 ... 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
 | Benjamin Greenleaf - 1869 - 516 pages
...altitudes, and parallelograms having equal altitudes are to each other as their bases ; and, in general, parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION VI. — THEOREM. 227. The area of any triangle is equal to the product of its base by half its altitude... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...bases ; triangles having equal bases are to each other as their altitudes ; and any two triangles are to each other as the products of their bases by their altitudes. PROPOSITION VI.— THEOREM. 17. The area of a trapezoid is equal to the produet of its altitude by half the sum... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...to be understood " surface of the rectangle." PROPOSITION II.— THEOREM. 5. Any two rectangles are to each other as the products of their bases by their altitudes. Let _R and R' be two rectangles, k and k' their bases, h and h' their h altitudes; then, R' k' X h'... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...buses ; triangles having equal bases are to each other as their altitudes ; and any two triangles are to each other as the products of their bases by their altitudes. PROPOSITION VI.— THEOREM. 17. The area of a trapezoid is equal to the product of its altitude by half the sum... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...are to each other as their altitudes ; of equal altitudes, as their bases ; and in general they are to each other as the products of their bases by their altitudes. PROPOSITION TII. 325. Theorem. — The area of a trapezoid is equal to the product of its altitude into one-half... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...are to each other as their altitudes ; of equal altitudes, as their bases ; and in general they are to each other as the products of their bases by their altitudes. PROPOSITION VII. 325. TJieorem. — The area of a trapezoid is equal to the product of its altitude into one-half... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...cutting a pyramid are as the squares of their distances from the vertex. (39 ; II. 31.) 75. Pyramids are to each other as the products of their bases by their altitudes. (51.) 76. Pyramids with equivalent bases are as their altitudes ; with equal altitudes, as their bases.... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...dimensions. 71. In a cube the square of a diagonal is three times the square of an edge. 72. Prisms are to each other as the products of their bases by their altitudes. (25.) 74. Polygons formed by parallel planes cutting a pyramid are as the squares of their distances... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...to be understood " surface of the rectangle." PROPOSITION II.—THEOREM. 5. Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R' be two rectangles, k and k' their bases, h and h' their 4 altitudes; then, £' k' X h'... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...altitudes, and parallelograms having equal altitudes are to each other as their bases ; and, in general, parallelograms are to each other as the products of their bases by their altitudes. THEOREM VI. 189. The area of any triangle is equal to the product of its base by half its altitude.... | |
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