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 - Page 278by Daniel Cresswell - 1819 - 410 pagesFull view - About this book
| Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...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 - Geometry - 1819 - 574 pages
...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 - Architecture - 1823 - 210 pages
...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 - 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, 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 - 1825 - 570 pages
...: 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 - 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.... | |
| 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 :... | |
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