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" Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases. "
Elements of Geometry and Trigonometry: With Notes - Page 187
by Adrien Marie Legendre - 1822 - 367 pages
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - Mathematics - 1812 - 620 pages
...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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 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,...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 570 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,...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 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,...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 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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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 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...
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Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - Mathematics - 1834 - 484 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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 376 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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 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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