APIS Translation (English)
[Given 9900 drachmai, let it be divided into four parts; let the second be greater than the first by 1/7 of the first; let the third exceed the sum of the first two by 300 drachmai, and let the fourth exceed the sum of the first three by 300 drachmai; find the numbers.];(Col. I);. . . again multiply the 150 drachmai into the 30 numbers of the fourth term; it gives 4500; plus the 900 drachmai in its assigned value = 5100; this is the fourth term. Then add the four terms 1050 + 1200 + 2550 + 5100 = 9900.;Check: since he says, "Let the second exceed the first by 1/7", take 1/7 of the first term, 1050, = 150; add this to 1050 = 1200, which is the second term. Again, since he says, "Let the third exceed the two by 300 drachmai", add the first and the second = 2250, and add the 300 drachmai of the excess = 2550, which is the third term. And since he says, "Let the fourth exceed the three by 300 drachmai," add the three = 4800; and add the 300 drachmai of the excess = 5100, which is the fourth; the sum is 9900 in all.;(Table:); 1/7 300 dr. 300 dr. 9900 dr.; 7X 8X 15X 300 dr. 30X 600 dr.; = 60X [900 dr.]; 150 [. . . .];1050 = 1200 2550 5100 [9900]; 150 [- - -];[- - -];;(Col. II);[Since] the second is four times the first, multiply 4 x 42 = 168 and add the 12 of the excess = 180; this is the second number.;Check: take 1/6 of the second number = 30; but ad 12 = 42, which is the first; and multiply 42 by 4 = 168; moreover add 12 = 180, which is the second.;(Table:); 1/6 12 units(?) 4 times 12 units(?); 1X 4X 12 units(?); 2/3 2 units(?) = 2/3 + [14] units(?); 1/3 14 units(?); 1 42 168 + 12 = 180;-----;There are three numbers; the sum of the three is 5300; and let the first and the second be 24 times the third, and the second and third be 5 times the first. Let the three numbers thus be found.;Since the first and the second are 24 times the third, therefore the three together are 25 times the third. Divide 5300 by 25; it gives 216; this is [the third number - - -]