| Charles Hutton - Mathematics - 1812
...are the proper numeral measures of their quantities or magnitudes. THEOUEM CXI. Similar Prisms and **Cylinders are to each other, as the Cubes of their Altitudes, or** of any other Like Linear Dimensions. LET ABCD, F.FGH, be two similar prisms ; then will the prism CD... | |
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...cylinders of the same base are to each other as their altitudes. 518. CoroUary H. Similar cylinders arc to **each other as the cubes of their altitudes, or as the cubes of the diameters of** the bases. For the bases are as the squares of their diameters ; and, since the cylinders are similar,... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...their bases, and cylinders of the same base are to each other as their altitudes. 518. Corollary n. **Similar cylinders are to each other as the cubes of...their altitudes, or as the cubes of the diameters of** the bases. For the bases are as the squares of rheir diameters ; and, since the cylinders are similar,... | |
| Adrien Marie Legendre - 1825 - 224 pages
...their bases, and cylinders of the same base are to each other as their altitudes. 5 1 8. Corollary H. **Similar cylinders are to each other as the cubes of...their altitudes, or as the cubes of the diameters of** the bases. For the bases are as the squares of their diameters; and, since the cylinders are similar,... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...their bases, and cylinders of the same base are to each other as their altitudes. 518. Corollary n. **Similar cylinders are to each other as the cubes of...their altitudes, or as the cubes of the diameters of** the bases. For the bases are as the squares of their diameters ; and, since the cylinders are similar,... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of the **bases. For the bases are as the squares of their diameters; and,** since the cylinders are similar, the diameters of the bases are as the altitudes (510); consequently... | |
| Olinthus Gregory - Mathematics - 1834 - 427 pages
...these products are the proper numeral measures of their quantities or magnitudes. 7. Similar prisms and **cylinders are to each other aS the cubes of their altitudes, or** of any like linear dimensions. 8. In any pyramid a section parallel to the base is similar to the base... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...other as tKeir bases ; and cylinders of the same base are to each other as their altitudes. Cor. 2. **Similar cylinders are to each other as the cubes of...cylinders being similar, the diameters of their bases** are to each other as the altitudes (Def. 4.) ; hence the bases are as the squares of the altitudes... | |
| Adrien Marie Legendre - Geometry - 1837 - 359 pages
...and cylinders of the same base are to each other as their altitudes. Cor. 2. Similar cylinders arc to **each other as the cubes of their altitudes, or as...cylinders being similar, the diameters of their bases** are to each other as the altitudes (Def. 4.) ; hence the bases are as the squares of the altitudes... | |
| Adrien Marie Legendre - Mathematics - 1841 - 235 pages
...their bases, and cylinders of the same base are to each other as their altitudes. 518. Corollary n. **Similar cylinders are to each other as the cubes of...their altitudes, or as the cubes of the diameters of** the bases. For the bases are as the squares of their diameters ; and, since the cylinders are similar,... | |
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