| Sir James Kay-Shuttleworth - 1853 - Liczba stron: 500
...to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** Section 4. 1. Upon a given base to describe an isosceles triangle equal to a given rectangle. 2. To... | |
| Sir James Kay-Shuttleworth - 1853 - Liczba stron: 500
...their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms hare **to one another the ratio which is compounded of the ratios of their sides.** Section 4. 1. Upon a given base to describe an isosceles triangle equal to a given rectangle. . 2.... | |
| Euclides - 1853
...THEOE. If two parallelograms have one angle of the one equal to one angle of the other : then they shall **have to one another the ratio which is compounded of the ratios of** each pair of sides about the equal angles. Let ABCD, EFGH be two parallelograms, having the angle ABC... | |
| Royal Military Academy, Woolwich - 1853
...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 - 1853 - Liczba stron: 147
...the angle e С g '• the ratio of the parallelogram a С to the parallelogram. С fis the same with **the ratio which is compounded of the ratios of their sides. Let** bС, С g be placed in a straight line ; therefore d С and С e are also in a straight line (i. 14)... | |
| Euclides - 1855
...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
...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... | |
| Noble Heath - 1855 - Liczba stron: 455
...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... | |
| Euclides - 1855
...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 - 1856 - Liczba stron: 455
...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... | |
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