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the lower circle toward and as far as X, next up along 
the line of the straight edge as far as Y, and lastly right on 
to and over the higher drum j3i b along the higher circle. 
This string too, if only guided on to the lower drum a x a 
along the lower circle and pulled off from the higher drum 
/3i b along the higher circle, may be kept always unwinding 
itself off from the lower drum at X and always winding 
itself on to the higher drum at 
In like manner lay a straight edge in and along the 
straight line A, and shift this straight edge aside both ways 
so as never to be taken off either of the drums and so as 
always to touch each of the drum faces and be at right 
angles to the lower axis. Let S X AS be the locus of the point 
where the straight edge touches the higher drum face, and 
let A Si be the portion on the same side of the plane 
through A perpendicular to the higher axis as Aj3i and 
therefore AS the portion on the same side as a/3. If then 
through any point Y in the 
line Si A S two planes be drawn 
perpendicular to the axes, and 
therefore cutting one another 
in a vertical straight line and 
the drum faces in a higher 
and a lower vertical circle, 
the straight edge when pass- 
ing through Y touches the 
lower circle in some point X 1} and a string may be stretched 
over the higher drum (3ib along the higher circle toward 
and as far as Y, down along the straight edge line as 
far as Xi, and right on to and under the lower drum aid 
along the lower circle. And this string, if guided on to the 
higher drum ]3i6 along the higher circle and pulled off from 
the lower drum a x a along the lower circle, may be kept 
always winding off the higher drum at Y and always 
winding on the lower drum at Xi. 
