If a number be the least that is measured by prime numbers, it will not be measured by any other prime number except those originally measuring it.
如果一个数是被若干素数能量度的最小数，那么它不会被任何其他素数能量度，除了那些原本能量度它的素数。
设 A 是被质数 B、C、D 同时量度的最小数；假设另一质数 E 量 A 得 F，则 B、C、D 量 F，且 F < A，与最小性矛盾。
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For let the number A be the least that is measured by the prime numbers B, C, D; I say that A will not be measured by any other prime number except B, C, D. For, if possible, let it be measured by the prime number E, and let E not be the same with any one of the numbers B, C, D.
设数A是被素数B、C、D能量度的最小数。
Now, since E measures A, let it measure it according to F; therefore E by multiplying F has made A. And A is measured by the prime numbers B, C, D.
假设A也被不同于B、C、D的素数E能量度，设E量度A得F，则E乘以F得A。
But, if two numbers by multiplying one another make some number, and any prime number measure the product, it will also measure one of the original numbers; [VII. 30] therefore B, C, D will measure one of the numbers E, F. Now they will not measure E; for E is prime and not the same with any one of the numbers B, C, D.
由于A被B、C、D量度，根据VII.30，B、C、D必能量度E或F之一。
Therefore they will measure F, which is less than A: which is impossible, for A is by hypothesis the least number measured by B, C, D.
但B、C、D不能量度E（因E是素数且不同于它们），故它们量度F，而F小于A，与A是最小公倍数矛盾。