| Benjamin Theophilus Moore - 1863 - Liczba stron: 278
...area of a rectangle. In Euclid's Elements of Geometry, Book VI. Proposition 23, it is proved that " **Equiangular parallelograms have to one another the...ratio which is compounded of the ratios of their sides** ;" and therefore rectangles, which are equiangular parallelograms, have to one another this same ratio.... | |
| University of Cambridge - 1864
...its angular points on the same circle and all its angles equal, then shall all its sides be equal. 5. **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** If one parallelogram have to another parallelogram the ratio which is compounded of the ratios of their... | |
| Henry White - 1864
...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)... | |
| William Walton - 1864 - Liczba stron: 212
...sideAB = CD = EF=...= ZA = BC=..., the number of sides being odd. So that all the sides are equal. 5. **Equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** If one parallelogram have to another parallelogram the ratio which is compounded of the ratios of their... | |
| Euclides - 1864
...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 ? 37. To find two lines which shall have to each other, the ratio compounded of... | |
| Euclides - 1865
...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,... | |
| Civil service - 1866
...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 - Liczba stron: 400
...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 - Liczba stron: 400
...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 - Liczba stron: 141
...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.... | |
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