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 - Page 63by Adrien Marie Legendre - 1825 - 224 pagesFull view - About this book
| Euclid, John Keill - Geometry - 1723 - 364 pages
...to AE asGFis to FL. Now fince ABE, FGL, are two Triangles, having one Angle of the one equal to one **Angle of the other, and the Sides about the equal Angles proportional;** the Triangle ABE will be * equiangular * 6 of tin's. to the Triangle FGL; and fo alfo fimilar to it.... | |
| Euclid - 1728
...DEFINITIONS. [milar right-lined Figures, as ABC, DCE, are fuch chat have each Angle oí the one equal to each **Angle of the other, and the Sides about the equal Angles proportional.** в с" The Ang. В= DCE ; and AB : BC : : DC : CE. alfo the Ang. A = D ; and BA : AC : : CD : DE. and... | |
| Euclid, John Keill - Geometry - 1733 - 397 pages
...AE as GF is to* FL. Now fmce ABE, FGL, are two Triangles, having one Angle of the one equal to One **Angle of the other, and the Sides about the equal Angles proportional** ; .the Triangle ABE will be * equiangular * doftbit. to the .Triangle FGL; and alfo fimilar to it,... | |
| John Playfair - Euclid's Elements - 1806 - 311 pages
...Wherefore, if the sides, &c. QE *D. PROP. VI. THEOR. IF two triangles have one angle of one equal to one **angle of the other, and the sides about the equal angles proportional,** the triangles will be equiangular, and will have those angles equal which are opposite to the homologous... | |
| Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...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... | |
| Daniel Cresswell - Geometry - 1819 - 410 pages
...:HE::AF:AE; that is, FG is to GE in the given ratio. PROP. XVII. 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 figvres, about each of tJieir angles, be proportionals, the remaining... | |
| Peter Nicholson - Architecture - 1823 - 596 pages
...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
...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 manner to demonstrate, that the remaining... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 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 (Jig. 122), and let Fig.... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 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 let Fifr... | |
| |