assert If B is prime, what was enjoined will have been done
assert If it is composite, some number will measure it
assert Let a number measure it, and let it be C
assertC measures B, and B measures A,
assertC also measures A
assert if C is prime, what was enjoined will have been done
assert If it is composite, some number will measure it
assert if the investigation be continued in this way, some prime number will be found which will measure the number before it, which will also measure A
assert If it is not found, an infinite series of numbers will measure the number A, each of which < the other ⇒⇐ in numbers
assert some prime number will be found which will measure the one before it, which will also measure A
∴ any composite number is measured by some prime number
