| Daniel Cresswell - Euclid's Elements - 1817 - 454 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... | |
| 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 A = D (Jig. 122),... | |
| Daniel Cresswell - Geometry - 1819 - 486 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... | |
| Peter Nicholson - Architecture - 1823 - 210 pages
...equal to the sum of the two lines AD, DB, therefore AB2 = AC2 THEOREM 63. 161. Two triangles, which **have an angle of the one equal to an angle of the other,** are to each other as the rectangle of the sides about the equal Suppose* the two triangles joined,... | |
| Adrien Marie Legendre - 1825 - 570 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 in the same... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...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. 122), and let... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...AC : 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 in the same... | |
| Adrien Marie Legendre - Geometry - 1825 - 280 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 = GHF. These equal... | |
| Walter Henry Burton - Astronomy - 1828 - 84 pages
...F, are equal; and so, if 'the angles at F had been supposed equal, the triangles would have had each **angle of the one equal to an angle of the other, and the** side CF lying between correspondent angles in each; whence also DF is equal to FE. Is this sufficiently... | |
| George Darley - Geometry - 1828 - 190 pages
...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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