Adrien-Marie Legendre (1752-1833), one of the eminent eighteenth-century french analysts, began anew and considered three hypotheses acceding as the sum of the angles of a triangle is less than, equal to, or greater than two right angles. Tacitly assuming the infinitude of a straight line he was able to eliminate the third hypothesis, but, although he made several attempts, he could not dispose of the first hypothesis. In1794, Legendre published his very popular Elements de Geometrie, which was generally adopted in continental Europe and in the United States as a substitute for Euclid's Elements.