Mode of drawing Ellipses. 



369 



October to the 19th of November, and at Malaga, from the 23rd of 

 November to the 2nd of January, I saw none. 



From my limited reading on this subject, and my own observation 

 for many years, I felt inclined to a different opinion from that ex- 

 pressed by Mr. Lea, and I cannot but consider all the statements of 

 facts here exhibited, as inconclusive, especially as relative to the high- 

 er latitudes. 



Art. XXI. — Mode of drawing Ellipses; by S. DeWitt. 



TO PROFESSOB SILLIMAN. 



Some years ago, having occasion to draw elliptical figures, I de- 

 vised, for that purpose, the following method, which I believe is not 

 described in any book. As I have found much convenience from it, 

 and as it may be useful to others, the publication of it may contrib- 

 ute an item, though small, to our stock of useful knowledge. The 

 rule is founded on this proposition ; as the semi-diameter of a circle 

 is to the semi-conjugate diameter of an ellipse, inscribed in the circle, 

 so is any semi-ordinate of the circle to the semi-ordinate, (rightly 

 applied,) of the ellipse, at the same place : which is thus proved. 



In the annexed figure, AC xCB : CG' : : AE X EB : EH% from 

 the properties of the ellipse; but ACxCB = CD^ and AExEB = 

 EF^, from the properties of the circle; then, by substituting CD'^ 

 for ACxCB and EF' for AExEB, we have CD' : CG' : : 

 EF' : EH' and CD : CG: :EF : EH. 



Let AB and GI be the u 



transverse and conjugate di- ^""^ T^-^-^i" 



ameters of the ellipse to be 

 drawn. On AB describe 

 the circle ADBO ; continue 

 the conjugate diameter to D, 

 and, parallel to it, on each 

 side of the centre, draw 

 equidistant lines across the 

 circle. From the center C, 

 with the distance GI, draw 

 the arc IN, and from B, 

 draw BK, a tangent to it ; 



