 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...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 - 574 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 ECA — GHF. These... | |
 | Daniel Cresswell - Geometry - 1819 - 486 pages
...: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
...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 : DE : :... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...: 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... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...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. 122), and... | |
 | Adrien Marie Legendre - 1825 - 570 pages
...properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an ungle 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. 122),... | |
 | Timothy Walker - Geometry - 1829 - 138 pages
...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 AB : AD... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...side (r). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . »r. 14 5. Au angle of the one equal to an angle of the other, and the sides about two other angles, each to each, and the remaining an;;!« of the same affection, or one... | |
 | Mathematics - 1835 - 684 pages
...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, or one... | |
| |
Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional. 
