...two dimensions in common are to each other as their third dimensions. PROPOSITION IX.— THEOREM. 30. Two rectangular parallelopipeds having equal altitudes are to each other as their bases. Let jR be a third rectangular parallelopiped whose dimensions are ra, b and c; then, B has the two dimensions...

...THEOREM. 32. Any two rectangular parallelopipeds are to each other as the ducts of their three dimensions. Let a, b and c be the three dimensions of the rectangular parallelopiped P; n and p those of the rectangular IN parallelopiped Q. Let R be a third rectangular parallelepiped whose...

...PAGB I. Two rectangular parallelopipeds having equal bases are to each other as their altitudes 78 II. Two rectangular parallelopipeds having equal altitudes, are to each other as their bases So III. Any two rectangular parallelopipeds are to each other as the products of their dimensions 80...

...two dimensions in common are to each other as their third dimensions. PROPOSITION IX.— THEOREM. 30. Two rectangular parallelopipeds having equal altitudes...of the rectangular parallelopiped Q; the dimension e, or the altitude, being common. Let R be a third rectangular parallelopiped whose dimensions are...

...two dimensions in common are to tach other as their third dimensions. PBOPOSITION IX.— THEOREM. 30. Two rectangular parallelopipeds having equal altitudes...three dimensions of the rectangular parallelopiped P; m,n and c those of the rectangular parallelopiped Q; the dimension c, or the altitude, being common....

...the product, ofiU three dimensions, the unit of volume being a cube whose edge is the linear unit. Let a, b, and c be the three dimensions of the rectangular parallelopiped P, and let the cube U be the unit of volume. We are to prove volume of P •• _aXbXc = ix ix r a X i...

...С \ \ A \ \ ^x GEOMETRY. BOOK VII. PROPOSITION VIII. THEOREM. 535. Two rectangular parallelоpipeds having equal altitudes are to each other as their bases. Let a, b, ande, and a', У, c, be the three dimensions respectively of the two rectangular parallelopipeds P...

...QED •y SS S \ f \\ \ \ С ч s s P \ \ \ N л \ GEOMETRY. BOOK VII. PROPOSITION VIII. THEOREM. 535. Two rectangular parallelopipeds having equal altitudes are to each other as their bases. 7 Let a, b, ande, and а', Ы, c, be the three dimensions respectively of the two rectangular parallelopipeds...

...however far the approximation be carried. PA Hence - — (II., 8) ; or, pa P ip—A : a. v. Theorem. Two rectangular parallelopipeds having equal altitudes are to each other as their bases. HYPOTH. P and p are two rectangular parallelopipeds, having the same altitude A, and the bases s X...

...in (II. 35). Therefore, whether the altitudes are commensurable or not, M:N=AE:CF THEOREM VIII. 33. Rectangular parallelopipeds having equal altitudes are to each other as their bases. Let the rectangular parallelopipeds AB, CD, have equal altitudes ; then «,» If the parallelopipeds are...