 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 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, 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),... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 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.... | |
 | Euclid - 1826 - 234 pages
...these triangles having one angle " « <- is У of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional they are equal to one another; therefore the triangle ABG is equal to the triangle DEF. And because it is as BC to EF so is EF to... | |
 | Euclides - 1826 - 226 pages
...proportional. But if these triangles having one angle в of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional they are equal to one another; therefore the triangle ABG is equal to the triangle DEF. And because it is as BC to EF so is EF to... | |
 | George Lees - 1826 - 276 pages
...equal angles reciprocally proportional ; and triangles which have one angle of the one equal to- one angle of the other, and their sides about the equal angles reciprocally proportional, are equivalent. Let the triangles be so placed that their sides CA, AD, may be in the same straight... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...angles reciprocally proportional .- and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal : the... | |
 | 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... | |
 | 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... | |
 | Timothy Walker - Geometry - 1829 - 156 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 angle A = A (fig. 45), and if AB : AD :... | |
| |
... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another. 
