 ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.  Elements of Plane and Solid Geometry - Page 179by George Albert Wentworth - 1877 - 398 pagesFull view - About this book
 | William Chauvenet - 1893 - 340 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 R and K be two rectangles, k and k their bases, h and h' their altitudes; then E k X h R' A' X... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...other as their bases. 2. Two parallelograms having equal bases are to each other as their altitudes. 3. Any two parallelograms are to each other as the products...bases by their altitudes. PROPOSITION V. THEOREM. 313. The area o/ a triangle is equal to one-half the product of its base and altitude. \f Let ABC be... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...other as their altitudes ; parallelograms having equal altitudes are to each other as their bases ; any two parallelograms are to each other as the products of their bases by their altitudes. 368. The area of a triangle is equal to one-half the product of its base by its altitude. 369. Cor.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...386. COR. I. Parallelograms having equal bases and equal altitudes are equivalent. 387. COR. II. — Any two parallelograms are to each other as the products of their bases and altitudes. Hint. — Let the areas of the parallelograms be P and f, their bases b and b' ., and... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...386. COR. I. Parallelograms having equal bases and equal altitudes are equivalent. 387. COR. II. — Any two parallelograms are to each other as the products of their bases and altitudes. Hint, — Let the areas of the parallelograms be P and P' , their bases b and b' ' ,... | |
 | George D. Pettee - Geometry, Modern - 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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 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.]... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...386. COR. I. Parallelograms having equal bases and equal altitudes are equivalent. 387, COR. II.—Any two parallelograms are to each other as the products of their bases and altitudes. Hint.—Let the areas of the parallelograms be P and f, their bases b and b', and altitudes... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...respectively ; and p a second parallelogram, with a and b its altitude and base respectively. COR. 1.—Two parallelograms are to each other as the products of their bases by their altitudes. For P= A X B, and p — a X b (§ 229). COR. 2.— Two parallelograms having equal bases are to each... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...other as their bases ; two parallelograms having equal bases are to each other as their altitudes ; and any two parallelograms are to each other as the products of their bases by their altitudes. 260. 261. Cor. V. Can you show how to find the area of any triangle? 262. Cor. VI. Can you show that... | |
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