 | Euclides - 1865 - 402 σελίδες
...is to CD, as EF to OH. (T. 7.) If, therefore, four straight lines, &c. QED PROP. XXIII.— THEOREM. Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides, (References— Prop. i. U ; v. 11, 22, def. A ; VI. 1, 12.) Let AC, CF be eqniangolar parallelograms,... | |
 | Robert Potts - 1865 - 528 σελίδες
...parallelograms, are proportional to the squares on 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 ? 37. To find two lines which shall have to each other, the ratio compounded of... | |
 | Civil service - 1866 - 270 σελίδες
...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)... | |
 | Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...the following theorem, triangles which have one angle of tJie 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. ig is an immediate consequence of this theorem. For let ABC and DEF be similar triangles,... | |
 | Euclid, Isaac Todhunter - 1867 - 424 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | Woolwich roy. military acad - 1868 - 426 σελίδες
...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... | |
 | 1868 - 272 σελίδες
...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.) - 1869 - 196 σελίδες
...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)... | |
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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... 
