G.259 number part number¶
If a number be that part of a number, which a number subtracted is of a number subtracted, the remainder is the same part of the remainder that the whole is of the whole.
number_part_number_vii_7()
prove / E B / is also the same part of / F D / that / A B / is of / C D /
assert Let the number / A B / be that part of the number / C D / which / A E / subtracted is of / C F / subtracted
assert Whatever part / A E / is of / C F /, the same part also let / E B / be of / G C /
assert Now since, whatever part / A E / is of / C F /, the same part also is / E B / of / G C /,
∵ number_part_numberassert whatever part / A E / is of / C F /, the same part also is / A B / of / G F /
assert But, whatever part / A E / is of / C F /, the same part also, by hypothesis, is / A B / of / C D /
assert whatever part / A B / is of / G F /, the same part is it of / C D / also
assert / G F / = / C D /
construct Let / C F / be subtracted from each
assert / G C / = / F D /
assert Now since, whatever part / A E / is of / C F /, the same part also is / E B / of / G C /, while / G C / = / F D /,
assert whatever part / A E / is of / C F /, the same part also is / E B / of / F D /
assert But, whatever part / A E / is of / C F /, the same part also is / A B / of / C D /
∴ also / E B / is the same part of / F D / that / A B / is of / C D /