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# 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.