Euclid:Proposition/III/7

Proposition

In the words of Euclid:

If on the diameter of a circle a point be taken which is not the center of the circle, and from the point straight lines fall upon the circle, that will be greatest on which the center is, the remainder of the same diameter will be least, and of the rest the nearer to the straight line through the center is always greater than the more remote, and only two equal straight lines will fall from the point on the circle, one on each side of the least straight line.

(The Elements: Book $\text{III}$: Proposition $7$)

Sources

• 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 2 (2nd ed.) ... (previous) ... (next): Book $\text{III}$. Propositions