38 — Blake on the Teeth of Cog-Wheels. 
eycloidal teeth; and in this view of the subject, the suc- 
ceeding writers have hastily concurred with him. That 
they are entirely distinct from that principle may be seen 
by referring to the subsequent re remarks on involutes of cir- 
cles, taken in connexion with the rest of the subject. 
The hese discoveries of Roemer, De la Hire and Robison 
constitute the whole extent to which the science has hith- 
erto been carried. 
I apprehend that the subject has not yet been placed on 
its true and proper basis, and that those who have written up- 
on it have commenced their labours at one of the branches, 
and not at the root of the principle; in consequence 0: 
which they have not only failed to cireumscribe it with 
those clear and distinct outlines which should always define 
the extent of mathematical truth, but, as the following trea- 
tise will show, have embraced in their views only an infi- 
nitely small part of the subject. It is true, as shown by 
Roemer and De la Hire, that opioyeloidal curves peanan 
poh ie ip na same. property, 
or are capable of being generated by 
any curve or line whatever, rolling on the pitch circles.— 
Nor is it necessary, as in epicycloidal curves, that the tra- 
cer or describing point should be situated in the generating 
curve, for the curve generated will possess the same prop- 
erty if the describing point is any where else in the plane 
of the generating curve. 
propose in the first part of the following treatise to set 
forth in a few concise propositions the true principle in its 
whole extent ; embracing all possible curves which possess 
the p of transmitting a uniform force and velocity ; 
to which will be added such remarks and illustrations as 
readily flow from the subject, and are thought of practical 
ity. 
Since the principle thus exhibited will be found to em- 
brace an ean variety of curves, most of which are un- 
to maticians by any appropriate name, yet 
 salanca one common property ; to avoid circumlocu- 
tion we shall call them Isosacistic curves, a term sig- 
nificant of characteristic property. It is proper to re- 
