| John Playfair - 1842 - 332 sider
...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. 1.); complete... | |
| Euclides - 1845 - 546 sider
...to CD, as EF to GH. (v. 7-) If, therefore, four straight lines, &c. QED PROPOSITION XXIII. THEOREM. **Equiangular parallelograms have to one another the...parallelograms, having the angle BCD • equal to the angle ECG.** Then the ratio of the parallelogram AC to the parallelogram CF, shall be the same with the ratio which... | |
| Euclid - 1845 - 218 sider
...; AB is to CD, as EF to GH. If therefore four straight lines, &c. QED PROPOSITION XXIII. THEOB. — **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** BOOK VI. PROP. XXIV. • 14. 1. t 12. 6. t 12. 6. A. Def. 5. V 11.5. Let BC, CG be placed in a straight... | |
| Euclides, James Thomson - 1845 - 382 sider
...&c.* Cor. Triangles which have one angle of the one equal, or supplemental, to one angle of the other, **have to one another the ratio which is compounded of the ratios of** the sides containing those angles. For, if BD and EG be joined, the triangles BCD, ECG bemg (I. 34)... | |
| Euclides - 1846 - 292 sider
...having the angle BCD equal to the angle ECG : the parallelogram AC shall be to the parallelogram CF in **the ratio which is compounded of the ratios of their sides. Let** BC, CG be placed in a straight line ; therefore DC and CE will be also in a straight line : complete... | |
| Euclides - 1848 - 52 sider
...straight lines be proportionals, those straight lines shall be proportionals. PROP. XXIII. THEOREM. **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** PROP. XXIV. THEOREM. The parallelograms about the diameter of any parallelogram, are similar to the... | |
| John Playfair - 1849 - 332 sider
...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...parallelograms having the angle BCD equal to the angle ECG** ; tbe ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded... | |
| 1851 - 268 sider
...have their sides about their equal angles reciprocally proportional. .3. Equiangular paralellograms **have to one another the ratio which is compounded of the ratios of their sides.** SECTION IV. 1. Upon a given base to describe an isosceles triangle equal to a given rectangle. 2. To... | |
| Sir James Kay-Shuttleworth - 1853 - 554 sider
...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 - 524 sider
...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.... | |
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