It is not known when the systematic use of the $360$ degree circle came into mathematics, but it seems to be largely due to Hipparchus in connection with his table of chords.

Hipparchus of Nicaea (ca. 180 - ca. 125 BCE).

• The problem with the quotation from A. Fisher is that it assumes he had a map he could "draw lines" on. In fact, accurate maps only became possible after coordinates had been calculated. – fdb Apr 28 '17 at 15:39
• @fdb Is Eratosthenes not simply inferring that each of the named locations lay on the same line of latitude, independent of any map which may or may not exist. Here, Fisher's use of the expression "drawing a line" being metaphorical. – Nick R Apr 28 '17 at 18:08
• Yes, I think she is speaking about a figurative "line". But it is very misleading. – fdb Apr 28 '17 at 18:38
• @fdb Yes, it certainly can be seen as a misleading expression. – Nick R Apr 28 '17 at 18:42