| John Playfair - Geometry - 1855 - 350 pages
...5.) : 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** ih* other have their sides about the equal angles reciprocally proportional ; And triangles which have... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and **triangles which 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 ABC,... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and **triangles which 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 ABC,... | |
| Edinburgh univ - 1868 - 336 pages
...rectangle contained 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 (x + y + z),... | |
| Mathematics - 1868 - 272 pages
...Let the lines 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 triangles... | |
| E. M. Reynolds - Geometry - 1868 - 172 pages
...equiangular to A' B'C' ; 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'... | |
| Robert Potts - 1868 - 434 pages
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOREM. 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... | |
| Education, Higher - 1884 - 538 pages
...other pair of homologous sides shall either be equal, or be together equal to two right angles. 15. **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 their sides. Algebra. Junior, Senior,... | |
| Simon Newcomb - Geometry - 1881 - 418 pages
...such sides is equal to the rectangle of the sides of the parallelogram. THEOREM 8. If two triangles **have one angle of the one equal to one angle of the other,** and the perpendiculars from the other two angles upon the opposite sides proportional, they are similar.... | |
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