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G.258 number parts number¶

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

number_parts_number()

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

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

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

assert as many parts of C as there are in / A B /, so many parts of F are there also in / D E /

assert Let / A B / be divided into the parts of C, namely / A G /, / G B /, and / D E / into the parts of F, namely / D H /, / H E /

assert the multitude of / A G /, / G B / will be equal to the multitude of / D H /, / H E /

assert Since, whatever part / A G / is of C, the same part is / D H / of F also,

∵ number_part_numberassert whatever part / A G / is of C, the same part also is the sum of / A G /, / D H / of the sum of C, F

assert For the same reason,

assert Whatever part / G B / is of C, the same part also is the sum of / G B /, / H E / of the sum of C, F

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

Dependency Graph¶