In Linneus backyard: Möckelsnäs manor house, Älmhult

The Italian mathematician Giovanni Ceva’s published in 1678 Menalao’s theorem and that which is credited to him.

Use Menlao’s theorem for collinearity and Ceva’s theorem för concurrency.

Menelao’s theorem (named after MEnelaos from Alexandria  100 A.D) states that if points P, Q and R are taken on sides AC, AB or BC of triangle ΔABC  these points are collinear if and only if

AQ/QB · BR/RC · CP/PA = -1.

Ceva’s theorem says that three lines drawn from the vertices  A, B and C of ABC meetinng the opposite sides in points L, M, N respectively , are congruemt if and only if

AN/NB · BL/RC ·  CP/PA =1.

Ceva’s theorem

Simson’s line: The feet of the perpendiculars drawn from any point on the circumference of a circumscribed circle to the sides of the triangle are collinear.

Simson’s line