522 Mr. MILNER on the 
his way, from the laws of motion, that it is the fame thing 
as if thofe two forces were at once imprefied in the com- 
mon interfe&ion of the equators of thofe motions, and 
upon this principle we fuppofed a t in art. 7. to he the 
direction of the new equator. In order to remove any 
doubts that might arife about the juftnefs of this mode 
of compounding motion, frisius has given a geometri- 
cal demonftration of the principle: but the thing may 
be fhewn much more eafily in the following manner. 
Suppofe (fig. 9.) rb, ab, to be two axes about which 
every point in the plane abpr tends to move with veloci- 
ties as the refpeCtive diftances from the axes; let pq^ per- 
pendicular to ab be to pr perpendicular to rb as the an- 
gular velocity of p about rb to the angular velocity of 
the fame point about ab, and let the velocities be in con- 
trary directions : then, I fay, every point in the plane 
will move with a velocity proportional to its diftance from 
the axis pb. Firft, it is evident, that any point c in the 
axis rb will move round pb with a velocity proportional 
to its diftance cm: for the point c lying in the axis rb 
has no velocity round rb, and cm is proportional to cn. 
Draw p c parallel to ab, and any point d in that line will 
move with a velocity proportional to dv, which is per- 
pendicular to pb, for the following reafon. 
The 
