 | Euclid - 1868 - 138 pages
...я-apaXX1)Xóуpa/1/ш irpоc a\\rf\a \oyov ?^fi TÔv avyKfifiivov ÍK TÜV ir\evpwv. Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Statement Let AC and CF be equiangular parallelograms, having the angle BCD equal to the angle ECG.... | |
 | Robert Potts - 1868 - 434 pages
...proportional to the squares of their homologous 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 r 37. To find two lines which shall have to each other, the ratio compounded of... | |
 | 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
...same ratio which the other sides of the triangle have to one another. 7. Equiangular parallelograms have to one another the ratio 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
...triangle, the greatest of these shall be equal to the other two together. 6. Equiangular parallelograms have to one another the ratio 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... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...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 have to EH... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...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, and therefore... | |
 | Charles Astor Bristed - 1874 - 632 pages
...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 how to find the... | |
 | Euclides - 1874 - 342 pages
...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. Then the ratio... | |
 | 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... | |
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Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. 
