| War office - 1861 - 12 sider
...that is, to divide it into two equal parts. VOLUNTARY PORTION. 1. Define compound ratio. Prove that **equiangular parallelograms have to one another the...which is compounded of the ratios of their sides.** 2. Define a plane. When is a straight line perpendicular to a plane ? Draw a straight line perpendicular... | |
| Euclides - 1861
...DFalso = fig. AC; — which is impossible : .-. EF not ф BC ; ,. e., EF = BC. QED PÜOP. 23. — THEOR. **Equiangular parallelograms have to one another the ratio which is compounded of the** ratio of their sides. CON. 14, 1. 31, I. 12, VI. DEM. Def. AV of Compound Ratio. When there arc any... | |
| Edward Butler (A.M.) - 1862
...triangles, a and a' homologous sides. Then, T= )rf , and T'=j . smA " smA Whence, J_£ 70. 7%« areas of **equiangular parallelograms have to one another, the ratio which is compounded of the ratios** iff the sides. (B. vi., Prop, xxiii.) Let P and P' be equiangular parallelograms, a and b two adjacent... | |
| George Sturton Ward - 1862 - 79 sider
...the ratio) compounded of 'the ratios of their sides." The same parallelopipeds may also be shewn to **have to one another the ratio which is compounded of the ratios of their** edges. When a ratio is compounded of several ratios, all of •which are the same, it is termed a duplicate... | |
| Benjamin Theophilus Moore - 1863 - 278 sider
...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.... | |
| William Walton - 1864 - 212 sider
...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... | |
| 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)... | |
| 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... | |
| 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,... | |
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