 | Daniel Cresswell - 1817 - 454 pàgines
...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 - 1819 - 574 pàgines
...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... | |
 | Daniel Cresswell - 1819 - 446 pàgines
...: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 an angle of the other, and if, also, the sides of the two figvres, about each of tJieir angles, be proportionals, the remaining... | |
 | Peter Nicholson - 1823 - 210 pàgines
...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 - 280 pàgines
...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 anglgs proportional, are similar (208), consequently the angle BCA —... | |
 | Adrien Marie Legendre - 1825 - 276 pàgines
...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 (fig.... | |
 | George Darley - 1828 - 190 pàgines
...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 - 218 pàgines
...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... | |
 | Timothy Walker - 1829 - 138 pàgines
...vertices by the space of a quadrant, the sides will become parallel each to each. 3. — When they have an angle of the one equal to an angle of the other, and the sides including these angles proportional — . Thus if the F45 angle A=A (fig. 45), and if... | |
 | 1835 - 684 pàgines
...interjacent side (c). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . cor. 14 5. An angle of the one equal to an angle of the other, and the sides about two other angles, each to each, and the remaining angles of the same affection,... | |
| |
Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles... 
