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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... "
The Elements of Geometry, Symbolically Arranged - Σελίδα 32
των Great Britain. Admiralty - 1846
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Elements of Geometry and Conic Sections

Elias Loomis - 1857 - 226 σελίδες
...is parallel to CD, the alternate angles GHE, HEF are also equal. Therefore, the triangles HEF, EHG have two angles of the one equal to two angles of the other, each to each, and the side Eli included between the equal angles, common ; hence the triangles are equal (Prop. VII.)...

Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - 1857 - 448 σελίδες
...consequently, the two equiangular triangles BA C, CUD, are similar figures. Cor. Two triangles which have two angles of the one equal to two angles of the other, are similar; for, the third angles are then equal, and the two triangles are equian gular (BI, p. 25,...

Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...to assist in the demonstration of the following propositions. PROP. 26.— THEOR. — (Important.) If two triangles have two angles of the one equal...viz., either the sides adjacent to the equal angles in each, or the sides opposite to them, then shall the other sides be equal, each to each, and also...

Elements of Geometry and Conic Sections

Elias Loomis - 1858 - 234 σελίδες
...is parallel to CD, the alternate angles GHE, HEF are also equal. Therefore, the triangles HEF, EHG have two angles of the one equal to two angles of the other, each to each, and the side Eli included between the equal angles, common ; hence the triangles are equal (Prop. VII.)...

Skeleton propositions &c. of Euclid, books i and ii, with ..., Τόμος 1

Euclides - 1868
...Hyp. Cone. Sap. HP 24. HypConol. D. 5. 9. Concl. Recap. PROP. XXVI. THEOR. If tu-o triangles have t\co angles of the one equal to two angles of the other, each to and one side equal to one side, viz., either the sides adjacent to the equal angles in each, or the...

The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - 1858 - 324 σελίδες
...angle in each, contained by proportional sides, are similar to each other. Any two triangles having two angles of the one equal to two angles of the other, are similar triangles, because the three angles of the one triangle are equal to the three angles of...

Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 σελίδες
...line on one side of it, either arc two right angles, or are together equal to two right angles. 2. If two triangles have two angles of the one equal...other, each to each ; and one side equal to one side, namely, either the sides adjacent to the equal angles, or the sides which are opposite to equal angles...

Treatise on Trigonometry ...

William Ernest Johnson - 1889 - 504 σελίδες
...draw IX, IT, IZ perpendiculars on the sides. Then, the triangles BXI, BZ1 having a common side BI and two angles of the one equal to two angles of the other, are equal in all respects, so that IX=IZ. Similarly IX=IY, :.IY=IZ. Therefore, the triangles AZI, A...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 σελίδες
...the obverse of Prop. 8. From what Proposition is it an immediate inference ? PROPOSITION 26. THEOREM. If two triangles have two angles of the one equal...other, each to each, and one side equal to one side, namely, either the sides adjacent to the equal angles or sides which are opposite to equal angles in...

Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 400 σελίδες
...necessitates that BC < EF. AA It remains .'. that A > D. Proposition 26. (First Part.) THEOREM — If two triangles have two angles of the one equal to two angles of the other, each to each, and have likewise the two sides adjacent to these angles equal ; then the triangles are identically equal,...




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