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
| Euclides - 1876
...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 one another the ratio which is the same with the ratio compouaded of the ratios of their... | |
| 1876
...antecedents to the rectangle contained by the consequents. THEOR. 14. Triangles and parallelograms **have to one another the ratio compounded of the ratios of their** bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio... | |
| J. G - 1878
...including sides of the first to the including sides of the second. " 23." Triangles and parallelograms **have to one another the ratio compounded of the ratios of their** bases and of their altitudes. We may observe that Prop. 7, which in ordinary editions of Euclid is... | |
| James Maurice Wilson - Geometry - 1878 - 261 pages
...antecedents to the rectangle contained by the consequents. THEOREM 14. Triangles and parallelograms **have to one another the ratio compounded of the ratios of their** bases and of their altitudes. Let ABC, DEF be two triangles, having the altitudes AG, DHrespectively;... | |
| Mathematical association - 1883
...antecedents to the rectangle contained by the consequents. THEOR. 14. Triangles and parallelograms **have to one another the ratio compounded of the ratios of their** bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio... | |
| Mathematical association - 1886
...and DC, the triangle ADE will be equal to the triangle BDC. THEOR. 15. Triangles and parallelograms **have to one another the ratio compounded of the ratios of their** bases and of their altitudes. Let ABC, HKL be two triangles, AD, HM their altitudes: then shall the... | |
| Henry Sinclair Hall, Frederick Haller Stevens - Geometry - 1892 - 211 pages
...ratio compounded of BC to FG and BM to FQ, for these par ms . are equiangular. .'. par ms . BD, FH **have to one another the ratio compounded of the ratios of their** bases and of their altitudes. But A ABC = half par" 1 . BD and AEFG = half par™. FH- Hence the same... | |
| T. L. HEATH - 1897
...cylinder passes through P. Proposition IO. It was proved by the earlier geometers that any two cones **have to one another the ratio compounded of the ratios of their** bases and of their heights*. The same method of proof will show that any segments of cones have to... | |
| Archimedes - Geometry - 1897 - 326 pages
...of their bases and of their heights*. The same method of proof will show that any segments of cones **have to one another the ratio compounded of the ratios of their** bases and of their heights. The proposition that any 'frustum' of a cylinder is triple of the conical... | |
| |