 | Euclides - 1816 - 588 pągines
...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 Mason Good - 1819 - 800 pągines
...similarly described upon four straight lines be proportionals, those straight lines shall be proportionals. Prop. XXIII. Theor. Equiangular parallelograms have...which is compounded of the ratios of their sides. Prop. XXIV. Theor. The parallelograms about the diameter of any parallelogram, are similar to the whole,... | |
 | Euclid, Robert Simson - 1821 - 514 pągines
...PR, 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...which is compounded of the ratios of their sides.* Lot AC, CF be equiangular parallelograms, having the angle BCD ^qual to the angle ECG: the ratio of... | |
 | Peter Nicholson - 1825 - 1046 pągines
...PR is equal to GH ; AB is to CD, as EF to GH. If therefore four straight lines, &c. QED PROP. XXJIL THEOR, Equiangular parallelograms have to one another...is compounded of the ratios of their sides. Let AC, С F be equiangular parallelograms, baring the angle BCD CEOMETRV. logram CF, is the same with the... | |
 | Euclid - 1826 - 234 pągines
...QED Deduction, PROPOSITION XXIII. THEOREM. Equiangular parallelograms are to one another in a ratio compounded of the ratios of their sides. Let AC, CF,...equiangular parallelograms having the angle BCD equal to ECG, then the parallelogram AC is to the parallelogram CF in a ratio compounded of the ratios of their... | |
 | Euclides - 1826 - 226 pągines
...QED Deduction. PROPOSITION XXIII. THEOREM. Equiangular parallelograms are to one another in a ratio compounded of the ratios of their sides. Let AC, CF,...equiangular parallelograms having the angle BCD equal to ECG, then the parallelogram AC is to the parallelogram CF in a ratio compounded of the ratios of their... | |
 | John Martin Frederick Wright - 1827 - 344 pągines
...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... | |
 | John Martin F. Wright - 1827 - 632 pągines
...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... | |
 | Robert Simson - 1827 - 546 pągines
...the sides. And with 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 edition,... | |
 | John Playfair - 1829 - 210 pągines
...duplicate ratio of that which their homologous sides have to each other. ED. PROPOSITION XXIII. THEOREM. Equiangular parallelograms have to one another the...ratio which is compounded of the ratios of their sides about the equal angles ; " that is, they are to one another as the rectangles contained by the sides... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
