Page:A History Of Mathematical Notations Vol I (1928).djvu/37

Rh Proof.—5½⅐$1/undefined$ is multiplied by (1½¼) and the partial products are added. In the first line of the proof we have 5½⅐$1/undefined$, in the second line half of it, in the third line one-fourth of it. Adding at first only the integers of the three partial products and the simpler fractions ½, ½, ¼, ¼, ⅛, the partial sum is 9½⅛. This is ¼⅛ short of 10. In the fourth line of the proof (l. 9) the scribe writes the remaining fractions and, reducing them to the common denominator 56, he writes (in red color) in the last line the numerators 8, 4, 4, 2, 2, 1 of the reduced fractions. Their sum is 21. But $21⁄56$=$14+7⁄56$=$1⁄4$ $1⁄8$, which is the exact amount needed to make the total product 10.

A pair of legs symbolizing addition and subtraction, as found in impaired form in the Ahmes papyrus, are explained in §200.

25. The Egyptian Coptic numerals are shown in Figure 8. They are of comparatively recent date. The hieroglyphic and hieratic are