| Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...which any other 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...shall be equal to the remaining angles of the other.** PROP. VIII. (xvin.) To divide a given finite straight line into two parts, such, that another given... | |
| Daniel Cresswell - Geometry - 1819 - 410 pages
...bisects the L 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...shall be equal to the remaining angles of the other.** Let the two trapeziums ABCD, EFGH, which A ~~~--^ Tk E B CFG have the sides about each of their u.... | |
| Daniel Cresswell - Geometry - 1819 - 410 pages
...bisects the L FAE, FH :HE::AF:AE; that is, FG is to GE in the given ratio. PROP. XVII. 23. THEOREM. **If two trapeziums have an angle of the one equal to...angle of the other, and if, also, the sides of the two** figvres, about each of tJieir angles, be proportionals, the remaining angles of the one shall be equal... | |
| 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 =... | |
| Peter Nicholson - Building - 1823
...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 - 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... | |
| 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, John Farrar - Geometry - 1825 - 224 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),... | |
| 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 = GHF.... | |
| George Darley - Geometry - 1828 - 169 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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