Page:A History of Mathematics (1893).djvu/151

 constructed with the ruler and compass only. He contented himself with finding a very close approximation to the required root. His work on this cubic is found in the Flos, together with the solution of the following third problem given him by John of Palermo: Three men possess in common an unknown sum of money t; the share of the first is $$\scriptstyle{\frac{t}{2}}$$; that of the second, $$\scriptstyle{\frac{t}{3}}$$; that of the third, $$\scriptstyle{\frac{t}{6}}$$. Desirous of depositing the sum at a safer place, each takes at hazard a certain amount; the first takes x, but deposits only $$\scriptstyle{\frac{x}{2}}$$; the second carries y, but deposits only $$\scriptstyle{\frac{y}{3}}$$; the third takes z, and deposits $$\scriptstyle{\frac{z}{6}}$$. Of the amount deposited each one must receive exactly $$\scriptstyle{\frac{1}{8}}$$, in order to possess his share of the whole sum. Find x, y, z. Leonardo shows the problem to be indeterminate. Assuming 7 for the sum drawn by each from the deposit, he finds $$\scriptstyle{t=47}$$, $$\scriptstyle{x= 33}$$, $$\scriptstyle{y=13}$$, $$\scriptstyle{z=1}$$.

One would have thought that after so brilliant a beginning, the sciences transplanted from Mohammedan to Christian soil would have enjoyed a steady and vigorous development. But this was not the case. During the fourteenth and fifteenth centuries, the mathematical science was almost stationary. Long wars absorbed the energies of the people and thereby kept back the growth of the sciences. The death of Frederick II. in 1254 was followed by a period of confusion in Germany. The German emperors and the popes were continually quarrelling, and Italy was inevitably drawn into the struggles between the Guelphs and the Ghibellines. France and England were engaged in the Hundred Years' War (1338-1453). Then followed in England the Wars of the Roses. The growth of science was retarded not only by war, but also by the injurious influence of scholastic philosophy. The intellectual leaders of those times quarrelled over subtle subjects in