 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14. i.) ; and... | |
 | Euclides - 1855 - 270 pages
...described upon them, are also continual proportionals ; and amversely. PROP. XXIIL THEOREM. taugu/ar parallelograms have to one another the ratio which is compounded of the ratios of their sides Let AC and CF be equiangular parallelograms, having the angle BCD equal to the angle EC G. The ratio of the... | |
 | Robert Potts - 1855 - 1050 pages
...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 - 230 pages
...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 pages
...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 - Arithmetic - 1856 - 472 pages
...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... | |
 | Education - 1857 - 1266 pages
...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... | |
 | Euclid - 1859 - 150 pages
...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 pages
...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 - Geometry - 1860 - 334 pages
...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... | |
| |
Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF... 
