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Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Elements of Geometry: With Practical Applications to Mensuration - Page 199
by Benjamin Greenleaf - 1863 - 320 pages

Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 331 pages
...to be understood " surface of the rectangle." PROPOSITION III.—THEOREM. 7. Any two rectangles are to each other as the products of their bases by their altitudes, Let E and R' be two rectangles, k and k their bases, h and h ' their altitudes; then E _ k XA R ' Jfx...

A Text-book of Geometry

George Albert Wentworth - Geometry - 1888 - 386 pages
...the altitudes, AD and AD as the bases. PROPOSITION II. THEOREM. 362. The areas of two rectangles are to each other as the products of their bases by their altitudes. r s L_ b V b i Let R and R' be two rectangles, having for their bases b and b', and for their altitudes...

The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 393 pages
...is the same as that of the first ? Proposition 2. Theorem. 358. The areas of any two rectangles are to each other as the products of their bases by their altitudes. Hyp. Let R and R' be two rectangles, b and b' their bases, a and a' their altitudes, R a X b To prove...

Educational Review, Volume 3

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1892 - 544 pages
...criticism, it will be necessary to reproduce the demonstration given. To prove that two rectangles are to each other as the products of their bases by their altitudes. R and R' are two rectangles, having for their bases b and b' and for their altitudes a and a'. It is...

Elementary Geometry

William Chauvenet - 1893 - 340 pages
...rectangles having equal bases are to each other as their altitudes. PROPOSITION III. Any two rectangles are to each other as the products of their bases by their altitudes. PROPOSITION IV. The area of a rectangle is equal to the product of its base and altitude. PROPOSITION...

Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 50 pages
...altitudes ; triangles having equal altitudes are to each other as their bases ; any two triangles are to each other as the products of their bases by their altitudes. 371. The area of a trapezoid is equal to one-half the sum of the parallel sides multiplied by the altitude....

Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 556 pages
...— area of R = a X b, provided U is the unit of area. R axb = axb. §380 U ixi [Two rectangles are to each other as the products of their bases by their altitudes.] But — = area of R. U §374 [The area of a surface is the ratio of that surface to the unit surface.]...

Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...Proposition XI, Bk. II, and Proposition X, Bk. Ill PROPOSITION III 242. Theorem. Any two rectangles are to each other as the products of their bases by their altitudes. Appl. Cons. Dem. b Prove M = abN~a'b' Construct rectangle P, as indicated Ma — = — Pa' | 1 M ab...