In any triangle the greater side subtends the greater angle.
任一三角形中，较大的边所对的角也较大。
三角形 ABC，AC>AB。在 AC 上取 AD=AB；连 BD，把不等关系传递到角。
正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
For let ABC be a triangle having the side AC greater than AB; I say that the angle ABC is also greater than the angle BCA. For, since AC is greater than AB, let AD be made equal to AB [I. 3], and let BD bejoined.
设 AB 大于 AC。从 AB 上截取 AD 等于 AC（euclid-elements/book1-prop-003）。
Then, since the angle ADB is an exterior angle of the triangle BCD, it is greater than the interior and opposite angle DCB.
连接 CD，则三角形 ACD 是等腰三角形，相关底角相等。
[I. 16] But the angle ADB is equal to the angle ABD, since the side AB is equal to AD; therefore the angle ABD is also greater than the angle ACB; therefore the angle ABC is much greater than the angle ACB.
再用 euclid-elements/book1-prop-016 比较外角与内角。
Therefore etc.
得到较大边 AB 所对的角 ACB 大于较小边 AC 所对的角 ABC。