1450 Nicholas of Cusa studies geometry and logic. He studied the infinitely large and the infinitely small, considered the circle as the limit of regular polygons. Claimed the orbits of planets to be elliptic.
1470 Chuquet writes Triparty en la science des nombres, the first French algebra book. Zero and negative exponents are considered. Rationals/irrationals are discussed. Theory of equations: allowed negative coefficients. Introduced words “billion”, “trillion”, “quadrillion”.
1472 Peurbach publishes Theoricae Novae Planetarum (New Theory of the Planets). He uses Ptolemy's epicycle theory of the planets but believes they are controlled by the sun.
1474 Regiomontanus (Johannes Muller) Ephemerides, astronomical tables for the years 1475 to 1506 AD, and proposes a method for calculating longitude by using the moon. 1475 De triangulis planis et sphaericis (Concerning Plane and Spherical Triangles), studies spherical trigonometry to apply it to astronomy.
