History of mathematical notation back to any school or period before that of the Ionian Greeks, but the subsequent history may be divided into periods, the distinctions between which are tolerably well marked. Greek mathematics, which originated with the study of geometry, tended from its commencement to be deductive and scientific. Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of
Medial triangle of "ABC": the parallel to "AB" through "C", the parallel to "AC" through "B", and the parallel to "BC" through "A". Trilinear coordinates for the vertices of the anticomplementary triangle, X'Y'Z', are given by The name "anticomplementary triangle" corresponds to the fact that its vertices are the anticomplements of the vertices A, B, C of the reference triangle. The vertices of the medial triangle are the complements of A, B, C. Medial triangle Each side of the medial triangle is called a "midsegment" (or "midline"). In general, a midsegment of a triangle is a line segment which joins the midpoints