# External Angle of Triangle equals Sum of other Internal Angles/Historical Note

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## Historical Note

This theorem is the first part of Proposition $32$ of Book $\text{I}$ of Euclid's *The Elements*.

Euclid's proposition $32$ consists of two parts: the first of which is this, and the second part of which is Sum of Angles of Triangle equals Two Right Angles.

It is not known for certain, but this theorem is traditionally ascribed to Pythagoras.

However, it is plausible that Pythagoras himself received it (either directly or indirectly) from Thales of Miletus, who may well have used it in his proof of what is now known as Thales' Theorem.

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.1$: Thales (ca. $\text {625}$ – $\text {547}$ B.C.) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.2$: Pythagoras (ca. $\text {580}$ – $\text {500}$ B.C.)