 | George Washington Hull - 1807 - 408 σελίδες
...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 - 516 σελίδες
...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 - 138 σελίδες
...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 - 272 σελίδες
...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 - 166 σελίδες
...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 - 520 σελίδες
...that ab : AB :: 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 - 1008 σελίδες
...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 - 380 σελίδες
...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 - 124 σελίδες
...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 - 284 σελίδες
...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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... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional. 
