In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle.
在直角三角形中，直角所对边上的图形等于两直角边上相似且相似放置的图形之和。
直角三角形 ABC（直角在 A）：从 A 向 BC 作垂线 AD；在三边 AB、AC、BC 上分别构造相似且同向的图形，斜边上图形面积等于两直角边上图形面积之和。
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Let ABC be a right-angled triangle having the angle BAC right; I say that the figure on BC is equal to the similar and similarly described figures on BA, AC. Let AD be drawn perpendicular.
设直角三角形ABC，角A为直角，作AD垂直于BC。
Then since, in the right-angled triangle ABC, AD has been drawn from the right angle at A perpendicular to the base BC, the triangles ABD, ADC adjoining the perpendicular are similar both to the whole ABC and to one another. [VI. 8] And, since ABC is similar to ABD, therefore, as CB is to BA, so is AB to BD.
由VI.8，三角形ABD和ADC分别与三角形ABC相似，且彼此相似。
[VI. Def. 1] And, since three straight lines are proportional, as the first is to the third, so is the figure on the first to the similar and similarly described figure on the second. [VI. 19, Por.] Therefore, as CB is to BD, so is the figure on CB to the similar and similarly described figure on BA.
由VI.定义1及VI.19推论，CB比BA等于AB比BD，故CB比BD等于BC上的图形比BA上的相似图形。同理，BC比CD等于BC上的图形比CA上的图形。
For the same reason also, as BC is to CD, so is the figure on BC to that on CA; so that, in addition, as BC is to BD, DC, so is the figure on BC to the similar and similarly described figures on BA, AC. But BC is equal to BD, DC; therefore the figure on BC is also equal to the similar and similarly described figures on BA, AC.
因此，BC比BD与DC之和等于BC上的图形比BA与AC上的相似图形之和。但BC等于BD与DC之和，故BC上的图形等于BA与AC上的相似图形之和。