| Euclides - 1865 - 402 Seiten
...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 Seiten
...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 - 272 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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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