 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...hava the following theorem, triangles which, ham 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 their sides. Then VI. 19 is an immediate consequence of this theorem. For let ABC and DEF be similar triangles,... | |
 | Euclid - 1868 - 138 pages
...Та laoyúvia я-apaXX1)Xóуpa/1/ш irpоc a\\rf\a \oyov ?^fi TÔv avyKfifiivov ÍK TÜV ir\evpwv. Equiangular parallelograms have to one another the...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
...parallelograms are 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... | |
 | Woolwich roy. military acad - 1868 - 426 pages
...circles in E and F respectively, show that if AB produced meet EF in C then EC is equal to FO. 11. Equiangular parallelograms have to one another the ratio which is compounded of the ratio of their sides. Assuming that the area of a triangle may be represented by half the product of... | |
 | 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... | |
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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... 
