| Euclides - 1848
...mean proportional between two given straight lines. PROP. XIV. THEOREM. 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, parallelograms... | |
| Harvey Goodwin - 1851 - 173 pagina’s
...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
...similar to 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... | |
| Rev. William R. Williams - 1852
...: A b,. that is, A c : 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...about the equal angles proportionals, the triangles** are equiangular, and consequently similar ; we have seen that the two triangles A bc, A!' F"E" are... | |
| 1852
...triangles on 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... | |
| Euclides - 1853
...hence AB is to BC as DE to EF, and BC to CA as EF to FD. . Which was to be proved. PEOP. VII. THEOE. **If two triangles have (!•) one angle of the one equal to one angle of the other** ; (2) the sides about one of the other two pairs of angles proportionals ; and if each of the third... | |
| Euclides - 1853 - 147 pagina’s
...equiangular to the triangle def Wherefore, if two triangles, &c. QED PROPOSITION VII. — THEOREM. **If two triangles have one angle of the one equal to one angle of** tJie other, and the sides about two other angles proportionals, then if each of tlie remaining angles... | |
| Sir James Kay-Shuttleworth - 1853 - 500 pagina’s
...triangles on each side of it arc 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... | |
| Royal Military Academy, Woolwich - 1853
...proportional DB is found. Which was to be done. PROPOSITION XIV. THEOR. 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 parallelograms that have one... | |
| 1855
...the segments of the hase shall have the same ratio which the other sides of thi; triangle have. 2. **If two triangles have one angle of the one equal to...about the equal angles proportionals, the triangles** bhall be equiangular, and shall have those angles equal which are opposite to the homologous sides.... | |
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