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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. "
The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 27
by Peter Nicholson - 1823 - 596 pages
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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 the...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 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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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 the...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...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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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 1

Euclides - 1868 - 88 pages
...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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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pages
...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 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 the sides which...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...the |_'s PFB and PEC, we have the remaining [_'s, AFC and AEB, equal. Hence, the A's, AFC and AEB, have two angles of the one equal to two angles of the other, each to each, and the included sides equal; the remaining sides and angles are therefore equal, (Cor., Prop. 9). Therefore,...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884
...to it ; therefore the angle BAC is greater than EDF. XXVI. — 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 the sides opposite...
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