Page:The Rhind Mathematical Papyrus, Volume I.pdf/225

Rh fractional parts of a hekat, Cairo tablets,170, 182; Problems 47, 80, and 81: 40. Measures of length, cubit, 32; khet, called rod, chain, 33; palm, finger, 34. Meret, side of a triangle, trapezoid, 36. Moscow papyrus, 142, 178; see Golenishchev papyrus. Multiplication, mostly by 2, 10, ⅔, ⅓ and $1/10$, 3, 4; checks used in multiplications, 4, 50; multiplicand and product may be things of some kind (concrete numbers), multiplier must be a mere number (abstract number), 6; this distinction is sometimes made clear by the notation,30; multiplication by ½ to infinity, 159 Multiplication of the second kind, when the multiplicand and product are given (division), 5, see Vetter, 185; the threesteps, 5; rule for the third step, 6; Egyptian method of stating the problem, 5. Multiplication problems when the multiplier and product are given. Problems 24-38, 25; first method, interchange of multiplier and multiplicand, 6,25; second method, false position, 7, 25; see False position; proofs of certain of these problems, 27. Newberry, discoverer of the New York fragments of the Rhind papyrus, 2, 161, 183. Neugebauer, theory of Problems 7-20, 23; on Problem 79, 30. Numbers and their signs,136, 172. Palm, $1/7$ of a cubit, 34. Papyri,Akhmtm,7,9; Ebers,46;Golenishchev (Moscow), 43, 93; Rhind, see Rhind papyrus; Smith, Edwin, 2, 43. Peet, arranged the New York fragments, 2; views on applying fractions to a number, 9; on Problem 40, 12; on the method of dividing 2 by odd numbers, 15; calls the hekat a bushel, 31, the khet a chain, 33, the seked batter, 37; explains mistakes of copying, 40; the omission in Problem 28, 70; discussion of the mistake in Problem 43, 88; on the division of selat by sekat', 96; two forms of statement for multiplication of fractions, 100; on the misplaced column in Problem 81, 114. Pefsu, 105. Prôt, season of going forth, 44. Problems,  'aha ' problems, 25; typical, 28, 29; inverse, 35; numbering by Eisenlohr, 71; problems equivalent to simultaneous equations, 13,159,162, 164, 166, 168 Progression, arithmetical, explanation of Problem 40,12; an example in the Petrie papyri, 159; a geometrical progression with ratio 7; 112, 134, 144.

Pyramid, great, its geometry, 131; pyramid, angles, 147, 180; mysticism, 174; lines in a pyramid, Borchardt's argument, 37; seked, batter, 37.

Quantièmes, unit fractions, 149.

Reciprocal numbers, see fractions. Rectangular parallelepiped, volume, 35. Rhind papyrus, date, description, history, 1; corrections, alterations, patches, 41; New York fragments, 1; first announcement of its existence, 135; supposed by E. and V. Revillout to be a pupil's copybook, 39, 143; as characterized by Bobynin, 172; three divisions, 2; references to the calendar, 43; the expression, "I return filled," in Problems 35-38, 169; Problem 43: 159, 164, 168, 187; Problem 60, 168; Problem 62, 170; Numbers 86 and 87, 151. Ro, 31 ; see Measures of capacity. Rodet, on applying fractions, 9; on Problem 79, 112.

Saint Ives, children's rhyme about, 112. Schack-Schackenburg, explained Problem 43. 88. Seasons, see Year.