 | Daniel Cresswell - 1817 - 454 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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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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'... 
