ON THE CEVA’S AND MENELAUS’S THEOREMS

Abstract

Ceva’s and Menelaus’s theorems are known formulas in the triangle geometry. Both theorems are concerning to the products of ratios of lengths involving straight lines cutting off parts of a triangle. The theorem of Menelaus is about 1600 years older than Ceva's theorem. In this paper, we present a briefly state of these theorems. In addition, the Ceva-Menelaus  transformation  of a line into four curves is discussed. This turned out to be  an ellipse, a hyperbola or a parabola. Each conic is tangent to the three straight lines of the triangle. In addition,  we found that for a ceviana  the harmonic transform has no envelope because it is a beam of straight lines passing through a point.