| George Roberts Perkins - Geometry - 1856 - 460 pages
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they have an angle of the one equal to an angle of the other. All squares are similar figures. All regular polygons of the same number of sides are similar figures.... | |
| Euclid - 1859 - 136 pages
...rpiywvwv, àvriirtirèvQaaiv at ir\tvpai, ai irepi ràç; îffaç ywviaç, laa iariv iKtlva. Equal triangles which have an angle of the one equal to an angle of the other have their sides about the equal angle* reciprocally proportional ; and triangles which have an angle... | |
| Eucleides - 1860 - 396 pages
...If equal parallelograms have an angle of the one equal to an angle of the other. If parallelograms have an angle of the one equal to an angle of the other, and their sides about the equal angles reciprocally proportional. If parallelograms are about the diameter... | |
| George Roberts Perkins - Geometry - 1860 - 474 pages
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they have an angle of the one equal to an angle of the other. All squares are similar figures. All regular polygons of the same number of sides are similar figures.... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...They are almost sufficient of themselves for all applications to subsequent reasoning, and for the solution of all problems ; since the general properties...the two triangles ABC, DEF have the angle A equal to the angle D, and the sides containing these angles proportional, so that AB:DE::AC:DF; then the triangles... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...problems ; since the general properties of triangles include, by implication, those of all f1gures. PROPOSITION XXIV. — THEOREM. 264. Two triangles,...the two triangles ABC, DEF have the angle A equal to the angle D, and the sides containing these angles proportional, so that AB:DE::AC:DF; then the triangles... | |
| Euclides - 1863 - 122 pages
...angles reciprocalla proportional (tbat is, DB is to BE a« GB /stoBF); and, converseln, parallelograms which have an angle of the one equal to an angle of the other, and their sides about the equalangles reciprocallg proportional, are equal to one another. Place the parallelograms... | |
| Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...: hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM V. Two triangles having an angle of the one equal to an angle of the other, and the sides about those angles proportional, are similar. Let the two triangles ABC, DEF, have the angle A equal... | |
| Euclides - 1865 - 402 pages
...the three sides of a triangle to the opposite angles meet in the same point. 14. If two trapezinms have an angle of the one equal to an angle of the other, and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
| Benjamin Greenleaf - Geometry - 1866 - 328 pages
...They are almost sufficient of themselves for all applications to subsequent reasoning, and for the solution of all problems ; since the general properties...proportional, are similar. Let the two triangles ABC, DBF have the angle A equal to the angle D, and the sides containing these angles proportional, so that... | |
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