 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'...  A Supplement to the Elements of Euclid - Strona 278autor: Daniel Cresswell - 1819 - Liczba stron: 410Pełny widok - Informacje o książce
 | Daniel Cresswell - 1817 - Liczba stron: 454
...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... | |
 | Adrien Marie Legendre - 1819 - Liczba stron: 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 A =... | |
 | Peter Nicholson - 1823 - Liczba stron: 210
...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, John Farrar - 1825 - Liczba stron: 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. 122),... | |
 | Adrien Marie Legendre, John Farrar - 1825 - Liczba stron: 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 - Liczba stron: 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 - Liczba stron: 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 = GHF.... | |
 | George Darley - 1828 - Liczba stron: 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... | |
 | Walter Henry Burton - 1828 - Liczba stron: 84
...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 - 1829 - Liczba stron: 156
...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 :... | |
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