| 1852
...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... | |
| Rev. William R. Williams - 1852
...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... | |
| Sir James Kay-Shuttleworth - Church and education - 1853 - 500 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 have to one another the... | |
| Royal Military Academy, Woolwich - Mathematics - 1853
...equiangular to the triangle DEF. Wherefore, if the sides, etc. QED PROPOSITION VI. THEOR. 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... | |
| Euclides - Geometry - 1853 - 147 pages
...other, have their sides about the equal angles reciprocally proportional ; and parallelograms that **have one angle of the one equal to one angle of the other,** and their sides about the equal angles reciprocally proportional, are equal to one another. LET ab,... | |
| Euclides - Geometry - 1853
...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... | |
| William Somerville Orr - Science - 1854
...PROPOSITION XV.— THEOKBM. Equal triangles (ABC, ADE), which have an angle (A) of the one equal to au **angle of the other, have their sides about the equal angles reciprocally proportional ; and** triangles which have an angle of the one equal to an angle of the other, and their sides about those... | |
| John Playfair - Geometry - 1855 - 318 pages
...wherefore the parallelogram AB is equal (9. 5.) to the parallelogram BC. PROP. XV. THEOR. Equal triangles **which have one angle of the one equal to one angle of the other have their** sfdes about the equal angles reciprocally proportional; And triangles which have one angle in the one... | |
| 1855
...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
...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... | |
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