380 Mr. ludlam on the Engine 
Produce pm till it meets the circle in n, and draw the 
radius cn; then ph=pn and ca : cb :: pn : pm. Again, 
becaule pch=pcn, therefore ncd=ecl=elc and cn is 
parallel to lm, and cl=nm. Draw up perpendicular to 
B by cutting cn in n, and for the like reafon czz=sm=cb, 
and cs=mtz. While the point m defcribes an oval, the 
point e defcribes a circle whofe center is c and radius 
ce=|sl. 
To the ruler mel (fig. 2. and 3.) fix another ruler or 
right line zzzek palling through e, fo that the ruler ?«ek 
may be carried about by the ruler mel, keeping the 
angle me« between the two rulers invariable. On ?;zek. 
take ev=ek, and each = es or el, I fay, the point v will 
defcribe a right line a\ cot palling through c, and making 
an angle acs with ca, equal to half uvjn the angle made 
by the two rulers ; the point k will alfo defcribe a right 
line /jkc /3 palling through c, and making an angle hcL f 
with cl, alfo equal to half me m. 
On the center £ (fig. 2. and 3.) and with the radius 
ec defcribe a circle and it will pafs through the points 
s, v, c, l, k; draw the lines vc and kc, and the angles 
sev, and scv, both Hand on the fame arch sv; the for- 
mer at the center e, the latter at the circumference c ; 
therefore the former is double the latter. In like manner 
the angles kel and kcl both Hand on the fame arch kl, 
the 
1 
