Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Of, relating to, or based on the number 60.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. of, pertaining by, proceeding by, or based on the number sixty
 n. a sexagesimal fraction
from the GNU version of the Collaborative International Dictionary of English
 adj. Pertaining to, or founded on, the number sixty.
 n. A sexagesimal fraction.
from The Century Dictionary and Cyclopedia
 Sixtieth; pertaining to the number sixty.
 n. A sexagesimal fraction. See I.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. of or relating to or reckoning in sixtieths
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
Examples

It also doesn't fit into the Babylonians' sexagesimal system that is based on 60 and 12 the same system that gave us 60 minutes in an hour and two sets of 12 hours in a day.

He has written out tables of factors in a base 60, or sexagesimal, system, and stared in wonder at the patterns they revealed.

The Babylonians, who made great advances in math and astronomy, embraced the Sumerian sexagesimal base, and later the Egyptians, followed by the Greeks, based their timecounting methods on the Babylonian way—which is why, to this day, there are 60 seconds in a minute and 60 minutes in an hour.

While base 60 seems like the creation of an extraordinarily fertile imagination, sexagesimal has historical pedigree.

But the ancient Sumerians eschewed simplicity and, counting various bones in each finger, came up with the 60based, vaguely erotic sexagesimal numerical system.

Ptolemy could have worked out those epicycles much faster with Pentiumbased hardware although the IEEE sexagesimal floating fraction standard is pretty dodgy.
Rambles at starchamber.com » Blog Archive » Electric Ptolemy

The Sumerians and Akkadians normally used a sexagesimal numbering system, the basis of our division of the hour and minute into 60 units.

Hence, while one race may use a decimal, another a quinaryvigesimal, and another a sexagesimal scale, and while one system may actually be inherently superior to another, no user of one method of reckoning need ever think of any other method as possessing practical inconveniences, of which those employing it are ever conscious.

In the case of the subsidiary base 12, for which the Teutonic races have always shown such a fondness, the dozen and gross of commerce, the divisions of English money, and of our common weights and measures are probably an outgrowth of this preference; and the Babylonian base, 60, has fastened upon the world forever a sexagesimal method of dividing time, and of measuring the circumference of the circle.

Aside from our common decimal scale, there exist in the English language other methods of counting, some of them formal enough to be dignified by the term _system_  as the sexagesimal method of measuring time and angular magnitude; and the duodecimal system of reckoning, so extensively used in buying and selling.
chained_bear commented on the word sexagesimal
Ever wonder why an hour has sixty minutes, and a minute sixty seconds?
"Sexagesimals, or Sexagesimal Fractions, are fractions whose denominators proceed by the powers of 60, instead of by the powers of 10, as in common decimal fractions...
"Anciently there were no other than sexagesimals used in astronomical operations, for which reason they are sometimes called astronomical fractions, and they are still retained in many cases, as in the division of time, and of the circles."
—Falconer's New Universal Dictionary of the Marine (1816), 449
October 13, 2008