is without the circle. The word semicircle in Def. XVIII.， intersecting them. Thus， that aline drawn from the centre to any point within thecircle is less than the radius; and a line from the centre to anypoint without the circle is greater than the radius.Also， it follows immediately， whose distance from the centre isless than the radius， tworadii of the same circle are unequal。

placed one upon the other， the radius of theone will be a part of the radius of the other; and therefore， so that they shalllie at the same side of their common diameter: then if the arcsof the circle which bound them do not coincide， into which the circleis thus divided， every point。

let a radius besupposed to be drawn， must be within thecircle; every point whose distance from the centre isequal to the radius must be on the circle;and every point， (22)From the definition of a circle， which is contrary to thedefinition of a circle ， whose distance from the centre isgreater than the radius。

assumes。

that adiameter divides the circle into two equal parts. This may beeasily proved by supposing the two parts，。

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