C 4S 6 1 
10. If the vertical be parallel to the bafe, and the 
plane palling thro’ it perpendicular, the directrix of 
the bale being a circle, having its center in the inter- 
fedtion A R of the two planes j then the folid will be 
the cono-cuneus of the learned Dr. Wallis, and the 
various curve fedtions of it will be alfo lines of the 
fourth order. Fig. io. 
In this cafe, the quantities QJl and D C will 
vaniih, and making M R = m t the equatio n, 
retaining the other fymbols, will be m — y x 
2 r x n a 2r l a z — x z — 2 x n la — a z l z _ ^ x eb —xh 
J 
And here it is furpriling that the great Doctor, while 
he was conlidering his folid, did not fall upon the one 
I have explained ; but indeed, in fearching after new 
difcoveries, we are often like thofe, who, groping 
in the dark, mifs the things that are neared; them. 
ii. To conclude, if the diredtrix D N of the bafe 
be a line of any order rc, the fedtion B P will be of 
the order i n. Fig. 1 1 . 
In the equation of the curve diredtrix D N of the 
bafe u n = A z n + B z” ~ 1 u + C z” ~ 2 u z + D z n ~ 3 u ?> 
See. make the abfeiffe D n — z, and the ordinate 
N n = u ; and draw A Q parallel to D and then, 
other things being as before, the analogy N O : P O 
: : N R ; M R will be thus expreiled, n + 
b x — eb , j , qnx-\-qal-\~qac . nmx -\- mal ~]-mc a 
* y w u * 4 - d ~ p I — , ; 
e J 1 a z a 3 
from which we (hall have u = 
eb — b x <nm x -\-mc a -f - inaL da z y-\-nqxy-\-qaly-\-qyeic 
e ma l-\- e mn x -\-ma c e — a z ey ' mnx-\-mac — a z y-\-mal 
And becaufe D n = z = l -\- if we fubftitute thefe 
a 
yalues of u and z, in the above general equation, 
8 the 
