| Daniel Cresswell - Euclid's Elements - 1817 - 436 pages
...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 - Geometry - 1819 - 410 pages
...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 - Geometry - 1819 - 490 pages
...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 - Geometry - 1819 - 208 pages
...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 - Architecture - 1823 - 596 pages
...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 - Geometry - 1825 - 280 pages
...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 - Geometry - 1825 - 280 pages
...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 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... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...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 - Geometry - 1828 - 190 pages
...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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