Can a Philologist Crack Complex Math in Plato's Music Theory?

[Kobzar]

Hello, everybody:

I am a philologist who is fond of mathematics, but who unfortunately has just an elementary high school knowledge of them. I am translating La leçon de Platon, by Dom Néroman (La Bégude de Mazenc, Arma Artis, 2002), which deals with music theory and mathematics in the works of Plato. The problem which brings me here is not about translation, but about mathematics. Please see attached document.

Any help will be welcome. Thank you very much in advance!

Best regards.

Kobzar.

 

[mrtwhs]

Rewrite the first equation as $y=\dfrac{M-x^2}{2x}$ and then substitute into the second equation. After quite a bit of multiplying, you will get $5x^4-(2M+4N)x^2+m^2=0$. Use the quadratic formula to solve for $x^2$ and you will get the value for $x^2$ given in the statement. The value for $y^2$ is incorrect. In addition to the error in the denominator that you pointed out, there is another error in the numerator.

 

[Kobzar]

Rewrite the first equation as $y=\dfrac{M-x^2}{2x}$ and then substitute into the second equation. After quite a bit of multiplying, you will get $5x^4-(2M+4N)x^2+m^2=0$. Use the quadratic formula to solve for $x^2$ and you will get the value for $x^2$ given in the statement. The value for $y^2$ is incorrect. In addition to the error in the denominator that you pointed out, there is another error in the numerator.

Thank you very much for your useful and quick answer!