← elements / Elements 2.0 (G Index)

G.264 whole whole number — Heath¶

If, as whole is to whole, so is a number subtracted to a number subtracted, the remainder will also be to the remainder as whole to whole.

As the whole / A B / is to the whole / C D /, so let / A E / subtracted be to / C F / subtracted;

I say that the remainder / E B / is also to the remainder / F D / as the whole / A B / to the whole / C D /.

Since, as / A B / is to / C D /, so is / A E / to / C F /,

whatever part or parts / A B / is of / C D /, the same part or the same parts is / A E / of / C F / also; [G.263]

Therefore also the remainder / E B / is the same part or parts of / F D / that / A B / is of / C D /. [G.259, G.260]

[G.263]Therefore, as / E B / is to / F D /, so is / A B / to / C D /.

Therefore etc. Q. E. D.

Dependency Graph¶