 | 1851 - 268 pages
...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... | |
 | 1852 - 316 pages
...2. 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... | |
 | Baptists - 1852 - 1080 pages
...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 one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular, and consequently... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...lines AB, BC, a mean 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... | |
 | Euclides - Geometry - 1853 - 176 pages
...lines ab, b С, a mean proportional db is found. Which was to done. PROPOSITION 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 parallelograms that have one... | |
 | Sir James Kay-Shuttleworth - Church and education - 1853 - 554 pages
...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 parallelograms... | |
 | Euclides - Geometry - 1853 - 334 pages
...straight lines A, B has been found a mean proportional HE. Which was to be done. PEOP. XIV. THEOE. If two parallelograms, which have one angle of the one equal to one angle of tie other, be equal : then they shall have their sides about this pair of equal angles reciprocally... | |
 | 1855 - 264 pages
...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 one angle of the other, and the sides about the equal angles proportionals, the triangles bhall be equiangular, and shall have... | |
 | Euclides - 1855 - 270 pages
...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... | |
 | Mathematics - 1871 - 420 pages
...the proposition and reduces it to a case of ambiguous equality. Let the triangles ABC, DEF (fig. 9) have one angle of the one equal to one angle of the other; namely, L ВАС =¿ DEF, and the sides about two other angles ABC, EDF proportionals, so that AB :... | |
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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. 
