 | 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.... | |
 | Dennis M'Curdy - 1846 - 166 σελίδες
...have their sides about the equal angles reciprocally proportional : and triangles are equal, which have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional. Given two equal triangles ABC, ADE,... | |
 | 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.... | |
 | 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,... | |
 | Eli Todd Tappan - 1864 - 288 σελίδες
...diagonal. 11. Two triangles having an angle in the one equal to an angle in the other, have their areas in the ratio of the products of the sides including the equal angles. 12. If, of the four triangles into which the diagonals divide a quadrilateral, two opposite ones are... | |
 | Eli Todd Tappan - 1868 - 432 σελίδες
...diagonal. 11. Two triangles having an angle in the one equal to an angle in the other, have their areas in the ratio of the products of the sides including the equal angles. 12. If, of the four triangles into which the diagonals divide a quadrilateral, two opposite ones are... | |
 | 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.... | |
 | Eli Todd Tappan - 1873 - 288 σελίδες
...diagonal. 11. Two triangles having an angle in the one equal to an angle in the other, have their areas in the ratio of the products of the sides including the equal angles. 12. If, of the four triangles into which the diagonals divide a quadrilateral, two opposite ones are... | |
 | William Henry Harrison Phillips - 1878 - 236 σελίδες
...ABC ABD The same is true of parallelograms. BE BF' VI. Theorem. If two triangles have an angle of the one equal to an angle of the other, the ratio of their areas is equal to that of the products of the sides which contain those angles. ELEMENTS OF GEOMETRY. [BOOK... | |
 | George Anthony Hill - 1880 - 204 σελίδες
...equiangular with respect to each other. (b) K they have their homologous sides proportional. (c) If they have an angle of one equal to an angle of the other, and the sides including these angles proportional. (18) The perpendicular upon the hypothenuse of a... | |
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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. 
