This theorem was first published by Giovanni Ceva 1678.
Let
be an arbitrary -gon,
a given point, and a positive integer such
that .
For ,
..., ,
let
be the intersection of the lines and , then
(2)
Here,
and
(3)
is the ratio of the lengths and with a plus or minus sign depending on whether these segments
have the same or opposite directions (Grünbaum and Shepard 1995).
Another form of the theorem is that three concurrent lines from the polygon vertices of a triangle
divide the opposite sides in such fashion that the product of three nonadjacent segments
equals the product of the other three (Johnson 1929, p. 147).