 | Robert Simson - 1827 - 546 sider
...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 sider
...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... | |
 | John Martin Frederick Wright - 1831 - 282 sider
...axis intercepted between the origin and the normal. TRINITY COLLEGE, 1829. 1 . EQUIANGULAR / — 73 have to one another the ratio which is compounded of the ratios of their sides. 2. If two straight lines be J_ to the same plane, they are || to one another. 3. Required the value... | |
 | 1831 - 532 sider
...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... | |
 | John Playfair - 1832 - 358 sider
...equal to GH, AB is to CD, as EF to GH. If therefore four straight lines, &c. QED PROP. XXIII. THEOR. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Let AC,CF be equiangular parallelograms having the angle BCDequal to the angle ECG; the ratio of the parallelogram... | |
 | John Playfair - 1833 - 346 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 EC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14. 1.) ; complete... | |
 | Euclides - 1834 - 518 sider
...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... | |
 | Robert Simson - 1835 - 544 sider
...GH; AB is to CD, as EF to GH. " If, therefore, four straight lines, &c. QED PROP. XXIII. THEOR. See N. Equiangular parallelograms have to one another...the same with the ratio which is compounded of the ratio of their sides. Let BC, CG be placed in a straight line ; therefore DC Book vI. and'CE are also... | |
 | Euclid - 1835 - 540 sider
...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 Playfair - 1836 - 488 sider
...equal to GH, AB is to CD, as EF to GH. If therefore four straight lines, &c. QED PROP. XXIII. THEOR. Equiangular parallelograms have to one another the...the parallelogram AC to the parallelogram CF is the saine with the ratio which is compoundgd of the ratios of their sides. Book VI. Let BC, CG be placed... | |
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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 CF... 
