In the example above he would say that the Egyptian, for purposes of addition, makes 1⁄ 105 a new unit, in terms of which the given fractions become whole numbers that can be readily added. Excluded are papyri found abroad or containing Biblical texts which are listed in separate lists. He supposes that the Egyptian introduces an auxiliary unit. This list of ancient Egyptian papyri includes some of the better known individual papyri written in hieroglyphs, hieratic, demotic or in Greek. Hultsch (1895) has a theory still more formidable. His idea may be somewhat like that which I have expressed, but his explanation seems a little abstract, and the use of a technical term, while very convenient, makes the process seem more improbable for so ancient a people. Rodet (1882, page 37) calls the number taken a bloc extractif out of which these fractions are drawn. This method of applying an expression to a particular number was continued for many generations and is found in the papyrus of Akhmîm already mentioned. Thus in many cases the parts are not all whole numbers, but are whole numbers and simple fractions. The number taken is often the largest number whose reciprocal is among them. Naturally it would be desirable to take a number for which it was easy to find the parts indicated by the given fractions. The examples in the papyrus seem to indicate that there was no definite rule for determining what number would be most convenient to take. The next expression, 1 + 1⁄ 18, makes 152 things, and so for the others. The multiplicand, 1 ⅓ ¼, makes one whole group and ⅓ and ¼ of another, or 228 things in all. Regarding all of them as referring to a group of 144 things of some kind, assuming perhaps that he has several such groups, he finds the values of these partial products as applied to 144 and seeks to make up in this way the number of things in two groups, that is, 288. Thus in the first multiplication of Problem 32 of the Rhind Papyrus the author desires to select partial products that will add up to 2. Sometimes the Egyptian wishes to use this method with an expression involving a whole number as well as fractions. This example illustrates what I mean by “applying a fractional expression to some particular number.”
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