To find the number which is the least that will have given parts.
求一个最小的数，使其含有给定的几个部分。
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Let A, B, C be the given parts; thus it is required to find the number which is the least that will have the parts A, B, C. Let D, E, F be numbers called by the same name as the parts A, B, C, and let G, the least number measured by D, E, F, be taken. [VII. 36] Therefore G has parts called by the same name as D, E, F.
设A、B、C为给定的部分，取与各部分同名的数D、E、F。
[VII. 37] But A, B, C are parts called by the same name as D, E, F; therefore G has the parts A, B, C. I say next that it is also the least number that has.
取被D、E、F量尽的最小数G（根据VII.36）。
For, if not, there will be some number less than G which will have the parts A, B, C. Let it be H. Since H has the parts A, B, C, therefore H will be measured by numbers called by the same name as the parts A, B, C.
则G含有与D、E、F同名的部分（根据VII.37），即含有A、B、C。
[VII. 38] But D, E, F are numbers called by the same name as the parts A, B, C; therefore H is measured by D, E, F. And it is less than G : which is impossible.
假设存在更小的数H也含有A、B、C，则H被D、E、F量尽（根据VII.38），但H小于G，矛盾。故G为最小。