The following is as given in Sir Thomas L. Heath's translation, which can be found in the book The Thirteen Books of The Elements, Vol. 2.
|Book I||Book II||Book IX|
|Definitions, Postulates, and Common Notions||Definitions||Proposition 20|
|Proposition 1, Proposition 3,||Proposition 14||Proposition 36|
|Proposition 5, Proposition 6,|
|Proposition 29, Proposition 47|
Prime numbers are more than any assigned multitude of prime numbers.
Let A, B, C be the assigned prime numbers;
For let the least number measured by A, B, C be taken,
Then, EF is either prime or not.
First, let it be prime;
Next, let EF not be prime;
Let it be measured by the prime number G.
I say that G is not the same with any of the numbers A, B, C.
For, if possible, let it be so.
Now A, B, C measure DE;
But it also measures EF.
Therefore G, being a number, will measure the remainder, the unit DF;
Therefore G is not the same with an y one of the numbers A, B, C.
And by hypothesis it is prime.
Therefore the prime numbers A, B, C, G have been found which are more than the assigned multitude of A, B, C.