Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The center of a planetary epicycle.
 adj. Having comparable measurements in all directions; equidimensional.
from the GNU version of the Collaborative International Dictionary of English
 n. A circle around whose circumference a planet or the center of ann epicycle was conceived to move uniformly;  called also eccentric equator.
from The Century Dictionary and Cyclopedia
 Having equal arcs described in equal times; figuratively, regulating. See II.
 n. In the Ptolemaic system of astronomy, a circle about whose center the center of the epicycle of a planet was supposed to describe equal angles in equal times. Also called eccentric equator.
Etymologies
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Examples

Nor should we attribute Copernicus's desire for uniform circular motions to an aesthetic need, for this idea was philosophical not aesthetic, and Copernicus's replacing the equant with epicyclets made his system more complex than Ptolemy's.

Surprisingly, given that the elimination of the equant was so important in the

Reinhold did not accept the heliocentric theory, but he admired the elimination of the equant.

Disturbed by the failure of Ptolemy's geocentric model of the universe to follow Aristotle's requirement for the uniform circular motion of all celestial bodies and determined to eliminate Ptolemy's equant, an imaginary point around which the bodies seemed to follow that requirement, Copernicus decided that he could achieve his goal only through a heliocentric model.

What appealed to them in Copernicus™ model was its ability to do away with ad hoc devices in Ptolemy's system (such as the equant), to explain key phenomena in a pleasing fashion (the observed retrograde motion of the planets), and to explain away otherwise inexplicable coincidences in Ptolemy's system (such as the alignment of the Sun and the centres of the epicycles of the inferior planets).

On the apseline at a distance from the deferent's center equal and opposite to the earth's, Ptolemy placed an equant.

At the same time in the Islamic world Ibn alShatir of Damascus rejected Ptolemy's equant as a violation of the principle that a cosmic body's orbit must be compounded from absolutely uniform circular motions.

To this Tycho objected, and Kepler had great difficulty in convincing him that the new move would be any improvement, but undertook to prove to him by actual examples that a false position of the orbit could by adjusting the equant be made to fit the longitudes within five minutes of arc, while giving quite erroneous values of the latitudes and second inequalities.

Their aim was to find a position of the “equant,” such that these observations would show a constant angular motion about it; and that the computed positions would agree in latitude and longitude with the actual observed positions.

[Footnote 4: I.e. the angular motion about the equant was uniform.]
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