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F

D

B

CE

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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 48 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 with-
out 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 + D + CG2

FB? + KD2 + c +
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, perpendiculars 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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