| Euclides - 1845 - 544 pages
...cylinders of the same altitude are to one another as their bases. QED PROPOSITION XII. THEOREM. Similar **cones and cylinders have to one another the triplicate ratio of that which the diameters of their** bases have. Let the cones and cylinders of which the bases are the circles ABCD, EFGH, and the diameters... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...cylinders upon them of the same altitude. Cones and cylinders, therefore, &c. PROP. XII. THEOR. — Similar **cones and cylinders have to one another the triplicate ratio of that which the diameters of their** bases have. If there be similar cones and cylinders of which the hases are the circles ABCD, EFGH ;... | |
| Euclides - 1848 - 52 pages
...THEOREM. Cones and cylinders of the same altitude are to one another as their PROP. XII. THEOREM. Similar **cones and cylinders have to one another the triplicate ratio of that which the diameters of their** bases have. PROP. XIII. THEOREM. If a cylinder be cut by a plane parallel to its opposite planes, or... | |
| Euclides - 1855 - 230 pages
...upon them of the same altitude. PROPOSITION XII. THEOREM.—If cones and cylinders are similar, they **have to one another, the triplicate ratio of that which the diameters of their** bases have. DEMONSTRATION. Let the cones and cylinders of which the bases are the circles ABCD, EFGH,... | |
| Euclides - 1855 - 262 pages
...altitude are to one another as their bases. QED PROP. XII. THEOREM. Similar cones and cylinders ham **to one another the triplicate ratio of that which the diameters of their** bases have. Let the conts and cylinders of which the circles AB СD and EFGH are the bases, A С and... | |
| Eucleides - 1860 - 396 pages
...them of the' same altitude. PROPOSITION XII. THEOBEM. — If cones and cylinders are similar, they **have to one another, the triplicate ratio of that which the diameters of their** bases have. DEMONSTRATION. Let the cones and cylinders of which the bases are the circles ABCD, EFGH,... | |
| Robert Potts - 1865 - 528 pages
...cylinders of the same altitude are to one another as their \ases. PROPOSITION XII. THEOREM. Similar **cones and cylinders have to one another the triplicate ratio of that which the diameters of their** bases have. PROPOSITION XIII. THEOREM. If a cylinder be cot by a plane parallel to its opposite planes,... | |
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