| John Playfair - 1846 - 332 Seiten
...which is compounded of the ratios of the solid AF to the solid GS, and of the solid GS to the solid GO, **is the same with the ratio which is compounded of the ratios of** the base AC to the base GK, and of the altitude AE to the altitude GM (F. 5.). But the ratio of the... | |
| Euclides - 1846 - 292 Seiten
...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 Seiten
...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 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...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 Seiten
...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 Seiten
...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 - 516 Seiten
...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 - 334 Seiten
...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... | |
| Euclides - 1853 - 176 Seiten
...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 - 258 Seiten
...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... | |
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