which, given the rudimentary trigonometry at his disposal, are fairly impressive (65° 25' 39'' and 1 /24.17 are more accurate solutions to the equations). Modern computations show that in Hipparchus' time the true value of the longitude of the Sun's apogee was nearer to 66°.

Hipparchus made another hugely significant discovery concerning the Sun's motion. By comparing his own observations of the longitudes of certain stars with those made by Timocharis some 150 years previously, he discovered the

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