 | 1852 - 316 σελίδες
...About a given circle, to describe i triangle equiangular to a given triangle. 3. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals the triangles shall be equiangular, and shall have those angles... | |
 | Harvey Goodwin - 1851 - 196 σελίδες
...shall have to the second a greater ratio than the fifth has to the sixth. 8. Equal triangles which have one angle of the one equal to one angle of the other have the sides about the equal angles reciprocally proportional ; and conversely. 9. If two planes... | |
 | 1851 - 268 σελίδες
...the whole triangle and to one another. PAPERS FOE THE SCHOOLHASTEB. 2. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. .3. Equiangular paralellograms... | |
 | 1852 - 1080 σελίδες
...A b : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that if two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we... | |
 | 1852 - 512 σελίδες
...each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular paralellograras... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...parallelogram BC. Therefore, equal parallelograms, etc. QED PROPOSITION XV. THEOR. Equal triangles which have one angle of the one equal to one angle of the other, have their sidis about the equal angles reciprocally proportional; and triangles which have one angle... | |
 | Euclides - 1853 - 334 σελίδες
...the three angles DEF, EFD, FDE. "Which -was to be proved. PEOP. VI. THEOE. If two triangles have (1) one angle of the one equal to one angle of the other ; (2) the sides about this pair of angles proportional : then these two triangles shall be similar,... | |
 | Sir James Kay-Shuttleworth - 1853 - 524 σελίδες
...each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms... | |
 | Euclides - 1853 - 176 σελίδες
...Therefore equal parallelograms, &c. QED PROPOSITION XV. — THEOREM. Eqii.al triangles, which have one angle of the one equal to one angle of the other, have tlieir sides about tlie equal angles reciprocally proportional ; and triangles which have one... | |
 | Euclides - 1855 - 270 σελίδες
...parallels passes through the extremities of all the parallels. PROP VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about another angle in each, proportionals ; and if the remaining angle in each be of the same affection... | |
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If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. 
