...number" has been adopted to signify the " third power of a number." PROPOSITION XII— THEOREM. 37. The volume of any parallelopiped is equal to the product of its base by its altitude. Let ABCD-A' be any oblique parallelopiped, whose base is ABCD, and altitude B' O. 0' Produce...

...of its edge. Thence comes the name of cube, to designate the third power of a number. MODEL CUBES. 694. Draw six equal squares, as in the diagram. Cut...parallelopiped is equal to the product of its base by its altitude. GOO. Corollary. — The volumes of any two parallelopipeds are to each other as the products...

...number" has been adopted to signify the " third power of a number." ' ''PROPOSITION XII.—THEOREM. 37. The volume of any parallelopiped is equal to the product of its base by its altitude. Let ABCD-A' be any oblique parallelopiped, whose base is ABCD, and altitude B'O. Produce...

...area of its base, the linear unit being the same for the measure of all the edges. 486. COR. 3. — The volume of any parallelopiped is equal to the product of its altitude and the area of its base. For any parallelopiped is equivalent to a rectangular parallelopiped...

...area of its base, the linear unit being the same for the measure of all the edges. 486. COR. 3. — The volume of any parallelopiped is equal to the product of its altitude and the area of its base. For any parallelopiped is equivalent to a rectangular parallelopiped...

...the tliird power of its edge. For, if d = c = a, P— aXaXa = a3. 396. Proposition XIII. — Theorem. The volume of any parallelopiped is equal to the product of its base by its altitude. Let P denote the volume ; b, the base ABCD; a, the altitude HR of the parallelopiped ABCDF,...

...equivalent rectangular parallelopiped is equal to the product of its base by its altitude (35) ; therefore the volume of any parallelopiped is equal to the product of its base by its altitude. 2d. A triangular prism is half of a parallelopiped which has the same altitude and a base...

...divides it into two equivalent triangular prisms), and AEC=\ AECD. §133 But A EC DE' = 2 BXH, §542 (the volume of any parallelopiped is equal to the product of its base by Us altitude). XH = BX H. CASE II. — When the base is a polygon of more than three sides. Planes passed...

...1 / / / ' / ' y ' , / { p / / ,_ , f ' /W^\ 1/7 / / (1 / A / PÜISMS. PROPOSITION XL THEOREM. 542. The volume of any parallelopiped is equal to the product of its base b1 its altitude. G ' II — W- V-« К BJ Let AB С DF be a parallelopiped having all its faces...

...that any two parallelopipeds having equal altitudes are to each other as their bases. VI. Theorem. Any two parallelopipeds are to each other as the products of their bases by their altitudes. HYPOTII. P and p are two parallelopipeds whose bases are B and &, and whose...