14 
In a projection right down 
on a horizontal plane let 
AiOA he the lower and 
BiOB the higher of two 
given horizontal skew axes 
about which two pulleys of 
given diameters are seve- 
rally to turn in such a way 
that, looking along A x OA in 
the direction from A 1 to A 
and along B x OB in the direc- 
tion from B 1 to B, the rising 
points are to be on the left hand of the vertical plane 
through the axis and the falling points on the right. 
To A x OA as axis fit a round roller or shaft or drum 
A^aAdCLiAi, of the same circular cross section everywhere 
throughout as the pulley which is to turn about A x OA, and 
so that a x a and a x a may be severally the straight lines in 
which a horizontal plane through A x OA cuts the drum face 
to left and to right. Also to B x OB as axis fit a drum 
BibibBflfaBi, of the same circular cross section as the pulley 
which is to turn about B x OB, and so that b x b and ]3ij3 may 
be severally the straight lines in which a horizontal plane 
through B x OB cuts the face of BJiibBfifiiBi to left and to 
right. Moreover let G and A be the common sections 
severally of the vertical planes through a x a and b x b and 
of the vertical planes through 
If now the drums were 
to turn round in the same 
manners severally as the 
pulleys which are to have 
the severally same axes and 
cross sections ; though all 
points in the drum faces 
would move in their own 
and several circles at one 
