A straight line commensurable in length with an apotome is an apotome and the same in order.
与一条余线段长度可公度的线段也是余线段，且与原来的余线段同阶。
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Let AB be an apotome, and let CD be commensurable in length with AB; I say that CD is also an apotome and the same in order with AB. For, since AB is an apotome, let BE be the annex to it; therefore AE, EB are rational straight lines commensurable in square only. [X. 73] Let it be contrived that the ratio of BE to DF is the same as the ratio of AB to CD; [VI. 12] therefore also, as one is to one, so are all to all; [V. 12] therefore also, as the whole AE is to the whole CF, so is AB to CD.
设AB为余线段，CD与AB长度可公度。取BE为AB的附加线段，则AE、EB为仅平方可公度的有理线段。
But AB is commensurable in length with CD. Therefore AE is also commensurable with CF, and BE with DF. [X. 11] And AE, EB are rational straight lines commensurable in square only; therefore CF, FD are also rational straight lines commensurable in square only.
作比例BE:DF = AB:CD，则AE:CF = AB:CD。因AB与CD可公度，故AE与CF、BE与DF均可公度。
[X. 13] Now since, as AE is to CF, so is BE to DF, alternately therefore, as AE is to EB, so is CF to FD. [V. 16] And the square on AE is greater than the square on EB either by the square on a straight line commensurable with AE or by the square on a straight line incommensurable with it. If then the square on AE is greater than the square on EB by the square on a straight line commensurable with AE, the square on CF will also be greater than the square on FD by the square on a straight line commensurable with CF.
由AE、EB仅平方可公度，得CF、FD也仅平方可公度。又由AE:EB = CF:FD，且AE上的正方形大于EB上的正方形之差，与CF上的正方形大于FD上的正方形之差，其可公度性一致。
[X. 14] And, if AE is commensurable in length with the rational straight line set out, CF is so also, [X. 12] if BE, then DF also, [id.] and, if neither of the straight lines AE, EB, then neither of the straight lines CF, FD. [X. 13] But, if the square on AE is greater than the square on EB by the square on a straight line incommensurable with AE, the square on CF will also be greater than the square on FD by the square on a straight line incommensurable with CF. [X. 14] And, if AE is commensurable in length with the rational straight line set out, CF is so also, if BE, then DF also, [X. 12] and, if neither of the straight lines AE, EB, then neither of the straight lines CF, FD.
若AE与设定有理线段可公度，则CF亦然；若BE可公度，则DF亦然；若两者皆不可公度，则CF、FD亦然。因此CD是余线段且与AB同阶。