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LE FL

. в Constr.

.: CD, CE, DE = AF, AG, FG, ea. to ea. Prop. 7. ..

DCE = L FAG. Therefore, at the given point A in AB, the z angle FAG is made = given L DCE, which was to be done.

PROP. XXIII. THEOR. 24. 1 Eu. If two triangles have two sides of the one, equal

to two sides of the other, each to each, but the angle contained by the two sides of one of them, greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Let ABC, DEF, be two As, having the sides AB, AC = sides DE, DF, ea. to ea., but

< BAC > LEDF: then, base BC > base EF.

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PROP. XXIV. THEOR. 25. 1 Eu.
If two triangles have two sides of the one, equal

to two sides of the other, each to each, but
the base of the one, greater than the base of
the other ; the angle contained by the sides
of that which has the greater base, shall be

greater than the angle contained by the sides equal to them, of the other.

Let ABC, DEF, be two As, having the sides AB, AC = sides DE, DF, ea. to ea., and base BC > base EF; then _ BAC > _EDF.

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PROP. XXV. THEOR. 26. 1 Eu, If two triangles have two angles of the one,

equal to two angles of the other, each to each, and one side equal to one side ; viz. either the sides adjacent to the equal angles, or the sides opposite to equal angles in each ; then

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Prop. 3.

join GC. . GB, BC = DE, EF, ea. to ea. 1 GBC = L DEF; base GC = base DF, A GBC = A DEF,

< GCB = L DFE; but IBCA = Z DFE,

i. GCB = _ BCA, i. e. less = greater,

which is absurd; :: AB is not # DE, i e. AB = DE. Then

(AB, BC = DE, EF, ea, to each,
i ABC = L DEF;

Prop. 4.
Hyp.
Ax l.

Hyp.

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