 | Mathematics - 1868 - 272 pages
...points a, /3. The areas of triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides. Applying this to the triangles PAB, Pa/8, which have the angle at P common, we have algebraically... | |
 | Robert Johnston (F.R.G.S.) - Civil service - 1869 - 196 pages
...extremities of the base have the same ratio which the other sides of the triangle have to one another. 7. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 8. Trisect a given straight line. 9. Construct a rectangle which shall be equal to a given square (1)... | |
 | Edinburgh univ - 1871 - 392 pages
...angular points of the triangle, the greatest of these shall be equal to the other two together. 6. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. 8. If the angle of a triangle be bisected, and perpendiculars be drawn to the bisecting line from the... | |
 | Dublin city, univ - 1871 - 366 pages
...triangles will be equiangular, and will have those angles equal about which the sides are proportional ? 8. Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides ? DR. STUBBS. 1. The square of the bisector of the vertical angle of a triangle... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...are together equal to four times the quadrilateral figure. PROPOSITION XXVI. THEOREM. (Eucl. vi. 23.) Equiangular parallelograms have to one another the...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 have to EH... | |
 | Euclides - 1874 - 342 pages
...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...parallelograms, having the angle BCD equal to the angle ECG. Then the ratio of the parallelogram AC to the parallelogram CF, shall be the same with the ratio which... | |
 | Charles Astor Bristed - 1874 - 632 pages
...of gravity. SENATE-HOUSE EXAMINATION. FRIDAY, Jan. 3, 1845. 9 . . . ll£. 1. DEFINE compound ratio. Equiangular parallelograms have to one another the...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 how to find the... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...the other, have the sides ahout the equal angles reciprocally proportional. Cor. 3. — Hence also equiangular parallelograms have to one another the...which is compounded of the ratios of their sides. Schol. — If an oblique-angled parallelogram be taken, and the same construction made as in I. App.,... | |
 | Braithwaite Arnett - 1874 - 130 pages
...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 upon the diagonals... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...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 of... | |
| |
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... 
