In any triangle the greater angle is subtended by the greater side.
任一三角形中，较大的角所对的边也较大。
三角形 ABC：角 ABC 大于角 BCA，则对边 AC 大于 AB。
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 ABC be a triangle having the angle ABC greater than the angle BCA; I say that the side AC is also greater than the side AB. For, if not, AC is either equal to AB or less.
设角 ACB 大于角 ABC。若 AB 不大于 AC，则 AB 等于 AC 或小于 AC。
Now AC is not equal to AB; for then the angle ABC would also have been equal to the angle ACB; [I. 5] but it is not; therefore AC is not equal to AB. Neither is AC less than AB, for then the angle ABC would also have been less than the angle ACB; [I. 18] but it is not; therefore AC is not less than AB.
若相等，由 euclid-elements/book1-prop-005 底角相等，矛盾。
And it was proved that it is not equal either. Therefore AC is greater than AB.
若小于，由 euclid-elements/book1-prop-018，较大边 AC 所对角 ABC 应大于 ACB，也矛盾。
Therefore etc.
所以 AB 必大于 AC。