 | 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... | |
 | Daniel Cresswell - 1819 - 446 σελίδες
...CJDF: .-. AC : DF : : AG or AB X BC~: DI or DE X EF. 10. COR. Triangles, having equal vertical angles, are to one another as the rectangles contained by the sides about those equal angles. PROP. VI. 11. THEOREM. The straight lines, drawn from the bisections of the three sides... | |
 | 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... | |
 | 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... | |
 | Peter Nicholson - 1823 - 210 σελίδες
...triangle ABC ; therefore, also, the triangles DEF, ABC, are equiangular and similar. THEOREM 60. 158. Two triangles which have an angle of the one equal to an angle of the other, and the sides about them proportionals, are similar. Let the angle A equal D, and suppose that AB :... | |
 | 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.... | |
 | 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.... | |
 | 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 - 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... | |
 | George Darley - 1828 - 190 σελίδες
...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... | |
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Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. 
