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AUTOLYCUS ON RISINGS AND SETTINGS 333 
‘ apparent ’ morning- and evening-risings and settings of fixed 
stars. The ‘true’ morning-rising (setting) is when the star 
rises (sets) at the moment of the sun’s rising; the ‘ true ’ 
morning-rising (setting) is, therefore invisible to us, and so is 
the ‘true’ evening-rising (setting) which takes place at the 
moment when the sun is setting. The ‘apparent’ morning 
rising (setting) takes place when the star is first seen rising 
(setting) before the sun rises, and the ‘ apparent ’ evening 
rising (setting) when the star is last seen rising (setting) after 
the sun has set. The following are the enunciations of a few 
of the propositions in the treatise. 
I. 1. In the case of each of the fixed stars the apparent 
morning-risings and settings are later than the true, and 
the apparent evening-risings and settings are earlier than 
the true. 
I. 2. Each of the fixed stars is seen rising each night from 
the (time of its) apparent morning-rising to the time of its 
apparent evening-rising but at no other period, and the time 
during which the star is seen rising is less than half a year. 
I. 5, In the case of those of the fixed stars which are on the 
zodiac circle, the interval from the time of their apparent 
evening-rising to the time of their apparent evening-setting is 
half a year, in the case of those north of the zodiac circle 
more than half a year, and in the case of those south of the 
zodiac circle ,less than half a year. 
II. 1. The twelfth part of the zodiac circle in which the 
sun is, is neither seen rising nor setting, but is hidden; and 
similarly the twelfth part which is opposite to it is neither 
seen setting nor rising but is visible above the earth the whole 
of the nights. 
II. 4. Of the fixed stars those which are cut off by the 
zodiac circle in the northerly or the southerly direction will 
reach their evening-setting at an interval of five months from 
their morning-rising. 
II. 9, Of the stars which are carried on the same (parallel-) 
circle those which are cut off' by the zodiac circle in the 
northerly direction will be hidden a shorter time than those 
on the southern side of the zodiac.