 | Education - 1843 - 582 pages
...angle, and one of the other sides of a triangle are given ; construct it. 4. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional: and triangles which have one angle... | |
 | Education - 1844 - 688 pages
...this line makes with the touching line, shall be equal to the angles in the alternate segments. 12. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular. MECHANICS AND... | |
 | Scottish school-book assoc - 1845 - 444 pages
...equal to one angle of the other, have the sides about these angles reciprocally proportional ; and if two triangles have one angle of the one, equal to one angle of the other, and the sides about these angles reciprocally proportional, the triangles are equal. PLANE GEOMETRY.... | |
 | Euclides - 1845 - 546 pages
...is equiangular to the triangle DEF. Wherefore, if two triangles, &c. O..ED PROPOSITION VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then, if each of the remaining angles be either... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. — If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals; the remaining angles are equal, each to each, viz.... | |
 | Euclid - Geometry - 1845 - 218 pages
...ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — If two triangles have one angle of the one equal to one angle of the oiher, and the sides about the equal angles proportionals, the triangles shall be equiangular, and... | |
 | Euclides - 1846 - 292 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, If the sides to. QED s PROP. VI. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have... | |
 | Euclides - 1846 - 272 pages
...therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which have one angle of the one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3.... | |
 | Dennis M'Curdy - Geometry - 1846 - 168 pages
...of two triangles, &c. QED Kecite (a) p. 23, 1; Wp.9,5; (4) 32, 1 ; (Op.8,1: p. 4, 6; ax. 1,1. 6 Th. If two triangles have one angle of the one equal to one of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,... | |
 | Euclides - 1848 - 52 pages
...equiangular, and shall have those angles equal which are opposite to the homologous sides. PROP. VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then, if each of the remaining angles be either... | |
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If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. 
