 | Edward Olney - 1872 - 270 pages
...1.—The volume of a right prism is equal to the product of its edge into its base. £90. COR. 2.—Prisms of the same altitude are to each other as their bases; and prisms of the same or. equivalent bases are to each other as their altitudes; and, in general, prisms... | |
 | Herbert Spencer - Psychology - 1873 - 670 pages
...in which. a bulk is to a bulk as a weight to a weight — cases like those in which it is seen that triangles of the same altitude are to each other as their bases, or that the amounts of two attractions are to each other as the masses of the attracting bodies. Here... | |
 | Herbert Spencer - 1873 - 678 pages
...in which a bulk is to a bulk as a weight to a weight — cases like those in which it is seen that triangles of the same altitude are to each other as their bases, or that the amounts of two attractions are to each other as the masses of the attracting bodies. Here... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...contents of the cylinder are equal to the product of its base by its altitude. 342. Cor. 1. Cylinders of the same altitude are to each other as their bases ; and cylinders of equal bases are to each other as their altitudes. (Theo. XXX. Bk. IV.), and the cylinders... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...contents of the cylinder are equal to the product of its base by its altitude. 342. Cor. 1. Cylinders of the same altitude are to each other as their bases ; and cylinders of equal bases are to each other as their altitudes. (Theo. XXX. Bk. IV.), and the cylinders... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...bases, and triangles of equal bases are to each other as their altitudes; and, in general, triangles are to each other as the products of their bases and altitudes. THEOREM VII. 191. The area of any trapezoid is equal to the product of its altitude by half the sum of its... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...represented by 7rR2 (B. VI., Pr. 13, Cor. 3), and the volume of the cylinder will be 7rR2H. Cor. 2. Cylinders of the same altitude are to each other as their bases, and cylinders of the same base are to each other as their altitudes. Cor. 3. Similar cylinders are to each... | |
 | Charles Scott Venable - 1881 - 380 pages
...surface of the parallelogram =BCxAD (Prop. V.); therefore, that of the triangle =£BC x AD, or BC x £AD. COR. Two triangles of the same altitude are to each...the same base are to each other as their altitudes. PROPOSITION VII. THEOREM. Through I, the middle point of the side CB, draw KL, parallel to the opposite... | |
 | James Morton - Circle-squaring - 1881 - 236 pages
...triangles of equal altitude are to each other as their bases, and lf°' two triangles of equal bases are to each other as their altitudes ; and triangles...other as the products of their bases and altitudes. The square of the one side of an equilateral triangle inscribed in a circle is equal to three-fourths... | |
 | Herbert Spencer - Psychology - 1882 - 722 pages
...in which a bulk is to a bulk as a weight to a weight — cases like those in which it is seen that triangles of the same altitude are to each other as their bases, or that the amounts of two attractions are to each other as the masses of the attracting bodies. Here... | |
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Two triangles of the same altitude are to each other as their bases, and two triangles of the same base are to each other as their altitudes. And triangles generally, are to each other, as the products of their bases and altitudes. 
