Make the less side x, the difference of the sides = b; the greater side will be x+b. Let the Hypothenusa be = a. Therefore, 〈 math 〉〈 math 〉; and taking away 〈 math 〉〈 math 〉; and dividing by 〈 math 〉〈 math 〉.
Therefore by case 2, 〈 math 〉〈 math 〉 i. e. 〈 math 〉〈 math 〉.
The Geometrical Construction. Having described a semi-circle upon BD=BC or a, apply therein the equal lines BC and DC, and having described another semi-circle on DC apply in it DF =½b, and if at the same interval you cut off FA from FC, the remainder AC will be the lesser side sought, &c.
The Arithmetical Rule. From half the square of the Hy∣pothenusa substract the square of half the difference, and if you take half the difference from the root extracted out of the re∣mainder, you'l have the lesser side of the Triangle required, and by adding to it the given difference you'l have also the greater. E. g. Let the Hypothenusa be 20, and the difference of the sides 4.