 | Daniel Cresswell - 1817 - عدد الصفحات: 454
...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 - 1819 - عدد الصفحات: 486
...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 - 1819 - عدد الصفحات: 574
...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... | |
 | Peter Nicholson - 1823 - عدد الصفحات: 210
...angle CAG equal to D, take AG equal to DE or AB, and join CG ; and because the two triangles CAG, DEF, have an angle of the one equal to an angle of the other, and the sides which contain these angles are equal, CG shah1 be equal to EF (theorem 5). Now there... | |
 | Adrien Marie Legendre, John Farrar - 1825 - عدد الصفحات: 280
...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, John Farrar - 1825 - عدد الصفحات: 294
...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 - عدد الصفحات: 570
...: 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 - عدد الصفحات: 276
...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 - عدد الصفحات: 190
...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... | |
 | James Hayward - 1829 - عدد الصفحات: 218
...order, and suppress , BD . ... ABC ABXAC the common factor =-, we snail have —AE~V~AF' That is — If two triangles have an angle of the one equal to an angle of the other, their areas will be as the products of the sides containing the equal angles. Fig. 94. 17o if we take... | |
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Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. 
