... 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. New Plane and Solid Geometry - Page 138by Webster Wells - 1908 - 298 pagesFull view - About this book
| 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 - 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' ' ,... | |
| 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 f, their bases b and b', and altitudes... | |
| 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.]... | |
| 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... | |
| 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... | |
| Webster Wells - Geometry - 1898 - 284 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 of their bases by their altitudes.** PROP. V. THEOREM. '312. The area of a triangle is equal to one-half the product of its base and altitude.... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...equal altitudes are equivalent, because they are all equivalent to the same rectangle. 253. COR. 2. **Any two parallelograms are to each other as the products of their bases by their altitudes;** therefore, parallelograms having equal bases are to each other as their altitudes, and parallelograms... | |
| Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...two parallelograms having equal bases are to each other as their altitudes. 260. Cor. IV. Show that **any two parallelograms are to each other as the products of their bases by their altitudes.** 261. Cor. V. Can you show how to find the area of any triangle? 262. Cor. VI. Can yon show that triangles... | |
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