| Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...chord has to the aggregate of the two chords that are next to it. PROP. VI. (XVII.) If two trapeziums **have an angle of the one equal to an angle of the other,** and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
| Daniel Cresswell - Mathematics - 1819 - 582 pages
...FAE, FH :HE::AF:AE; that is, FG is to GE in the given ratio. PROP. XVU. 23. THEOREM. If two trapeziums **have an angle of the one equal to an angle of the other,** and if, also, the sides of the two ^figures, about each of their angles, be proportionals, the remaining... | |
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...general properties of triangles involve those of all figures, THEOREM. 208. Two triangles, whkh Iiave **an angle of the one equal to an angle of the other** and the sides about these angles proportional, are similar. Fig. 122. Demonstration. Let the angle... | |
| Rev. John Allen - Astronomy - 1822 - 494 pages
...BL oy HE. Cor. 1.—By a similar reasoning it may be proved, that triangles, which have an angle of **one, equal to an angle of the other, are to each other,** in a ratio, compounded of the ratios, of the sides including the equal angles, Cor. 2.—A right line... | |
| Peter Nicholson - Building - 1823
...triangle ABC ; therefore, also, the triangles DEF, ABC, are equiangular and similar. THEOREM 60. 158. **Two triangles which have an angle of the one equal to an angle of the other,** and the sides about them proportionals, are similar. Let the angle A equal D, and suppose that AB :... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...triangles. Thus the general properties of triangles involve those of all figures. j THEOREM. / (I 208. **Two triangles, which have an angle of the one equal to an angle of the other** and the sides about these angles proportional, are similar. Demonstration. Let the angle A = D (fig.... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...right-angled triangles. Thus the general properties of triangles involve those of all figures. THEOREM. 208. **Two triangles, which have an angle of the one equal to an angle of the other** and the sides about these angles proportional, are similar. Demonstration. Let the angle A = D (Jig.... | |
| Adrien Marie Legendre - 1825 - 224 pages
...: FH : : CD : HI ; but we have seen that the angle ACD = FHI; consequently the triangles ACD, FHI, **have an angle of the one equal to an angle of the other** and the sides about the equal angles proportional ; they are therefore similar (208). We might proceed... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...the sides FG, GH, so that AB:FG::BC: GH. It follows from this, that the triangles ABC, FGH, having **an angle of the one equal to an angle of the other** and the sides about the equal angles proportional, are similar (208), consequently the angle BCA =... | |
| George Darley - 1828 - 169 pages
...proportional, are equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, **which have an angle of the one equal to an angle of the other.** For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road... | |
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