Now, since F measures A, B, C, it also measures A, B; therefore it will also measure the greatest common measure of A, B. [VII. 2, Por.] But the greatest common measure of A, B is D; therefore F measures D. And it measures C also; therefore F measures D, C; therefore it will also measure the greatest common measure of D, C. [VII. 2, Por.] But the greatest common measure of D, C is E; therefore F measures E, the greater the less: which is impossible. Therefore no number which is greater than E will measure the numbers A, B, C; therefore E is the greatest common measure of A, B, C. Q. E. D.
Now, since F measures A, B, C, it also measures A, B; therefore it will also measure the greatest common measure of A, B. [VII. 2, Por.] But the greatest common measure of A, B is D; therefore F measures D. And it measures C also; therefore F measures D, C; therefore it will also measure the greatest common measure of D, C. [VII. 2, Por.] But the greatest common measure of D, C is E; therefore F measures E, the greater the less: which is impossible. Therefore no number which is greater than E will measure the numbers A, B, C; therefore E is the greatest common measure of A, B, C. Q. E. D.
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