| John Playfair - 1806 - 311 pagina’s
...equal angles reciprocally proportional ; and parallelograms which have one angle of one equal to one **angle of the other, and their sides about the equal angles reciprocally proportional,** are equal to one another. Let AB, BC be equal parallelograms, which have the angles at B equal ; the... | |
| Euclid, Robert Simson - 1806 - 518 pagina’s
...angles reciprocally proportional : and parallelograms that have one angle of the ono» equal to one **angle of the other, and their sides about the equal angles reciprocally proportional,** are equal to one another. Let AB, BC be equal parallelograms, which have the angles at B equal, and... | |
| Euclides - 1816 - 528 pagina’s
...equal angles reciprocally proportional: And parallelograms that have one angle of the one equal to one **angle of the other, and their sides about the equal angles reciprocally proportional,** are equal to one anothfen Let AB, BC be equal parallelograms, which have the angles at B equal, and... | |
| Daniel Cresswell - 1817 - 436 pagina’s
...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
...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 - 208 pagina’s
...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 =... | |
| John Playfair - 1819 - 333 pagina’s
...angles reciprocally proportional : And parallelograms which have one angle of the one equal to one **angle of the other, and their sides about the equal angles reciprocally proportional,** are equal to one another. Let AB, BC be equal parallelograms, which have the angles at B equal,, and... | |
| John Mason Good, Olinthus Gilbert Gregory - 1819
...angles reciprocally proportional : and parallelograms that iiive one angle of the one equal to one **angle of the other, and their sides about the equal angles reciprocally proportional,** are equal to one another. Prop. XV. Theor. Equal triangles which have one angle of the one «qual to... | |
| Peter Nicholson - 1823
...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 - 1825 - 224 pagina’s
...: 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... | |
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