Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 adjective Of, relating to, or based on the number 60.
from The Century Dictionary.
 Sixtieth; pertaining to the number sixty.
 noun A sexagesimal fraction. See I.
from the GNU version of the Collaborative International Dictionary of English.
 adjective Pertaining to, or founded on, the number sixty.
 adjective (Arith. & Alg.) those fractions whose denominators are some power of sixty; as, 1/60, 1/3600, 1/216000;  called also
astronomical fractions , because formerly there were no others used in astronomical calculations.  adjective the method of computing by the sexagenary scale, or by sixties.
 adjective (Math.) the sexagenary scale.
 noun A sexagesimal fraction.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics of, pertaining by, proceeding by, or based on the number
sixty  noun a sexagesimal
fraction
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adjective of or relating to or reckoning in sixtieths
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
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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.
Astrology Myths Debunked: The Truth About Your 'New' Sign Gahl Eden Sasson 2011

While base 60 seems like the creation of an extraordinarily fertile imagination, sexagesimal has historical pedigree.
HERE’S LOOKING AT EUCLID Alex Bellos 2010

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.
HERE’S LOOKING AT EUCLID Alex Bellos 2010

He has written out tables of factors in a base 60, or sexagesimal, system, and stared in wonder at the patterns they revealed.
HERE’S LOOKING AT EUCLID Alex Bellos 2010

While base 60 seems like the creation of an extraordinarily fertile imagination, sexagesimal has historical pedigree.
HERE’S LOOKING AT EUCLID Alex Bellos 2010

While base 60 seems like the creation of an extraordinarily fertile imagination, sexagesimal has historical pedigree.
HERE’S LOOKING AT EUCLID Alex Bellos 2010

He has written out tables of factors in a base 60, or sexagesimal, system, and stared in wonder at the patterns they revealed.
HERE’S LOOKING AT EUCLID Alex Bellos 2010

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.
HERE’S LOOKING AT EUCLID Alex Bellos 2010

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.
HERE’S LOOKING AT EUCLID Alex Bellos 2010

He has written out tables of factors in a base 60, or sexagesimal, system, and stared in wonder at the patterns they revealed.
HERE’S LOOKING AT EUCLID Alex Bellos 2010
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