 | 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... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...of a pair of corresponding sides involves the identity of the triangles. THEOREM 7. If two triangles have one angle of the one equal to one angle of the other; and the sides about the equal angles proportionals, then will the triangles be similar. Let the triangles ABC,... | |
 | Edinburgh univ - 1868 - 336 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... | |
 | 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... | |
 | 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'... | |
 | 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... | |
 | Sir Norman Lockyer - Electronic journals - 1902 - 1086 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... | |
 | George Bruce Halsted - Measurement - 1881 - 258 pages
...both sides of a rectangle from their ratio m : n, and its area R. \mR Ans. n \ m 521. If two triangles have one angle of the one equal to one angle of the other, and the sides about a second angle in each equal, then the third angles will be either equal or supplemental.... | |
 | Education, Higher - 1883 - 536 pages
...proportion. When is a straight line said to be cut in extreme and mean ratio ? 14. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angels reciprocally proportional ; and triangles which have one angle... | |
| |
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. 
