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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...
First principles of Euclid: an introduction to the study of the first book ... - Σελίδα 83
των T S. Taylor - 1880
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...angle EEC : and the angle AEG is equal * to the angle BEH ; * 15' l• therefore the triangles AEG, BEH have two angles of the one, equal to two angles of the other, each to each, and the sides AE, EB, adjacent to the equal angles, equal to one another ; wherefore they have their other...

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...together equal to the angles А С D, ACB, that is, to two right angles (2.). Therefore, &c. Cor. 1. If two triangles have two angles of the one equal to two angles of the other, their third angles will likewise be equal to one another. Cor. 1. (Eue. i. 26, second part of.) Hence,...

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...by BD, and because the right angle BED is equal to the right angle BFD, the two triangles EBD, FBD have two angles of the one equal to two angles of the other, and the side BD, which is opposite to one of the equal angles in each, is common to both; therefore...

## The Elements of Euclid: viz. the first six books, together with the eleventh ...

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...equal to KCF, and the right angle FHC equal to the right angle FKC; in the triangles FHC, FKC there are two angles of the one equal to two angles of the other, and the side FC, which is opposite to one of the equal angles in each, is common to both : therefore...

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...which has the greater base, shall be greater than the angle contained by the sides of the other. XXVI. If two triangles have two angles of the one equal...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 the equal angles in each;...

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...bisected by BD, and that the right angle BED is equal to the right angle BFD, the two Iriangles EBD, FBD have two angles of the one equal to two angles of the other, and the side BD, which is opposite to one of the equal angles in each, is common to both ; therefore...

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...SECTION IV. two angles of the one is equal to the sum of the remaining two angles of the other. 2. If two triangles have two angles of the one equal to two angles of the other, each to each, the third angle of the one is equal to the third angle of the other ; that is, the triangles are equiangular....

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...and if the equal angles be subtracted from these equals, the remaining angles must be equal. M.—If two triangles have two angles of the one equal to two angles of the other, each to each, what may be said of the remaining third angles ? P.—They must be equal,—for the reason alleged...

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...be > Z EOF. PROPOSITION XXVI. (Argument ad absurdum). Theorem. If two triangles have two angles of 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 opposite to the equal angles in each : then...

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...angle; therefore MLN is equal to LKH; and the angles at H and at N are right angles. Therefore the triangles have two angles of the one equal to two angles of the other ; and the side KL is equal to LM. Therefore the triangles are equal, and HL is equal to MN; that is,...