1 7 2 14 4 28 8 56 16 112 and then found which of the numbers of the first column added together would give the sum 9. These were 8 and 1. He then added the corresponding numbers in the second column and got the result, 56+7=63. So 50÷7 would have looked like this: 50-28=22; 22-14=8; 8-7=1. The result was (4+2+1) sevens with 1 as remainder. The Egyptian scribe could not handle fractions other than those with one as numerator. Two-thirds was the only exception. The Egyptian knew that the area of a rectangle was to be found by multiplying the two adjacent sides together, and that the area of a right angled triangle was equal to half the area of a rectangle whose base and altitude were equal respectively to the sides adjacent to the right angle. When his problem was to find the area of an isosceles triangle he applied the same rule, that is, multiplied the base by one of the sides and divided by two. Here theory might have helped him, had he been able to develop it. He never reached the conception of base and altitude. His rule for finding the area of a circle is worth mentioning. He took the diameter, subtracted one-ninth of it therefrom, and squared the result. In a word, he had not come far from the correct value of [Greek: pi]. But the Egyptian always dealt with concrete examples, he never was able to generalize and carry his mathematics into the theoretical. As a result he never attained scientific accuracy. Not that he did not set himself difficult problems. Indeed many of them are so complicated that they required an immense amount of reckoning, by his methods, to solve. Without giving his solution, let me add one more of his problems: "A man owns 7 cats; each cat eats 7 mice daily; each mouse eats 7 ears of grain; each ear contains 7 grains; each grain gives a sevenfold return in the harvest. What is the sum of the cats, mice, ears and grains?" The Egyptians observed the stars. They had names for all of the principal constellations; knew the circumpolar stars from those which at times disappeared below the horizon, but they never seem to have noticed the difference between fixed stars and planets. They invented a calendar with a year of 365 days as early as 4241 B.C. This was based upon the heliacal rising of Sirius (Sothis) coincident with the beginning of the inundation. But they never discovered, or if they did, never bothered about the fact that their year was one-fourth of a day too short. They were deeply interested in medicine, and their recipes prescribe everything that can be swallowed. Many of these were borrowed by the Greeks and from them have come down into the folk-medicine of modern Europe. No doubt many of their remedies were helpful, but magic always played the most important rôle in their medicine, as it does among all primitive peoples and as it did in our own until the beginning of our modern scientific age.