G.353 many odd numbers

IX.22

If as many odd numbers as we please be added together, and their multitude be even, the whole is even.
many_odd_numbers()
prove / A E / is even
A B C D E
construct Let as many odd numbers as we please, / A B /, / B C /, / C D /, / D E /, even in multitude, be added together
∵ odd_number_divisible_defassert each of the numbers / A B /, / B C /, / C D /, / D E / is odd, if an unit be subtracted from each, each of the remainders will be even
∵ many_even_numbersassert So that the sum of them will be even
assert The multitude of the units is also even
∵ many_even_numbers∴ / A E / is also even

Dependency Graph

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Required for

G.354, G.360, G.361, G.362