 Two rectangular parallelopipeds are to each other as the products of their bases and their altitudes. Given M and N, two rectangular parallelopipeds, B and B' their bases, and a and a' their altitudes respectively.  Plane and Solid Geometry - Page 364by Arthur Schultze, Frank Louis Sevenoak - 1925 - 480 pagesFull view - About this book
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...parallelopipeds having equal bases and altitudes a and 6 respectively ? PROPOSITION VIII. THEOREM 591. Two rectangular parallelopipeds are to each other...bases, and a and a' their altitudes respectively. Proof. Construct 0, a rectangular parallelopiped with base B, and altitude a'. ? = -,' ( 585 ) N~ B'... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...with base B, and altitude a'. M__ a O ~ a! N B' MB xa (585) (588) N B' x a' (Ax. 7.) QED 592. COR. Two rectangular parallelopipeds are to each other as the products of their three dimensions. PROPOSITION IX. THEOREM 593. The volume of a rectangular parallelopiped is equal... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 296 pages
...triangles having equal altitudes are to each other as their bases. 369. Theorem. Any two triangles are to each other as the products of their bases and their altitudes. EXERCISES 1. In Fig. 1, AB II CD. Prove that AEH _K_ A CED, CHD, and CKD are equivalent. \i 2. Prove... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...corresponding members of these two equalities, gives P bXc P' b'Xc'' (JKI). PROPOSITION IX. THEOREM 600. Any two rectangular parallelopipeds are to each other as the products of their three dimensions. p b b" b Let P and P' be two rectangular parallelopipeds having dimensions a, b,... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...of this book. 5. AREAS OF POLYGONS PROPOSITION II. THEOREM 336. The areas of any two rectangles are to each other as the products of their bases and their altitudes. Given the rectangles R and R', having the bases b and ', and the altitudes a and a', respectively. R ab Proof.... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...having equal bases are to each other as their altitudes. § 361. Theorem. Any two parallelograms are to each other as the products of their bases and their altitudes. § 362. Theorem. The area of a triangle is equal to half the product of its base and its altitude.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...base B, and altitude a'. %r *(585) 0 a' — = — N~ B'MBX a N B' x a' (588) (Ax. 7.) QED 592. COR. Two rectangular parallelopipeds are to each other as the products of their three dimensions. PROPOSITION IX. THEOREM 593. Tlie volume of a rectangular parallelopiped is equal... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...parallelograms having equal altitudes are to each other as their bases. 361. Theorem. Any two parallelograms are to each other as the products of their bases and their altitudes. EXERCISES 1. Show that the three parallelograms in Fig. 1 are equivalent. 2. Will a yard of velvet... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...rectangular parallelopiped with base B, and altitude a'. (585) O a' N~ B' MBX a (588) (Ax. 7.) QED 592. COR. Two rectangular parallelopipeds are to each other as the products of their three dimensions. PROPOSITION IX. THEOREM 593. The volume of a rectangular parallelopiped is equal... | |
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