PHILOSOPHERS' STONE.PART 64

that despite retarded intellectual output,borrowed from the medieval such as rudimental propositions of the prepythagorean geometry;the use of counting frame or abacus and some decimal fractions,so that by the end of 13th century,the mathematicians were tackling problems with advanced pythagorean theorem,approached cubic equations'solution by cones' intersection,extensively discussed spherical trigonometry and approacheddifferential calculus on the verge.Then the absorption of the ptolemaic astronomy of the ancients,the mastery of the maps of the skies,courses of planets and stars,by astrologists during the same period,was instrumental to the success of Copernican Revolution of the period possible.What the middle ages took over from the Greeks or the ancient they did not very much enrich.With this discovery,they were to change the situation with Renaisance as the magical response.Still,the accomplishment of the medieval alchemists,stumbled upon new facts,about gases and metals'properties,medieval lapidaries'