I'm a bit stuck on a problem — taken from Katz (2009) History of Mathematics — in which we're asked to solve Diophantus's Problem V-10 with the numbers 3 and 9.
Problem V-10: To divide unity into two parts such that, if we add different given numbers to each, the results will be squares.
Here are my thoughts so far:
If we arrange lengths 3, 1 and 9 on a numberline, we can see that the problem is equivalent to dividing 13 into two squares, say $x^2$ and $y^2$, such that one of the squares, say $x^2$, lies between 3 and 4.
Thinking about this geometrically, my understanding is: we are looking for a point on the circle $x^2+y^2=13$ in the region $\sqrt3<x<2$ with rational coordinates.
Have I understood the problem correctly? What would my next steps be?