If there be as many numbers as we please in proportion, then, as one of the antecedents is to one of the consequents, so are all the antecedents to all the consequents.
如果有任意多个数成比例，则一个前项与一个后项之比等于所有前项之和与所有后项之和之比。
本页以“比例序列的合比性质”整体图解辅助阅读；点、线、角、圆索引已按命题文字和证明步骤校订，可与证明和问答联动。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
Let A, B, C, D be as many numbers as we please in proportion, so that, as A is to B, so is C to D; I say that, as A is to B, so are A, C to B, D.
设A、B、C、D成比例，即A比B等于C比D。
For since, as A is to B, so is C to D, whatever part or parts A is of B, the same part or parts is C of D also.
根据定义20，A是B的同一部分或同几部分，C也是D的同一部分或同几部分。
[VII. Def. 20] Therefore also the sum of A, C is the same part or the same parts of the sum of B, D that A is of B.
因此，根据第五和第六命题，A与C之和是B与D之和的同一部分或同几部分，正如A是B的同一部分或同几部分。
所以A比B等于A、C之和比B、D之和。