| John Martin Frederick Wright - 1827 - 344 Seiten
...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 - 513 Seiten
...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,... | |
| Euclid, Robert Simson - 1829 - 516 Seiten
...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.** • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight... | |
| John Playfair - 1829 - 186 Seiten
...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... | |
| Pierce Morton - 1830 - 584 Seiten
...37. Cor. 4.) ; therefore, the ratio which is compounded of the ratios of С D* to QN= and N A2 to PT1 **is the same with the ratio which .is compounded of the ratios of** CP- to CNa — С P1 and С N - to С Р-, the same, that is, with the ratio of С N * to С N - —... | |
| John Martin Frederick Wright - 1831
...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 Seiten
...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 - 333 Seiten
...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 - 333 Seiten
...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 Seiten
...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... | |
| |