| 1857
...shall be equiangular, and shall have those angles equal about which the sides are proportional. 2. **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** 3. If the sides of any polygon be produced to meet the alternate sides, also produced, the angles formed... | |
| Euclides - 1859
...Ta "taoyúvia rrapaXXqXóypa/i/ia irpоçâXXqXa Xóyov ÉXC* Tоv ffvyKtípívov ¿K TÜV ir\ivpwv. **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** Statement — Let AC and CF be equiangular parallelograms, having the angle BCD equal to the angle... | |
| Sandhurst roy. military coll - 1859 - Liczba stron: 1869
...a circle for the base and the vertex on the circumference, determine that which is the greatest. 2. **Equiangular parallelograms have to one another the ratio which is compounded of the** ratio of their sides AB, AD, the sides of a rectangle, are 8 and 6, parallelograms are described about... | |
| Euclides - 1860
...squares are proportional, and conversely. For squares are similar figures. PROPOSmOS XXIII. THEOREM. **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** Given AC and CF two equiangular parallelograms, having the angle BCD equal to the angle ECG ; to prove... | |
| Robert Potts - 1860 - Liczba stron: 361
...parallelograms are proportional to the squares of their homologous sides. 36. How is it s.hewn that **equiangular parallelograms have to one another the ratio which is compounded of the ratios of their** bases and altitudes ? 37. To find two lines which shall have to each other, the ratio compounded of... | |
| Eucleides - 1860
...similarly situated. fThey are to one another as -j the rectangles under their ( bases and altitudes. They **have to one another the ratio which is compounded of the ratios of their sides.** Their sides about the eqnal angles are reciprocally proportional. They are equal to one another. .They... | |
| War office - 1861 - Liczba stron: 12
...that is, to divide it into two equal parts. VOLUNTARY PORTION. 1. Define compound ratio. Prove that **equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** 2. Define a plane. When is a straight line perpendicular to a plane ? Draw a straight line perpendicular... | |
| Euclides - 1861
...nowfig, DFalso = fig. AC; — which is impossible : .-. EF not ф BC ; ,. e., EF = BC. QED PÜOP. 23. — **THEOR. Equiangular parallelograms have to one another the ratio which is compounded of the** ratio of their sides. CON. 14, 1. 31, I. 12, VI. DEM. Def. AV of Compound Ratio. When there arc any... | |
| George Sturton Ward - 1862 - Liczba stron: 79
...the ratio) compounded of 'the ratios of their sides." The same parallelopipeds may also be shewn to **have to one another the ratio which is compounded of the ratios of their** edges. When a ratio is compounded of several ratios, all of •which are the same, it is termed a duplicate... | |
| Edward Butler (A.M.) - 1862
...triangles, a and a' homologous sides. Then, T= )rf , and T'=j . smA " smA Whence, J_£ 70. 7%« areas of **equiangular parallelograms have to one another, the ratio which is compounded of the ratios** iff the sides. (B. vi., Prop, xxiii.) Let P and P' be equiangular parallelograms, a and b two adjacent... | |
| |