 | Daniel Cresswell - 1817 - 454 σελίδες
...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... | |
 | Daniel Cresswell - 1819 - 486 σελίδες
...bisects the L 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...shall be equal to the remaining angles of the other. Let the two trapeziums ABCD, EFGH, which A ~~~--^ Tk E B CFG have the sides about each of their u.... | |
 | Daniel Cresswell - 1819 - 446 σελίδες
...bisects the L FAE, FH :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...angle of the other, and if, also, the sides of the two figvres, about each of tJieir angles, be proportionals, the remaining angles of the one shall be equal... | |
 | 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 =... | |
 | Peter Nicholson - 1823 - 210 σελίδες
...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... | |
 | Adrien Marie Legendre - 1825 - 570 σελίδες
...: 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, John Farrar - 1825 - 280 σελίδες
...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 - 1825 - 276 σελίδες
...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 - 1828 - 190 σελίδες
...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... | |
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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'... 
