| 1831
...and join AB and DE. The parallelograms CF and CO are evidently equiangular ; they have, therefore, **to one another the ratio which is compounded of the ratios of their sides** (23 of VI); that is, the ratio which is IMPROVED MODE OF PRESERVING BEBH FROM SOCRINC. of the ratios... | |
| Euclides - 1834
...ratios that are the same with the ratios of the sides. And to this demonstration agrees the enunciation **have to one another the ratio which is compounded of the ratios of** the sides ; for the vulgar reading, " which is compounded of their sides," is absurd. But, iu this... | |
| Euclid - 1835 - Liczba stron: 513
...of the sides. And to this demonstration agrees the enunciation which is at present in the text, viz. **Equiangular parallelograms have to one another the ratio which is compounded of the ratios of** the sides : For the vulgar reading, " which is compounded of their sides," is absurd. But, in this... | |
| John Martin Frederick Wright - 1836
...which the other sides of the triangle have to one another. Shew that the converse is also true. 2. **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** 3. The rectangle contained by the diagonals of any quadrilateral figure inscribed in a circle is equal... | |
| 1836 - Liczba stron: 472
...straight lines be proportionals, those straight lines shall be proportionals. XXIII. Equian. guiar **parallelograms have to one another the ratio which is compounded of the ratios of their sides.** XXIV. The parallelograms about the diameter of any parallelogram, are similar to the whole, and to... | |
| John Playfair - 1836 - Liczba stron: 114
...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 (2. 1.) ; and... | |
| Euclid, James Thomson - 1837 - Liczba stron: 390
...&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 being (I. 84.)... | |
| Andrew Bell - 1837 - Liczba stron: 240
...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** EC, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (I. 14) ; and... | |
| Euclid, Robert Simson - 1838 - Liczba stron: 416
...and that PR is equal to GH ; AB is to CD, as EF to GH. If, therefore, four straight lines, &c. QED **PROP. XXIII. THEOR. EQUIANGULAR parallelograms have...CF be equiangular parallelograms, having the angle** * See Note. BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF,... | |
| 1840
...at the heginning of the year. SENATE-HO.USE EXAMINATION. WEDNESDAY. Jan. 8, 1840 ____ 9 to 1IJ. 1. **EQUIANGULAR parallelograms have to one another the...which is compounded of the ratios of their sides.** 2. Every solid angle is contained hy plane angles which tire together less than four right angles.... | |
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