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G.257 number part number¶

If a number be a part of a number, and another be the same part of another, the sum is the same part of the sum that the one is of the one.

number_part_number()

prove the sum of A, D is also the same part of the sum of / B C /, / E F / that A is of / B C /

assert Let the number A be a part of / B C /, and another, D, the same part of another / E F / that A is of / B C /

assert For since, whatever part A is of / B C /, D is also the same part of / E F /,

assert as many numbers as there are in / B C / equal to A, so many numbers are there also in / E F / equal to D

assert Let / B C / be divided into the numbers = to A, namely / B G /, / G C /, and / E F / into the numbers = to D, namely / E H /, / H F /

assert Then the multitude of / B G /, / G C / will be equal to the multitude of / E H /, / H F /

assert since / B G / = A, and / E H / to D,

assert / B G /, / E H / are also equal to A, D

assert For the same reason

assert / G C /, / H F / are also equal to A, D

assert as many numbers as there are in / B C / equal to A, so many are there also in / B C /, / E F / equal to A, D

assert whatever multiple / B C / is of A, the same multiple also is the sum of / B C /, / E F / of the sum of A, D

∴ whatever part A is of / B C /, the same part also is the sum of A, D of the sum of / B C /, / E F /

Dependency Graph¶