| Daniel Cresswell - 1817 - 454 páginas
...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 - 1819 - 574 páginas
...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), and... | |
| Daniel Cresswell - 1819 - 486 páginas
...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... | |
| Rev. John Allen - 1822 - 508 páginas
...FE, as FD to AC). And triangles (ABC, DEF), which have an angle (ACB) of one, equal to an angle (F) **of the other, and the sides about the equal angles reciprocally proportional, are equal.** Part 1.—On BC and AC produced, take CG equal to FE, CH to FD, and join AG and GH. The angle HCG is... | |
| Peter Nicholson - 1823 - 210 páginas
...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, John Farrar - 1825 - 294 páginas
...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 in the same manner to demonstrate,... | |
| Adrien Marie Legendre - 1825 - 276 páginas
...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 (fig. 122), and let Fifr... | |
| Adrien Marie Legendre, John Farrar - 1825 - 280 páginas
...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 Fig.... | |
| Adrien Marie Legendre - 1825 - 570 páginas
...properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an ungle **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 Kig.... | |
| Euclides - 1826 - 226 páginas
...angles are reciprocally proportional; and if parallelogram* h.ave one angle of the one equal to one **angle of the other, and, the sides about the equal angles reciprocally proportional;** these parallelograms shall be equal to one another. • I*-1- foreFB, вс,аге in a direct line... | |
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