 | Euclides - 1845 - 546 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 - 382 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 - 270 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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SIMILAR cones and cylinders have to one another the triplicate ratio of that which the diameters of their bases have... 
