Page:First six books of the elements of Euclid 1847 Byrne.djvu/55

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BOOK I. PROP. XXI. THEOR.
21

F from any point () within a triangle straight lines be drawn to the extremities of one side (), these lines must be together less than the other two sides, but must contain a greater angle.

Produce ,

+ > (pr. 20.),

add to each,

+ > + (ax. 4.)

In the same manner it may be shown that

+ > + , ∴

+ > + ,

which was to be proved.

Again > (pr. 16.),

and also > (pr. 16.),

> .

Q.E.D.