AUTOLYCUS AND EUCLID 
351 
, The work On the moving Sphere assumes abstractly a 
sphere moving about the axis stretching from pole to pole, 
and different series of circular sections, the first series being 
great circles passing through the poles, the second small 
circles (as well as the equator) which are sections of the 
sphere by planes at right angles to the axis and are called 
the ‘parallel circles’, while the third kind are great circles 
inclined obliquely to the axis of the sphere; the motion of 
points on these circles is then considered in relation to the 
section by a fixed plane through the centre of the sphere. 
It is easy to recognize in the oblique great circle in the sphere 
the ecliptic or zodiac circle, and in the section made by the 
fixed plane the horizon, which is described as the circle 
in the sphere ‘ which defines (opi¿W) the visible and the 
invisible portions of the sphere’. To give an idea of the 
content of the work, I will quote a few enunciations from 
Autolycus and along with two of them, for the sake of 
comparison with Euclid, the corresponding enunciations from 
the Phaenomena. 
Autolycus. Euclid. 
1. If a sphere revolve uni 
formly about its own axis, all 
the points on the surface of the 
sphere which are not on the 
axis will describe parallel 
circles which have the same 
poles as the sphere and are 
also at right angles to the axis. 
7. If the circle in the sphere 
defining the visible and the 
invisible portions of the sphere 
be obliquely inclined to the 
axis, the circles which are at 
right angles to the axis and cut 
the defining circle [horizon] 
always make both their risings 
and settings at the same points 
of the defining circle [horizon] 
and further will also be simi 
larly inclined to that circle. 
3. The circles which are at 
right angles to the axis and 
cut the horizon make both 
their risings and settings at 
the same points of the horizon.