| Robert Potts - 1855 - 1050 Seiten
...angles to each of them in that point; these three straight lines are in cue and the same plane. 14. **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** Draw a straight line perpendicular to the plane of a triangle such that if any point in it be joined... | |
| Euclides - 1855 - 226 Seiten
...similarly situated. They are to one another as 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... | |
| Noble Heath - 1855 - 468 Seiten
...multiplying the base by its perpendicular height or altitude, (103,) it is evident that the areas of any two **parallelograms have to one another the ratio which is compounded of the ratios of their** bases and altitudes. Hence we deduce the following properties : 1. Parallelograms of equal base and... | |
| Noble Heath - 1856 - 472 Seiten
...multiplying the base by its perpendicular height or altitude, (103,) it is evident that the areas of any two **parallelograms have to one another the ratio which is compounded of the ratios of their** bases and altitudes. Hence we deduce the following properties : 1. Parallelograms of equal base and... | |
| 1857 - 1266 Seiten
...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 - 132 Seiten
...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 - 672 Seiten
...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... | |
| John Playfair - 1860 - 332 Seiten
...to CD, so is EF to PR, and because PR is equal to GH, AB is to CD, as EF to GH. PROP. XXIII. THEOR. **Equiangular parallelograms have to one another the...angle ECG; the ratio of the parallelogram AC to the** paral lelogram CF, is the same with the ratio which is compounded of the ratiot of their sides. 1 M... | |
| Euclides - 1860 - 286 Seiten
...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 - 361 Seiten
...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... | |
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