 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...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 follows from what has already been shown... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...proposed, articles 27, 32, 58, 59, and 69 become unnecessary. Theorem 178 is, The area of a trapezoidis equal to the product of its altitude by half the sum of its parallel sides. The labored demonstration here given is unnecessary. The truth follows from what has already been shown... | |
 | Charles Waterhouse - 1842 - 178 σελίδες
...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 base, divides the sides proportionally.... | |
 | Charles WATERHOUSE - 1844 - 228 σελίδες
...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 half of two of its parallel sides by... | |
 | Adrien Marie Legendre - 1852 - 436 σελίδες
...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 bases: then will its area be... | |
 | Joseph Bateman - 1852 - 376 σελίδες
...perpendiculars by the diagonal, and half the product will be the area. * A Trapezoid is equal in area to the product of its altitude by half the sum of its parallel sides ; and the perpendicular distance bctwcen its two parallel sides may be found by dividing the area by... | |
 | Charles Davies - 1854 - 436 σελίδες
...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 bases : then will its area... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 σελίδες
...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 bases : then will its area... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...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. — THEOREM.... | |
 | Benjamin Greenleaf - 1861 - 638 σελίδες
...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. — THEOREM.... | |
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The area of a trapezoid is equal to the product of its altitude, by half the sum of its parallel bases. 
