 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 Seiten
...additional axioms above proposed, articles 27, 32, 58, 59, and 69 become unnecessary. Theorem 1 78 is, The area of a trapezoid is equal to the product of its altitude by half the sum of its parallel sides. The labored demonstration here given is unnecessary. The truth... | |
 | Timothy Walker - 1829 - 156 Seiten
...altitude (84). But the area of ABCD=A DXC E (101). Therefore the area of ACD=half of A DXC E. 103. THEOREM. — The area of a trapezoid is equal to the product of its altitude by half the sum of its parallel sides. By the altitude of a trapezoid we mean the perpendicular let... | |
 | Timothy Walker - 1829 - 138 Seiten
...altitude (84). But the area of ABCD=A DxC E ^101). Therefore the area of ACD=half of A DxC E. 103. — The area of a trapezoid is equal to the product of ' . its altitude by half the sum of its parallel sides — . By the altitude of a trapezoid we mean the perpendicular... | |
 | Charles Waterhouse - 1842 - 178 Seiten
...the other two sides. 16. Every triangle is half of a parallelogram of the same base and,altitude. 17. The area of a trapezoid is equal to the product of its altitude by half the sum of its parallel sides. 18. A line drawn so as to divide a triangle parallel to its... | |
 | Charles WATERHOUSE - 1844 - 228 Seiten
...similar polygons are as their homologous sides, and their surfaces are as the squares of these sides. 14. The area of a trapezoid is equal to the product of its altitude by half the sum of its parallel sides. 15. A rhombus, or rhomboides, has for its area the product of... | |
 | Adrien Marie Legendre - 1852 - 436 Seiten
...generally, are to each other, as the products of their bases and altitudes. PROPOSITION VII. THEOEEM. The area . of a trapezoid is equal to the product of its altitude, ~by half the sum of its parallel bases. Let ABCD be a trapezoid, EF its altitude, AB and CD its parallel... | |
 | Charles Davies - 1854 - 436 Seiten
...triangles generally, are to each other, as the products of their bases and altitudes. PROPOSITION VII. THEOREM. The area of a trapezoid is equal to the product of its altitude, by half the sum of its parallel bases. Let .ABCD be a trapezoid, EF its altitude, AB and CD its parallel... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 Seiten
...triangles generally, are to each other, as the products of their bases and altitudes. PROPOSITION VII. THEOREM. The area of a trapezoid is equal to the product of its altitude, by half the sum of its parallel bases. Let ABCD be a trapezoid, EF its altitude, AB and CD its parallel... | |
 | Benjamin Greenleaf - 1862 - 518 Seiten
...sum of AB and CD ; therefore the area of the trapezoid is equal to the product of EF by H I. Hence, the area of a trapezoid is equal to the product of its altitude by the line connecting the middle points of the sides which are not parallel. PROPOSITION VIII. —... | |
 | Benjamin Greenleaf - 1861 - 638 Seiten
...sum of AB and CD ; therefore the area of the trapezoid is equal to the product of EF by HI. Hence, the area of a trapezoid is .equal to the product of its altitude by the line connecting the middle points of the sides which are not parallel. PROPOSITION VIII. —... | |
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Theorem. — The area of a trapezoid is equal to the product of its altitude... 
