C 45+ ] 
trie locus, in the conftrudion of a clock, by the 
celebrated M. De la Hire, in the French Memoir es 
for the year 1717 , intituled, ConftruBion d'nne Ho- 
rologe qui marque le r orai terns avec le moyen. 
Having now briefly confidered the various fedions 
of this folid, the directrix D N of the bafe being a 
right line, let us next fee what they are when it is a 
curve line of any order. But becaufe there are an 
infinite number of cafes, it will be Efficient to men- 
tion a few of them, when that directrix is a conic 
iedion or circle, and then to give a general propor- 
tion when it is any higher geometrical curve. 
8. If the diredrix DN of the bale be a parabola, 
having a diameter parallel to the interfedion A R of 
the plane, palling thro’ the vertical A, and other 
things being as before, the fedion B P will be a line 
of the third order. Fig. 8. 
Let the diameter be DL», the ordinate N n , and 
the equation of the parabola u 1 — zp , and make the 
moving plan M N R to pafs thro’ the ordinate N n , 
and the fedion to interfed the bafe in B O, and the 
diameter in E. From the points B and D draw BL 
and D C, parallel to N O, and meeting the lines 
A R and D n in C and L. Then fuppofe A R : R M 
::a:m y and B O : L n: :a : n 3 AC =c 3 DC=//, BL 
=by D L =/, B E=e, N n=u, D #=.■?, the abfcilfe 
BO=.v, the ordinate P_0=y,j and we have L n=z 
, nx bxx — e me- \-mz 
— / = — , no — , M R = — 
a e a 
m c T nxm . , apl-\-pxn „ 
— and u z = — — — But 
a z a 
from the limilar triangles N P O and N M R we have 
this proportion NO:PO;;NR:MR, which gives 
the 
