# Ceva, Giovanni (1647–1734)

Illustrtaion of Ceva's theorem.

Giovanni Ceva was a Jesuit-trained Italian mathematician who specialized in geometry. He studied first in Milan and then at the University of Pisa, where eventually he became a professor. In 1686, he was designated as professor of mathematics at the University of Mantua and worked there for the rest of his life. His greatest discovery is the theorem named after him.

## Ceva's theorem

Ceva's theorem states that three concurrent lines passing through the three vertices of a triangle intersect the sides of the triangles in such a way that the product of three non-adjacent intercepts on the sides is equal to the product of the other three intercepts. Referring to the diagram: *AY.BZ.CX = AZ.BX.CY*.

## Cevian line

The term **Cevian line** was coined by French geometers around
the end of the eighteenth century to honor Ceva. It is defined as any line joining
a vertex of a triangle to a point on the
opposite side. The median, altitude,
and angle bisector are all examples of Cevians. The perpendicular bisector,
however, in most cases, is not a Cevian because it doesn't usually pass
through a vertex.