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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. "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 17
by Euclides - 1871
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...BAC, and the angle ABE is equal to the angle ABC (being both right angles), the triangles ABC, ABE have two angles of the one equal to two angles of the other, and the side AB common to the two. Therefore the triangles ABC, ABE are equal, and the side AE is equal...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 226 pages
...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.) ; and...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre - Geometry - 1857 - 448 pages
...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,...
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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 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 in each, or the sides...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...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.) ; and...
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 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...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...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...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...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 to two angles of the other, each to each, and one side equal to one side, namely, either the sides adjacent to the equal angles or sides which are...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 400 pages
...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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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 393 pages
...their sum, the third angle can be found by subtracting this sum from two right angles, 100. COR. 3. If two triangles have two angles of the one equal to two angles of the other, the third angles are equal. 101. COR. 4. A triangle can have but one right angle, or but one obtuse...
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