...is called the altitude, of the parallelopiped, this proposition may also be expressed as follows : The volume of a rectangular parallelopiped is equal to the product of its base by its altitude. 35. Sclwlium II. When the three dimensions of the parallelopiped are each exactly...

...c is called the altitude, of the parallelopiped, this proposition may also be expressed as follows: The volume of a rectangular parallelopiped is equal to the product of its base by its altitude. 35. Scholium II. When the three dimensions of the parallelopiped are each exactly...

...gives rise to the term cube, as used in arithmetic and algebra, for " third power." 485. COR. 2. — The volume of a rectangular parallelopiped is equal to the product of its altitude into the area of its base, the linear unit being the same for the measure of all the edges....

...square whose side is of that length is the measure of area. VOLUME OF PARALLELOPIPEDS. 691. Theorem. — The volume of a rectangular parallelopiped is equal to the product of its length, breadth, and altitude. In the measure of the rectangle, the product of one line by another...

...2*RН, is the area of the convex surface of the cylinder. F1o. S9S. PROPOSITION X. 482* TJteorem. — The volume of a rectangular parallelopiped is equal to the product of the three edges of one of its triedrals. •4 DEM. — Let H.CBFE be a rectangular paral. lelopiped....

...\f\ *\ \ s s \ \p \ s \ \ s \ \ s x)_J \ \ V \ P- \ \ \, \ GEOMETRY.— BOOK VI. 395. Corollaries. 1. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude. For, let b denote the base ; then, b = o X d; .-. P — b X a. 2. The volume...

...gives rise to the term cube, as used in arithmetic and algebra, for " third power." 485. COR. 2.—The volume of a rectangular parallelopiped is equal to the product of its altitude into the area of its base, the linear unit being the same for the measure of all the edges....

...\ \ c' P' \ ч d Q \ с k a, \ ь \ al \ К a \ -, GEOMETRY. BOOK VII. PROPOSITION X. THEOREM. 538. The volume of a rectangular parallelopiped is equal to the product of its three dimensions, the unit of volume bein g a cube whose edye is the linear unit. Let a, b, and с be the...

...cubical unit taken as a standard, as the product of its base by its altitude is to unity ; therefore the volume of a rectangular parallelopiped is equal to the product of its base by its altitude. 36. Cor. 2. As the area of a rectangle is equal to the product of its two dimensions,...

...power of its edge. 540. COR. II. The product a X 6 represents the base when c is the altitude ; hence : The volume of a rectangular parallelopiped is equal to the product of its base by its altitude. 541. SCHOLIUM. When the three dimensions of the rectangular parallelopiped are...