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" If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent. "
The Elements of Euclid, containing the first six books, with a selection of ... - Seite 23
von Euclides - 1874
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 Seiten
...EDF. Therefore, if two triangles, &c. QED The enunciation of this proposition may be thus simplif'ed: If two triangles have two angles of the one, equal to two angles of the other, each to each, and a side of the one equal to a side of the other similarly situated as to the equal angles, the two triangles...
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 Seiten
...the angle EBC (4): and the angle AEG is equal to the angle BEH (a); 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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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 Seiten
...drawn to intersect one another, the greater segments will be equal to the sides of the pentagon. 3. If two triangles have two angles of the one equal to two angles of the other, and one side equal to one side, viz. either the sides adjacent to the equal angles in each, or the...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 334 Seiten
...it is not equal to it: therefore the angle BAC is greater than the angle EDF. PROP. XXVI. THLOR. Jf two triangles have two angles of the one equal to two angles of the otIirr, each to each; and one side equal to one side, viz. either the sides adjacent to the equal anglrs,...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 Seiten
...on the same side of it, are either two right angles, or are together equal to two right angles. 3. If two triangles have two angles of the one equal to two angles of the other, each to each, and one si ie equal to one side, via. the sides opposite to equal angles in each, then shall the other sides...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856 - 482 Seiten
...parallel to CD, the alternate angles, GFE, FGH, are also equal ; therefore the two triangles GEF, HFG, have two angles of the one equal to two angles of the other, each to each ; and the side FG, adjacent to the equal angles, common ; the triangles are therefore equal (theorem 6) ;...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 Seiten
...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 - 1857 - 242 Seiten
...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.)...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - 1857 - 442 Seiten
...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 - 1858 - 256 Seiten
...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.)...
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