What is a cevian?

Ceva's theorem is named afer Giovanni Ceva (prounounced joh-va-nee chay-va^[1]), an 17^th century Italian mathematitian, who published works on such diverse topics as geometry, physics, hydrolics, and economics.^[2] His most noted discovery is the theorem that bears his name. Before moving on to Ceva's Theorem and it's proofs, the concept of a cevian (prounounced chay-vee-an) must be discussed. "Cevian" is the term used for a line drawn from the the vertex of a triangle that intersects the opposite side.

Cevians play a large role in geometric theorems regarding triangles. The alitiude, median, and angle bisector are all special cases of cevians. Note that a cevian does not have to pass through the triangle. It can instead pass through the extension of the opposite side. In the diagram, both AD and AE are both cevians of ABC.