12 number shall be equal to that of the second remainder to the sum of all the terms in the series except the last. are is the reading of all the Mss. It is equal to the sum of all the terms beginning with an except the last. Prop. XXXVIII. This Prop. pertains to a perfect number. In a certain series of numbers beginning with unity, in which each succeeding number is double of the preceding one and the terms are in a duplicate ratio, if the sum of the terms be a prime number, then the product of this sum and the last number shall be a perfect number. 1, 2, 4, 8, 16-The sum of this series is 31, a prime number. Then the product of 16 and 31, which is 496, is a perfect number. BOOK X. Definitions. -Commensurable magnitudes (lines, superficies and solids). farma Incommensurable magnitudes. मिलितवर्गाभिधा रेखा-Lines commensurable in power. भिन्न वर्गाभिधा रेखा: = Lines incomnensurable in power Rational. It comprehends 1 The line first supposed and set forth, 2 Lines commensurable to it, 3 The square on it, 4 Such superficies as are commensurable to the squarc. oft-Surds or irrational. It comprehonds 1. The line which is incommensurable to the first line sup- posed and set forth, 2. The superficies which is incommensurable to the squaro described on the rational line first supposed and set forth, 3. The line the square of which shall be equal to the above superficies. oft or soft originally meant a cord of reeds used by
