Solid parallelepipeds contained by parallelograms equiangular to one another, each to each, that is, of which the solid angles are equal, each to each, have to one another the ratio compounded of the ratios of their sides. The The Thirteen Books of Euclid's Elements - Page 347by Euclid, Johan Ludvig Heiberg - 1908Full view - About this book
| Samuel Hunter Christie - 1847
...bases, and altitudes equal to the altitudes of the prisms, (to which the prisms are respectively equal,) **have to one another the ratio compounded of the ratios of their** bases and altitudes (Prop. 58), that is, the ratio compounded of the ratios of the bases and altitudes... | |
| Euclides - 1848
...straight line has to the fourth the triplicate ratio of that which it has to the second. PROP. D. THEOREM. **Solid parallelepipeds contained by parallelograms...equal, each to each, have to one another the ratio** which is the same with the ratio compounded of the ratios of their sides. PROP. XXXIV. THEOREM. The... | |
| Euclides - 1855
...triplicate ratio of that which it has to the second. PROPOSITION D. THEOREM.—If solid parallelepipeds are **contained by parallelograms equiangular to one another,...of which the solid angles are equal, each to each,** they have to oue another the ratio which is the same with the ratio compounded of the ratios of their... | |
| Euclides - 1855
...solid content i.lull uimilHi ..,.11.1. I i. . . . , i.<m* PROP. D. THEOREM. Parallelepipeds which are **contained by parallelograms equiangular to one another,...each, that is, of which the solid angles are equal,** ecck to each, have to one anotiier the ratio which is the same with the ratio compounded of the ratios... | |
| 1856
...HIGHER MATHEMATICS, No. I. Euclid, Surveying, and Practical Astronomy. 2. Equiangular parallelograms **have to one another the ratio compounded of the ratios of their sides.** SECT. I.—1. The sides about the equal angles of equiangular triangles are proportionals, and those... | |
| Great Britain. Privy Council. Committee on Education - 1856
...Practical Astronomy. (Three Hours allowed for this Paper.) Section 1. 2. Equiangular parallelograms **have to one another the ratio compounded of the ratios of their sides.** 1. The sides about the equal angles of equiangular triangles are proportionals ; and those which are... | |
| Euclid - 1866 - 388 pages
...fourth the trip, r° of that w h it has to the second. PROP. D THEOR. Solid parallelopipeds which are **contained by parallelograms equiangular to one another,...equal, each to each, have to one another the ratio** which is the same with the ratio compounded of the ratios of their sides. Let AB, CD be solid ßj s... | |
| Geometry - 1868
...another as their bases ....... 73 FIVE COROLLARIES , ... 74 THEOREM it. Equiangular parallelograms **have to one another the ratio compounded of the ratios of their sides** . . 76 Six COROLLARIES * 76 THEOREM 13. In any circle angles at the centre have to one another the... | |
| 1869
...altitude are to one another as their bases 153 FIVE COROLLARIES 154 THEOREM u. Equiangular parallelograms **have to one another the ratio compounded of the ratios of their sides** . .156 Six COROLLARIES 156 THEOREM 13. In any circle angles at the centre have to one another the ratio... | |
| Alexander Charles Ewald - Civil service - 1870 - 268 pages
...other part. In what numerical ratio is the line divided ? 3. Prove that equiangular parallelograms **have to one another the ratio compounded of the ratios of their sides.** What form does this theorem take in trigonometry ? 4. Solve the following equations:— m 1 2 3 5 V... | |
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