| George Washington Hull - 1807 - 398 páginas
...triangle, they are similar to each other. PROPOSITION XVIII. THEOREM. 254. Two triangles are similar when **they have an angle of one equal to an angle of the other,** ancL the sides including these angles proportional. *BD* Given — The triangles ABC and DEF, with... | |
| Rev. John Allen - 1822 - 494 páginas
...HG, and of PB to BL or HE. Cor. 1. — By a similar reasoning it may be proved, that triangles, which **have an angle of one, equal to an angle of the other,** are to each other, in a ratio, compounded of the ratios, of the sides including the equal angles. Cor.... | |
| Timothy Walker - 1829 - 129 páginas
...space of a quadrant, the sides will become parallel each to each. 3. — When they have an angle of the **one equal to an angle of the other, and the sides including these angles proportional** — . Thus if the F45 angle A=A (fig. 45), and if AB : AD : : AC : AF, then we say the triangles are... | |
| Euclides - 1846
...equal angles are reciprocally proportional (AB to BC as 1.I! to BD. And if two triangles (ABD and CBL), **have an angle of one equal to an angle of the other, and the sides** about the equal angles reciprocally proportional, they will be equal to one another. PART 1. — Let... | |
| Dennis M'Curdy - 1846 - 138 páginas
...opposite sides and angles of a parallelogram are equal : p. 34ofb. 1. 15 Th. Equal triangles which **have an angle of one equal to an angle of the other,** have their sides about the equal angles reciprocally proportional : and triangles are equal, which... | |
| Thomas Lund - 1854 - 362 páginas
...be : BC ; and by making C the centre, that be : BC :: ac : AC. COR. 1. Conversely, if two triangles **have an angle of one equal to an angle of the other, and the sides** forming the equal angles proportionals, the triangles will be similar. COR. 2. Hence, also, if a triangle... | |
| Trinity College (Hartford, Conn.) - 1870
...diagonals of the given quadrilateral. G. 4. Two triangles are similar, if they have an angle of the **one equal to an angle of the other and the sides including** those angles proportional. 5. In any triangle, if a straight line is drawn from the vertex to the middle... | |
| William Chauvenet - 1871 - 368 páginas
...proportional. PROPOSITION VI.— THEOREM. 32. Two triangles are similar, when an angle of the one is **equal to an angle of the other, and the sides including these angles** are proporportional. In the triangles ABC, A'B'C', let A A> A = A', and AB AC A'B' A'C'' / '" s then,... | |
| William Frothingham Bradbury - 1872 - 110 páginas
...equiangular (I. 35), and similar (20) ; therefore : EF D THEOREM X. 231 Two triangles having an angle of the **one equal to an angle of the other, and the sides including these angles proportional,** are similar. In the triangles ABC,DEF let tiifl angle A =: D and AB : DE= AC : DF then the triangles... | |
| Euclid - 1872 - 261 páginas
...equal angles are reciprocally proportional (AB to BC as LB to BD). And if two triangles (ABD and CBL), **have an angle of one equal to an angle of the other, and the sides** about the equal angles reciprocally proportional, they will be equal to one another. PART 1 . — Let... | |
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