Method of Infinite Descent/Historical Note

Historical Note on Method of Infinite Descent
The Method of Infinite Descent was devised by.

He used it to develop his proof of Fermat's Two Squares Theorem, as he describes in a letter to :
 * For a long time I was unable to apply my method to affirmative proposition, because the twist and the trick for getting at them is much more troublesome than that which I use for negative propositions. Thus, when I had to prove that every prime number which exceeds a multiple of $4$ by $1$ is composed of two squares, I found myself in a fine torment. But at last a meditation many times repeated gave me the light I lacked, and now affirmative propositions submit to my method, with the aid of certain new principles which necessarily must be adjoined to it. The course of my reasoning in affirmative propositions is such: if an arbitrarily chosen prime of the form $4 n + 1$ is not a sum of two squares, [I prove that] there will be another of the same nature, less than the one chosen, and [therefore] next a third still less, and so on. Making an infinite descent in this way we finally arrive at the number $5$, the least of all the numbers of this kind [$4 n + 1$]. [By the proof mentioned and the previous argument from it], it follows that $5$ is not a sum of two squares. But it is. Therefore we must infer by a reductio ad absurdum that all numbers of the form $4 n + 1$ are sums of two squares.