280] 
429 
280. 
ON THE CONICS WHICH TOUCH FOUR GIVEN LINES. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. hi. (1860), 
pp. 94—96. 
There are considerable practical difficulties in drawing a figure of the system of 
conics which touch four given lines, but a notion of the figure of the system may be 
obtained as follows: 
Figure 20 may be taken to represent any quadrilateral whatever, having all its 
sides real; and if we attend only to the unshaded spaces, it will be seen that there 
are five regions which are called the inner, upper, lower, right-hand, and left-hand 
regions respectively. The inner diagonals are AG the vertical diagonal and BD the 
horizontal diagonal; the former of these traverses the inner, upper, and lower regions; 
the latter the inner, right-hand, and left-hand regions; the outer diagonal is EF 
which traverses the upper region and the right-hand and left-hand regions. The 
inner or vertical and horizontal diagonals meet in the inner region, the vertical and 
outer diagonals meet in the upper region, the horizontal and outer diagonals meet in