Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.
"The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn". Book by Lucio Russo, 2004.
![Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis](http://cdn.quoteddaily.com/images/lucio-russo/euclid-manages-to-obtain-a-rigorous-proof-without-ever-dealing-with-infinity-by-reducing-the-problem-of-the-infinitude-of.jpg)