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D

B

CE

B

K

bisecting lines a line be drawn to the opposite angle of the triangle, it will bisect that angle.

Let ABC be a A; bisect the exterior ($ EAC, ACF in AD, CD, meeting in D, and join DB : the ABC is bi. sected in Bd. Drop the 1 rs DE, DF, DG.

(Depending on Prop. XIV. XXVI. XLVII.) PROP. N.

THEOR.-If from any point within or without any rectilinear figure perpendiculars be let fall on every side, the sum of the squares of the alternate segments made by them will be equal.

Let Abcd be the figure ; E the given pt.; drop the I'EF, EG, EH, EK ; then AF2 + BK + Da + cg2

FB? + KD+ Hc2 + GA', and so for any number of sides.

(Deducible from Prop. XLVII.) PROP. p. THEOR.— If, in the figure to Prop. XLVII., CF, Bk be joined, they will intersect AL, the perpendicular to bc, in the same point.

(See Prop. F.) PROP. O.

THEOR.-If, in the same figure, perpendi. culars be drawn from the points F, K, to Bc produced, the line intercepted between B and the perpendicular from F will be equal to the line intercepted between c and the perpendicular from K; and the sum of these lines will be equal to Bc.

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