370 GEOMETRY. 



points ; a string being stretched about the points 

 F, C, G, the ellipsis is described as above. 



Prob. 27. The same being given, to describe an 

 ellipsis by a trammel. 



The trammel is an instrument consisting of two 

 rulers fixed at right-angles to each other, with a 

 groove in each. A rod with two moveable nuts 

 works in this groove ; and, by means of a pencil 

 fixed in the end of the rod, describes the curve. 

 The operation is as follows : 



Let the distance of the first pin at B, from the 

 pencil at A, be equal to half the shortest axis ; and 

 the distance of the second pin at C, from A, to 

 half the longest axis ; the pins being put in the 

 grooves, move the pencil at A, which will describe 

 the ellipsis. 



Prob. 28. To draw a figure approaching to an 

 ellipsis with a compass to any length A B, and 

 width C D. 



Draw B P parallel and equal to E C, and bisect 

 it at 1 ; then draw 1 C and P D, cutting each 

 other at K ; bisect K C by a perpendicular, meet- 

 ing C D in O ; and on O, with the radius O C, de- 

 scribe the quadrant C G Q. 



Through Q and A, draw QG, cutting the qua- 

 drant at G; then draw G O, cutting A B at M ; 

 make EL equal to EM, also E N equal to EO. 

 From N, through M and L draw N H and N I; 

 then M, L, N, O, are the four centres by which 

 the four quarters of the figure are drawn. 



It must be observed, that this is not a true el- 

 lipsis, but only an approximation to it ; for it is 

 impossible to draw a perfect ellipsis by means of 

 compasses, which can only describe parts of cir- 

 cles. The curve of an ellipsis differs essentially 

 from that of a circle in every part; and no por- 



