ÜHhHHHH 
353 
FROM PLATO TO EUCLID 
Euclid. 
7. That the circle of the 
zodiac rises and sets over the 
whole extent of the horizon 
between the tropics is mani 
fest, forasmuch as it touches 
circles greater than those 
which the horizon touches. 
Autolycus. 
9. If in a sphere a great 
circle which is obliquely in 
clined to the axis define the 
visible and the invisible por 
tions of the sphere, then, of 
the points which rise at the 
same time, those towards the 
visible pole set later and, of 
those which set at the same 
time, those towards the visible 
pole rise earlier. 
11. If in a sphere a great 
circle which is obliquely in 
clined to the axis define the 
visible and the invisible por 
tions of the sphere, and any 
other oblique great circle 
touch greater (parallel) circles 
than those which the defin 
ing circle (horizon) touches, 
the said other oblique circle 
makes its risings and settings 
over the whole extent of the 
circumference (arc) of the de 
fining circle included between 
the parallel circles which it 
touches. 
It will be noticed that Autolycus’s propositions are more 
abstract in so far as the * other oblique circle ’ in Autolycus 
is any other oblique circle, whereas in Euclid it definitely 
becomes the zodiac circle. In Euclid ‘ the great circle defining 
the visible and the invisible portions of the sphere ’ is already 
shortened into the technical term ‘ horizon ’ (ôpiÇcov), which is 
defined as if for the first time : ‘ Let the name horizon be 
given to the plane through us (as observers) passing through 
the universe and separating off' the hemisphere which is visible 
above the earth.’ 
The book On Risings and Settings is of astronomical interest 
only, and belongs to the region of Phaenomena as understood 
by Eudoxus and Aratus, that is, observational astronomy. 
It begins with definitions distinguishing between ‘true’ and 
s,