| 1852 - 1080 páginas
...: 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 - 512 páginas
...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 - 334 páginas
...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 - 176 páginas
...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 - 522 páginas
...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 - 400 páginas
...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 - 264 páginas
...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.... | |
| Euclides - 1855 - 270 páginas
...extremity of one of the 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... | |
| Robert Potts - 1855 - 1050 páginas
...triangle and the other two sides produced. 6. If two triangles have one angle of the one equal to otie **angle of the other, and the sides about the equal angles proportionals, the** triangle shall be equiangular, and shall have those angles equal which are opposite to the homologous... | |
| John Playfair - 1855 - 334 páginas
...and the angle at A to the ;mgle at D. Therefore the triangle ABC is equiangular to the triangle DEF. **PROP. VI. THEOR. If two triangles have one angle of the one** efnaH to one angle of the other, and the sides about the equal angles proportinnals, the triangles... | |
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