| Euclides - 1865 - 402 pages
...equiangular, and shall have those angles equal which are opposite to the homologous sides. Prop. 7. **If two triangles have one angle of the one equal to one angle of** tha other, and the sides about two other angles proportionals ; then, if each of the remaining angles... | |
| Robert Potts - 1865 - 528 pages
...lines AB, BC, & mean proportional DB is iound. QBF PROPOSITION XIV. THEOREM. Equal parallelograms which **have one angle of the one equal to one angle of the other,** hate their sides about the equal angles reciprocally proportional: and conversely, parallelograms that... | |
| James Robert Christie - Mathematics - 1866 - 426 pages
...the 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. CO-ORDINATE... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...and shall have those angles equal about which the sides are proportionals. Let the triangles ABC, DEF **have one angle of the one equal to one angle of the other,** namely, the angle BA C equal to the angle EDF, and the sides about two other angles ABC, DEF, proportionals,... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...Hence the result may be extended to triangle?, and we hava the following theorem, triangles which, ham **one angle of the one equal to one angle of the other,** have to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 is an immediate... | |
| Mathematics - 1868 - 272 pages
...joining the point P to the points A and B cut a line in the points a, /3. The areas of triangles which **have one angle of the one equal to one angle of the other,** have to one another the ratio which is compounded of the ratios of the sides. Applying this to the... | |
| Robert Potts - 1868 - 434 pages
...AB, BC, a mean proportional DB is found. QEF PEOPOSITION 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 that... | |
| E. M. Reynolds - Geometry - 1868 - 172 pages
...; Therefore ABC is equiangular to A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which **have one angle of the one equal to one angle of the other,** are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC'... | |
| Edinburgh univ - 1868 - 334 pages
...by the segments of the other. 4. To inscribe a circle in a given triangle. 5- 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. 6. Find the continued product of... | |
| Sir Norman Lockyer - Electronic journals - 1902 - 846 pages
...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... | |
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