Select a problem from Diophantus Book III (three). Upload a screen shot, and CLEARLY INDICATE what is a translation of Diophantus, and what is commentary. Be sure to identify the problem you are using: e.g., Book Ill, Problem 45.Take the problem you selected and provide your own commentary, as given in the directions. You should: . Explain the reason for Diophantus's choice of expression, . Give a second solution, distinct from that given by Diophantus. (Note that if a second solution is impossible, you need to choose a different problem!)BOOK III I. To find three numbers such that, if the square of any one of them be subtracted from the sum of all three, the remainder is a square. Take two squares a', 4r" ; the sum is 5x. If then we take 5r' as the sum of the three numbers, and x, 2r as two of them, we satisfy two conditions. Next divide 5, which is the sum of two squares, into two other squares , It [II. 9], and assume ir for the third number. Therefore r + 2r + ur - 5x, andr = $1. The numbers are -7 34 34 25' 25' 125 [Diophantus writes ,y, for a and #45, (18 p for the numbers.] 2. To find three numbers such that the square of the sum of all three added to any one of them gives a square. Let the square of the sum of all three be r*, and the numbers 3r, 8x*, 152. Hence 261 = r r - , and the numbers are 696, 676' 676' 8 15 3. To find three numbers such that the square of the sum of all three minus any one of them gives a square. Sum of all three 4r, its square 16r;, the numbers 7x, 121 , 152 - Then 347 = 47, *= 4, and 28 48 60 the numbers are 280 289' 289 The fact that the problems III. 1-4 are very like II. 34, 35 makes Tannery suspect that they have found their way into the text from some ancient commentary