 | Robert Potts - 1868 - 434 σελίδες
...same reason, the angle A CB is equal to the angle DFE, and the angle at A equal to the angle at D : therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one... | |
 | James Maurice Wilson - 1869 - 260 σελίδες
...therefore, the ratio of DB : BG is compounded of the ratios AB : BE and CB : BF. COR. i. Triangles which have one angle of the one equal to one angle of the other, are to one another in the ratio compounded of the ratios of the sides containing that angle. COR. 2.... | |
 | Sir Norman Lockyer - 1902 - 1086 σελίδες
...committee suggest that the following proposition be adopted :— If two triangles (or parallelograms) have one angle of the one equal to one angle of the other, their areas are proportional to the areas of the rectangles contained by the sides about the equal... | |
 | Sir Norman Lockyer - 1902 - 846 σελίδες
...committee suggest that the following proposition be adopted : — If two triangles (or parallelograms) have one angle of the one equal to one angle of the other, their areas are proportional to the areas of the rectangles contained by the sides about the equal... | |
 | Henry William Watson - 1871 - 320 σελίδες
...polygon on AB + the area of the polygon on AC is equal to the area of the polygon on BC. EXAMPLES. 1. If two triangles have one angle of the one equal to one angle of the other, and likewise one angle of the one supplementary to one angle of the other, the sides opposite to these... | |
 | Edinburgh univ - 1871 - 392 σελίδες
...describe a square that shall be equal to a given rectilineal figure. 4. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and conversely. 5. If two chords... | |
 | Civil service - 1871 - 264 σελίδες
...cent. per annum ? 10. Extract the square root of 3312400. VOLUNTARY PORTION. 1. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. If the sides above mentioned are... | |
 | Euclides - 1871 - 136 σελίδες
...Euclid) of another case in which two triangles are equal in all respects. PROPOSITION E. THEOREM. If tico triangles have one angle of the one equal to one angle of the otlier, and the sides about a second angle in each equal; then, if the third angles in each be both... | |
 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...BC is to O Jj?. V. 5. and .'. O AB=CJ BC. V. 8. QED Pnoposmoif XV. THEOREM. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. Let A BO, ADE be equal AS, having... | |
 | Euclides - 1874 - 342 σελίδες
...triangle BGC are together not less than two right angles ; which is impossible (I. 17) ; therefore 3. The triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROPOSITION 8.— Theorem. In a right-angled triangle, if a perpendicular be drawn from the right angle... | |
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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 equal which are opposite to the homologous sides. 
