| Euclides, James Hamblin Smith - 1872 - 349 sider
...are together equal to four times the quadrilateral figure. PROPOSITION XXVI. THEOREM. (Eucl. vi. 23.) **Equiangular parallelograms have to one another the ratio, which is compounded of the ratios of** their sides. B. JI \ \. K. ZM Let AC and CF be equiangular Os, baving L BCD = L ECG. Then must LJ AC... | |
| Charles Astor Bristed - 1874 - 572 sider
...of gravity. SENATE-HOUSE EXAMINATION. FRIDAY, Jan. 3, 1845. 9 . . . ll£. 1. DEFINE compound ratio. **Equiangular parallelograms have to one another the ratio which is compounded of the ratios of** their sides. 2. Draw a straight line perpendicular to a plane from a given point above it. a. Show... | |
| Euclides - 1874
...to a similar and similarly described triangle upon the second, PROP. XIV.— THEOREM. (Eoo. VI. 23.) **Equiangular parallelograms have to one another the ratio which is compounded of the ratios of** their sides. Let ABCD and CHGF be two equiangular parallelograms, having the angles BCD and HCP equal,... | |
| Euclides - 1874
...is to CD, as EF to GH (V. 7). If therefore, four straight lines, &c. QED PROPOSITION 23. —Theorem. **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.... | |
| Braithwaite Arnett - 1874
...AE, AD will be equal to the rectangle AB, AC. 8. Parallelograms which are equiangular to one another **have to one another the ratio which is compounded of the ratios of** their sides. 9. ABCD is a rectangle, and E, F, G, and H are the feet of the perpendiculars let fall... | |
| Robert Potts - 1876 - 403 sider
...parallelograms are proportional to the squares of their homo-' logons sides. 36. How is it shewn that **equiangular parallelograms have to one another the ratio which is compounded of the ratios of** their bases and altitudes? 37. To find two lines which shall have to each other, the ratio com. pounded... | |
| Richard Wormell - 1876
...four straight lines be proportionals, those straight lines shall be proportionals. .. .. .. 215 23. **Equiangular parallelograms have to one another the ratio which is compounded of the** ratio of their sides. . . . . ' . . . . . . 215 24. The parallelograms about the diagonal of any parallelogram... | |
| Samuel H. Winter - 1877 - 413 sider
...through A in the points D,E respectively, prove that BD ; DA ; ; CE : EA. 12. Define compound ratio. **Equiangular parallelograms have to one another the ratio which is compounded of the ratios of** their sides. 13. Prove that every equilateral polygon inscribed in a circle must be equiangular. Is... | |
| Great Britain. Education Department. Department of Science and Art - 1877
...their angles proportional, the triangles will be similar. 2. Prove that the areas of two rectangles **have to one another the ratio which is compounded of the ratios of** their sides ; and thence show that, if a perpendicular be drawn from one of the angles of a rectangle... | |
| James McDowell - 1878
...we may concisely express it, as AB3 : CD3. Euclid has proved (YI. 23) that rectangles (for they are **equiangular parallelograms) have to one another the ratio which is compounded of the ratios of** their sides. If, therefore, BC, CD and CG, CE be the adjacent sides of two rectangles, Therefore the... | |
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