Square Root/Examples/3/Historical Note

Historical Note on Square Root of $3$
The square root of $3$ was the second number, after the square root of $2$, to be identified as being irrational.

This was achieved by.

provided the approximation:
 * $\dfrac {1351} {780} < \sqrt 3 < \dfrac {265} {153}$

What he actually demonstrated was:
 * $26 - \dfrac 1 {52} < 15 \sqrt 3 < 26 - \dfrac 1 {51}$

These can be achieved by interpreting Pell's Equation, to obtain:
 * $1351^2 - 3 \times 780^2 = 1$
 * $265^2 - 3 \times 153^2 = -2$

Thus it appears that was familiar with Pell's Equation.