3B2 Mr. ludlam on the Engine 
Scholium. This propofition is demonftrated in schoo- 
ten’s Exercitationes , Sec. p. 305..; but he makes twelve 
cafes of it: had he made ufe of the 20th of the 3d El, 
they might have been all comprehended under one. 
In the turning of ovals, the top of the reft which fup- 
ports the tool is always made to pafs through s and l 
( fig. I .) the two centers round which the oval engine 
turns ; and in this cafe the ruler or line ms ei. reprefents 
the top of the reft. If the tool be held on any part of 
the rejl between the work-man, and the neareft center as- 
at m, an oval will be turned having its longer axis a a (in 
one pofition of the work) coinciding with the top of the 
rejl. As the tool is removed towards s, the oval will grow 
narrower and at s become a right line. Beyond s towards 
E it will grow rounder, and at e become a circle ; beyond 
E it will grow narrower, and at l become a right line at 
right angles to the right line defcribed when the tool was 
at s. If the tool be removed beyond L,.it will deferibe an 
oval again, whofe longer axis is at right angles to the 
longer axis of the oval firft defcribed when the tool was 
at m. It may be very convenient to mark the points s 
and l and alfo, their middle point e on the top or face of 
the rejl that fupports the tool. If any thing be inter- 
pofed between the tool and the top of the rejl fo as to 
raife the tool above the line palling through the centers 
s and 
