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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... Elements of Geometry and Trigonometry - Page 86by Adrien Marie Legendre - 1837 - 359 pagesFull view - About this book
| Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...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 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 - 208 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 = D (Jig. 122),... | |
| Daniel Cresswell - Geometry - 1819 - 410 pages
...FAE, FH :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 - 596 pages
...BC2 but, since AB is 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 - Geometry - 1825 - 224 pages
...triangles. Thus the general properties of triangles involve those of all figures. j THEOREM. / (I 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 let... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...right-angled triangles. Thus 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), and let... | |
| Adrien Marie Legendre - 1825 - 224 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 in the same... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 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. These equal... | |
| George Darley - Geometry - 1828 - 169 pages
...proportional, are 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 - 68 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... | |
| |