isa-normaladvance-1903-00106

Description:	106THE NORMAL ADVANCE.evident that he knew something of arithmetic andgeometric progressions.According to Gow the Egyptians gave to theworld the science of geometry not, however, insuch a developed state as did the Greeks. Theearly Egyptians measured a portion of land bythe number of days it took a yoke of oxen toplow it by the time it took to walk around it or,by the amount of labor it took to cultivate it, andso on. It seems that the custom of measuringland areas by the extent of the perimeter prevailedfor a long time. A man who had a square field exchanged itfor a rhombus of equal perimeter, but did notknow the difference until he discovered that hegot less produce than before.Ahmes contribution to geometry seems to havebeen characterized thus: He calculated the areasof squares, oblongs isosceles triangles, isoscelesparallel-trapeziums, and circles. He found thearea of an isosceles triangle whose equal sides were10 ruths, and whose base was 4 ruths long, to be 20square ruths, while the real area is 19.58 squareruths to the nearest hundredth. He evidentlymultiplied the base by one-half the equal side, instead of one-half of the altitude.He found the area of an isosceles parallel-trapezium by multiplying together half the sum of theparallel sides by one of the non-parallel sides.To find the area of a circle Ahmes said: Deduct from the diameter 4th of its length andsquare the remainder. Thus, if the diameter ofa circle is 18, take 4th of it, which is 2, and theremainder is 16. The square of 16 is 256.Hence, the area is 256 square units. By modernmethods the area is 254.57 square units.At present we consider the circumference of acircle to be 3.1416 times as long as its diameter,while Ahmes considered this ratio to be 3.1604,which is not a gross error. It will be noticed thatby his plan a square could be found whose areawas exactly the same as that of a given circle.In other words, with him the quadrature of thecircle was complete, which has been proven impossible by modern mathematicians.Curiously Ahmes arranges the numbers 7, 49,343, 2,401, and 16,807 as thus shown. Thesenumbers are the first, second, third, fourth, andfifth powers of 7. Adjacent to these numbers andin the order named appear the words picture, cat,mouse, Barley, and measure. While nothing important is made of this, Leonardo of Pisa, in 1202A. D., proposed a problem which bears a strikingresemblance to it. Leonardo lived 3000 yearsafter Ahmes. His problem is as follows: 7 oldwomen go to Rome, each woman has 7 mules,each mule carries 7 sacks, each sack contains 7loaves, with each loaf are 7 knives, each knife isput into 7 sheaths. What is the sum and totalof all named?It is thought Ahmes problem was as follows: 7 persons have each 7 cats, each cat eats 7 mice,each mouse eats 7 ears of barley, from each ear 7measures of corn may grow.At the beginning of the present century, 600years after Leonardo, Daniel Adams lived andproposed the following in his arithmetic: As I was going to St. Ives,I met seven wives.Every wife had seven sacks Every sack had seven cats Every cat had seven kits:Kits, cats, sacks, and wives,How many were going to St. Ives?From this brief reference to Ahmes manuscript it will be inferred, no doubt, and properlyso, that mathematics flourished in a fairly developed state before this. Indeed, there is an oldmanuscript in the British museum, which has notbeen deciphered, and which treats of mathematics when deciphered it may be found to antedateAhmes work.O. L. Kelso, Class of 79.
Source:	http://indstate.contentdm.oclc.org/cdm/ref/collection/isuarchive/id/33871
Collection:	Indiana State University Archives

Further information on this record can be found at its source.