 | Euclides - 1842 - 316 pages
...c, D be four straight lines, and if л : в : : c : D, then A* : B* : : c* : D*. PROP. XXIII. THEOR. EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratio of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle... | |
 | John Playfair - Euclid's Elements - 1842 - 332 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. 1.); complete... | |
 | Euclides - 1845 - 546 pages
...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 - Geometry - 1845 - 218 pages
...; 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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...&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)... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 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...the same with the ratio which is compounded of the ratios of their sides. J L B ( 3 D M N 141 DH M the ratio compounded of the ratios of the sides of... | |
 | Euclides - 1846 - 292 pages
...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 pages
...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 - Euclid's Elements - 1849 - 332 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...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 pages
...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... | |
| |
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... 
